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The paucity of plants evolving genetic resistance to herbicides: Possible reasons and implications
J. theor. Biol. (1978) 75, 349-371
The Paucity of Plants Evolving Genetic Resistance to Herbicides : Possible Reasons and Implications J. GRESSEL Department of Plant Genetics AND
L. A. SEGEL Department of Applied Mathematics The Weizmann Institute of Science, Rehovot, Israel (Received 12 January 1978, and in revised form 19 July 1978) Resistances to antibiotics and pesticides except herbicides rapidly developed following their introduction. Despite repeated use of herbicides only a few cases of acquired genetic resistance have been reported. By extrapolation from analogous situations, it is suggested that this is due to a combination of low selection pressure of most herbicides, lower fitness of resistant weed strains in the absence of herbicide, the ability of herbicide thinned strands of susceptible weeds to produce relatively more seeds, as well as to the large soil reservoir of susceptible weed seeds. The few reported cases of resistance are to persistent, high selection pressure herbicides supporting our contentions. 1. Introduction
Shortly after the introduction of herbicides into commercial use thirty years ago, there were predictions that repeated use would select for resistance (Abel, 1954; Harper, 1956) as had happened with all other groups of pesticides from antibiotic drugs through rodenticides. These views remain ingrained (Anon, 1974a). From similar considerations, it was suggested that both herbicides and crops be rotated (Abel, 1954). Yet there are many areas where “heretical” agriculturists have successfully used the same herbicide annually on the same crop in the same field repeatedly without apparent selection for resistant mutants in the susceptible weed species. For example, 2,4-D,? a widely used selective herbicide, has been used to control annual i The WSSA or IUPAC common names of pesticides are used throughout ; their chemical names are as follows : atrazine = 2--chloro4-(ethylamino>d-(isopropylamino)-s-triazine ; diquat = 6,7--dihydrodipyrido DDT =: ]I]-trichlor+2, 2-bis(p
0022-5193/78/230349+23 002.00/O
0 1978Academic Press Inc. (London) Ltd.
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dicotyledonous weeds in grains, yearly, in many places without crop rotation for more than 25 years. To our knowledge, no substantial cases of genetic resistance to this herbicide have been reported. There are a few isolated reports of such selections occurring to S-triazine herbicides (see later). It appears then that predicted resistance seldom appears. The analysis of possible reasons for the non-appearance of resistance is the main topic of this paper. After remarking on the nature of herbicide resistance, we shall consider the various factors affecting the appearance of such resistance: mutation, selection pressure, fitness, and the particular “plasticity” of weed growth and especially the reservoir of seeds in the soil. To obtain an idea of how all these factors interact we present some mathematical models. Our paper concludes with a discussion of the agronomic implications of our findings. The discussion herein will be devoted to the appearance of resistance in species that were heretofore susceptible. We shall not consider well known changes of weed populations due to changes in agronomic procedures including the use of herbicides for species which are naturally insensitive, as discussed by Harper (1957), Harper, ed. (1960), Baker (1974) and Holm (1977). 2. The Nature of Resistance Resistances to phytotoxic compounds such as herbicides are known to occur at a multiplicity of levels (as is well reviewed in Ashton & Crafts, 1973). Selective permeation, for example, can occur at various levels, e.g. uptake into the root, through the cuticle, or uptake into target organelles. Prevention of toxicity by lack of translocation is also known, especially in the root endodermis. Selectivity can be based on the differential ability to detoxify a compound enzymatically. Phenological modes of resistance occur, for example, by germination after the normal time of application of contact herbicides or after degradation of mildly persistent herbicides. Thus the modes of selective resistance are quite varied, making it all the more surprising that there has been little selection for genetic resistance. Some ecological and genetic aspects of this problem have been recently reviewed by Holliday, Putwain & Dafni (1976). Resistance is often lumped with natural strain differences in tolerance. They are best differentiated by the effective dose. Intraspecific differential tolerance is known, i.e. small variations in dose affect biotypes differently. Further on the continuum is “resistance” (as herein defined) : resistant plants completely survive a dose, that is essentially completely toxic to the susceptible type. Our definitions of resistance and differential tolerance conform to those of the FAO (Anon., 1967).
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Known cases of resistance and differential tolerance are summarized in Gressel(l979). Of the many reports in the appearance of differential tolerance and the few on resistance, only those using S triazines claim that the more resistant strains occurred in the field as a result of herbicide treatment (Bandeen & McLaren, 1976; Ryan, 1970; Holliday & Putwain, 1977). Cases of phenological resistance would not be found by the methods used by the experimenters until now. We know of no ecological assessment of selection for this type of resistance. 3. Factors Affecting the Appearance of Resistance (A)
GENERATION
TIME
Antibiotics, chlorinated insecticides, dicoumarol rodenticides and herbicides were introduced into usage at about the same time. Acquired genetic resistance appeared rapidly for all these pesticides, except herbicides. Various arguments have been raised that it is premature to expect selection for herbicide resistance; the major one being that not enough generations have gone by (e.g. Crow, 1966). It is true that the generation time of higher plants is less than houseflies or mosquitoes, but the first field resistance of both these insects was noted within the first year DDT was used (reviewed by Newman, 1957; Crow, 1966). Moreover, some weed species (e.g. Amaranthus retroJlexus and Chenopodium album) are capable of more than one generation during an agricultural season. Even with one plant generation per year, as many generations have passed since herbicides were introduced as it took to achieve field resistance to insecticides. There are various reasons for the delay in appearance of resistance to herbicides by plants. Our contribution is to pinpoint the major factors involved and to combine them into a mathematical model that provides experimentally testable predictions of how long it would take resistance to appear under various conditions and allows the importance of each factor to be evaluated. To this end, we first discuss the various factors that affect the evolution of resistance. (B)
MUTATION
FREQUENCY
In untreated crops, the proportion of resistant individuals is governed by the mutation rate. There may be a particularly low mutation rate to herbicide resistance. This occurs with DDT resistance in the East African strains of the Yellow Fever Mosquito (vs. the Asian strains which can interbreed with it) which may account for the possible continual control of this problem in East Africa with DDT (Inwang, Khan & Brown, 1969). There is also the remote possibility that a gene for a particular herbicide resistance does not
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exist, in analogy to the case of continued control of streptococci by penicillin. The streptococci seem to lack both the gene for penicillinase and the ability to acquire a plasmid for penicillinase. Bacterial resistances are reviewed in Hahn (1976). Whereas it may be possible that some plant species lack genes for resistance (or have a low mutation frequency for resistance) to a given herbicide, it would appear to be highly unlikely that most plants could not genetically adapt to most herbicides. This would he highly dissimilar from the bacterial, fungal and animal situations. (C)
SELECTION
PRESSURE
Another factor that affects the evolution of resistant strains is selection pressure. In considering this factor, we begin by taking note of a series of ecological studies of plant succession on mine tailings in which Bradshaw’s group showed the selection of ecotypes of various species that are resistant to much higher levels of copper, zinc and lead than the normal ecotypes can survive. The frequency of such types in the normal population is low and yet it only takes a few seasons for such areas to become revegetated by resistant strains (Antonovics, 1970; Antonovics & Bradshaw, 1970; McNeilly, 1968, Bradshaw, 1975). There is a basic difference between the field phytotoxicities of heavy metals and herbicides, the degree of selection pressure. The metals are in such high concentrations (i.e. “overkill”) that only l&20% of the species can evolve resistance (cf. Bradshaw, 1975). Because of various agronomic/ economic considerations, herbicides are usually applied at rates predetermined to give 90-95x kill of the susceptible species. Heavy metals are at higher phytotoxicity levels and may be leached quite slowly from the soil, whereas many herbicides are rapidly leached or degraded, lessening their persistence. Thus there is a stronger pressure for selection of heavy metal tolerance than for resistance to most herbicides. Yet different levels of selection pressure alone cannot account for the nonappearance of herbicide resistance. Assuming even 90% kill and a natural frequency of one resistant plant in lOi repeated annual treatment would lead to a tenfold increase per year in the frequency of resistant strains. In ten years resistance will be apparent. But the effective selection pressure of the rapidly degraded herbicides is even less than the initial kill would suggest because of non-uniform germination of weed seeds throughout the crop year. Some seeds of a given weed species may germinate sufficiently late to be unaffected by the treatment and at a time when they do not greatly affect crop yield (see e.g. Chepil, 1946; Chancellor, 1960; Roberts & Dawson, 1967). Thus one expects a relatively slow increase in herbicide resistance compared to the almost immediate jump seen with heavy metal tolerance.
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FITNESS
Another major factor is fitness, the ability to compete and reproduce in non selective conditions. Important here is the much discussed “cost” of natural selection (see for example Haldane, 1960; van Valen, 1965). Pyle (1976) recently described an example of the lowering of fitness in Drosophila by artificial selection, together with a review of the pertinent genetic literature for insects. It had been claimed that the homozygosity required for recessive genes for resistance to occur is the cause for the decrease in fitness. This would not pertain to dominant resistant types (Crow, 1960, 1966; Kelding, 1967) yet resistant bacterial strains are also less fit (Hahn, 1976). To our knowledge little has been reported on the genetics of resistance in the few known cases. Differential tolerance of flax to atrazine was found to be quantitative (Comstock & Anderson, 1968), although in maize atrazine resistance is dominant and monogenic (Grogan, Eastin 8z Palmer, 1963). The inheritance of siduron tolerance in Hordeum jubatum is dominant and trigenic (Schooler, Bell & Nalawaja, 1972). DDT resistance in barleyis monogenic recessive(cf. Hayes & Wax, 1975); thus most forms of genetic inheritance have been observed. In the case of metal tolerance, it was shown that this “cost” is charged against “fitness”. When the metal tolerant genotypes were interseeded with the wild type plants on a normal non-selective soil, the metal tolerant type genetically “disappeared” back towards its normal frequency. The tolerant type was less fit to compete with the wild type (McNeilly, 1968). In this case, it was calculated that the coefficient of selection against tolerance on normal soils is 0.53. A preliminary report on the “lowered fitness” of S-triazine resistant Amaranthus was presented by Radosevich & Conard (1977) and this lesser fitness may be about a level of 0.5 (calculated from Conard & Radosevich, 1978). Similarly, S-triazine resistant Chenopodium germinated 2-3 days after the sensitive wild type (Bandeen & McLaren, 1976). That this can be a strong disadvantage has been discussed previously (Gressel & Holm, 1964). An example of a resistant mutant with an extremely high cost is an artificially selected mutant of maize resistant to diquat. This mutant is viable in the presence of diquat as it is blocked on the oxidizing side of photosystem 11 and thus is also defective in normal photosynthesis (Miles, 1976). Similarly, white (achlorophyllous) tissue cultures of higher plants are phenotypically resistant to herbicides working at the level of photosynthesis (Gressel, Zilkah & Ezra, 1978), but these are hardly able to exist outside of the test tube. (E)
PARKINSONIAN
PLASTICITY
A final set of factors that affect the appearance of resistance to herbicides is the “plastic” property of many plant species. Weed populations can often
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follow aspects of the expanded “Parkinson’s Law” (Parkinson, 1957), insofar as they often “expand to fill the space available”. This is well described by Harper (1960) and Harper & Gajic (1961), in a case where they adjusted seedling density; a 90% reduction of the seedling population of Agrostema githugo gave rise to larger plants and utimately less than a 10% reduction in seed yield. This “plasticity” of the population means that seed yield (within a certain range) is not a direct function of plant number, but a function of the space. Similar findings have been reported with crops (cf. Bleasdale, 1960). The “space available” is considerably increased by herbicide thinning of a population. This was demonstrated for many species and herbicides in the work of Isenee et al. (1973). They applied massive doses of 13 herbicides and followed the revegetation of 19 species. The herbicide levels were so high that the first effect was a contact killing of all plants, followed later by revegetation. The herbicides had varying selectivities, thus various numbers of plants germinated and grew to maturity in the first two years. We plotted their data on resulting plant numbers and area covered. It is apparent that even under these conditions of massive herbicide “overkill”, the plants that managed to grow followed Parkinson’s edict and “expanded to fill the space available”, by “expanding” in their seed yield to a level approaching that of a dense population. Unfortunately, Isenee et al. (1973) did not check any of the regrowth for herbicide resistance.
b.~LA
I
0 ,0203040~0660~080~0 Reduction of plant number
IOC by herblcldes
FIG. 1. An example of plasticity; revegetation following massive herbicide treatment (calculated and plotted from Table 1 in Isenee et al., 1973). Plots were treated with 2400 times the recommended agricultural doses of 13 herbicides. Revegetation occurring or reinfesting propagules was measured 1 and 2 years after treatment. Each point represents the effect of one herbicide (in three plots) on plant number and area covered for either the first or second year. The dashed line represents a linear proportionality between plant number and area covered and the deviation represents Parkinsonian plasticity.
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If after herbicide treatment we are left with a mixed population of lessvigorous resistant plants and fit susceptible plants that were for some reason untreated, it is apparent that the fit plants will “expand” much better to fill the gap than the resistant plants. Even without herbicides, there is a considerable amount of thinning. As more seeds germinate than reach maturity, fitness is a factor under natural conditions in governing which plants mature. A variety of factors govern fitness at this early stage, as described by Harper (1960) and Gressel & Holm (1964). The potential for “expanding” is much better realized under thinned conditions of herbicide treatment and the “normal” plants should realize this potential better than the less fit resistants. With contact herbicides or those rapidly degraded, the selection pressure is ephemeral, which would then allow the expression of fitness of the susceptible. (F)
SOIL
SEED RESERVOIR
Another important source helping to keep the resistant weed population constant is the “buffering action” of buried viable weed seeds, which have greater fitness (being susceptible strains). As these germinate over a period of years, they would be another factor which would delay the appearance of resistance. To the soil weed seed reservoir must also be added weed seed blown, dropped, washed or mistakenly planted in a treated field. Holm (1977) has clearly stated that “in a list of things about which weed science is ignorant, the source of resupply of weed seeds must rank near the top.” These latter are more a factor in smaller fields and irrigated fields. Other factors stabilizing weed populations which we will not consider herein are discussed in Harper (1957) and in Harper, ed. (1960) but are of interest when considered in the context of differential fitness. 4. Mathematical
Description of the Interrelated Affecting Resistance
Phenomena
The interrelation of selection pressure, fitness, Parkinsonian “plasticity” and the buffer capacity of the soil seed bank can be developed mathematically. We shall present such a development in a sequence of models of increasing complexity. A discussion of some of the mathematical aspects of the problem can be found in Segel (1978). Our goal is to illustrate the major factors that operate in typical situations. Only when specific data are available for particular systems does it appear worthwhile to consider all of the modifying influences involved. The first three sections describe the situation prior to herbicide treatment. In a repeatedly cropped field in which some method of cultivation other than
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herbicides is used to suppress weeds, a miniscule part of the weed population of a given species will be resistant to any given herbicide. The seed yields of the two types, “susceptible” and “resistant” in the nth generation are denoted by N$” and NiR’ respectively. For simplicity, we onlyconsider the case of one generation per year. (A)
NO SEED BANK
IN THE SOIL,
$1 = fW!!$ ll+t
II
NO MUTATIONS
, n = 0, 1,2, 3,4, . . .
Heref’“’ is a constant, the relative fitness. The superscript “u” denotes that we are considering the untreated situation, where no herbicide is being applied. IfJ’“’ < 1, the fraction of resistants will decrease until the resistants have effectively disappeared altogether. (B)
NO SEED BANK, WITH
Ignoring back mutation
MUTATION
TO RESISTANCE
A FREQUENCY
/l
the situation is governed by the equation (2)
As can be verified straightforwardly, NiR) P N(s) ” - ----@ 1-s
the solution of this equation is
1cm”*
+
(3)
When n = 0 the ratio of resistant to susceptible seeds has the initial value N’,R)/NbS’. Becausef’“’ < 1, the second term in equation (3) will decrease each year and the ratio will approach the steady-state value p/(1 -f’“‘). (C)
MUTATION.
SOIL
SEED BANK
WHOSE
DURATION
IS fi YEARS
(4)
In this model it is assumed that the seeds in (where E varies from species to species) and As illustrated in Fig. 2, such an assumption tive results even though it may be more
the soil are fully viable for C years then cease altogether to be viable. should give satisfactory qualitarealistic to assume that viability
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declines exponentially over a period of years which is different for different species (e.g. Chepil, 1946; Chancellor, 1960; Roberts & Dawson, 1967). The value of fi can reflect to some extent a gradual loss of vigor in the viable seeds; but of course this feature could be accurately represented in a more detailed model.
FIG. 2. A typical case in which a fixed portion of seeds from a given year germinate in the succeeding year and the same proportion of the remaining seeds germinate the next year, etc., giving an exponential loss. The average viability as de&-d in the text is such that the area under the dashed half rectangle is equal to the area under the broken line. This criterion can be used to select R from field data (cf. Chepil, 1946; Chancellor, 1960; Roberts & Dawson, 1967). A will typically not be too different from the half life r,-log 2/logI of seeds in the soil bank. See also discussion in the appendix.
If 1 is the probability (assumed constant) that a seed which is viable in one season is also viable in the next then the average duration of viability in years is l+~+%2+;13+...
= &,
and this value should be taken for Fi. Empirical data can also be used to establish the average duration of viability and hence the appropriate value of ii. An appendix shows a somewhat different and more complete model of the seed reservoir. That model leads to essentially the same results as the approach taken here. In general, equation (4) is not sufficient to describe the situation, as in any given year only one relation is provided for the two unknowns NiR) and Ni”. In the previous cases we were nonetheless able to solve for the ratio of these two unknowns, but this is no longer possible. To describe a complete model, let us denote by a,, and pn the percentages of the N seeds that germinate each year that are respectively susceptibles and
3%
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resistants. (That N can be regarded as constant is one aspect of Parkinsonism.) We shall assume that only a small proportion of seeds in the seed bank will germinate. In the simplest instance, o;, and P,, can then be computed by counting the seeds that have deposited in the last 6 years (neglecting “withdrawals”) and determining what percentage of these are susceptible and what resistant. To be somewhat more precise, we shall take into account relative germination ability by a factor x < I that describes how the probability of finding a germinating resistant is less than one would expect from counting the viable resistant seeds in the seed bank. That is n-t i=$+ NR’ Pn -=x,i--. (5) a;2 i=FM, *IS’ Given that the probabilities (T,~and P,, must add to unity, we deduce from equation (5) that n- 1 II- 1 x 1 NiR’ i=gm, W’ i=n-fi ----. (6) fJ!l = 1,- 1 i=g,
[N,!“‘+xNjl’l
’
“I =
“-I i=;‘+ C*?‘+x*iR’I
Let /I$‘) (/3$“) be the proportion of germinating susceptibles (resistants) that become established, $$‘)(I,@) the proportion of established plants that survive to the end of the season, and v$@(v$‘))the number of seeds per survivor. (Again, a superscript “u” is used in anticipation that parameters may change when herbicide is applied). Let us introduce the abbreviations (#p E ~~)~~)vp, (j$’ s p$0@$$0, (7) i.e. C& and +n are fitness parameters for each type. We have as the governing equations N@’ NCR’ ” = p,,N &” +/.m,N &“. (8% b) ” = g ” N &‘, We have neglected back mutations as well as the tiny loss of susceptibles from mutation to resistance. The combination of equations (6) and (8) allows the’.successive numbers of susceptibles and resistants to be computed given any initial situation. The quotient of equations (8b) and @a), with (6), gives (4), where the relative fitness is given by f’“’ = x qg+pp (9) The compound fitness f(“) reflects the joint influences of the germination fitness ratio 2 and the ratio &‘)/c#$” that describes the relative fitnesses in the period following germination through seed production.
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Equation (4) is sufficient to describe the situation if the resistant population is sufficiently low, as we shall now demonstrate. Indeed for our purposes we lose little by confining ourselves to instances where the number of resistants is considerably less than the number of susceptibles. Then each year the number of susceptible seeds germinating per unit area can be approximated by a constant N (i.e. a, x 1) because of the Parkinsonian plasticity described above. From equation (Sa) we see that the number of susceptible seeds deposited each year will be c#$‘N. With this equation (4) simplifies to
Even with the seed bank, it can be shown that iff@) < 1 the ratio of resistant to susceptible seeds will approach the same steady-state value as before, p/( 1 -f’““, ,. (D)
THE EFFECTS
OF HERBICIDE
TREATMENT
If gS(aR) is the fraction of established susceptibles (resistants) that survive spraying then the governing equations (8) must be modified to N@) NCR) n = g nNus~s 9 n = p nNuRc~R+p g ” Nu&, . (lla, b) We have dropped the superscript “u” for “untreated” and will shortly discuss how we expect fitness to change in the presence of spraying. Keeping in mind our assumption that o,, Y 1 and again employing equation (5), the quotient of equations (11 b) and (1 la) is taken to obtain the new governing equation.
Previously, with f(‘) < 1, the proportion of resistant seeds tended to a low value maintained only by mutation. The analogous result can be true here, only the condition is changed by selection pressure to foR& c 1: N(R)
fc? < 1,-J-%W
N(R) =
--f-
j& n
P l-c$f
;a=--.
CfR
%
(13)
But c+ is typically between O*l-O*Ol and CI~is little less than unity. We thus expect that although f < 1, faR/cxs> 1. In this case the proportion of resistants in the population will grow. A further approximation permits an esti-
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mate of the rate of growth. To obtain this, we subtract from equation (12) the corresponding equation when n is replaced by n - 1: (14) If enrichment approximation
for resistants is fast or even moderate,
we can make the
N;!$ - NS;R_‘,mii cz N:?,. In this case our equation simplifies to
(15)
, where CC= ER
as
(16)
with solution (17) or (18)
We note that equation (14) cannot be used in the first year of herbicide application, because N$?r + is not defined. Thus, use of equation (16) cannot be justified in computing the effect of the first year’s application of herbicide. There generally results an underestimate of the rate of resistant growth, which however is counterbalanced by the relatively small overestimate afforded by all future uses of equation (16). These errors, plus errors stemming from the linearization [equation (lo)], will typically result in a misestimate by one to three years in the appearance of resistance. The clarity afforded by the simple formula (18) outweighs gains in precision that would be obtained by more accurate calculations. In a complex situation such as that under investigation it is broad semi-quantitative trends that one should seek in a first attempt at mathematical modelling. We can now generate a sequence of graphs to clarify the influence of the various factors that appear in formula (18) for the annual enrichment in the proportion of resistant seeds deposited in the season of the herbicide treatment. In the first set of graphs (Fig. 3) we depict the effect of the seed bank on the increase of the proportion of resistant seeds in the field when there is a 90 % kill of susceptible plants (0~~= 0.1) and total immunity of the resistants (aR = l), a steady-state resistant frequency prior to spraying of just under 10 -lo, and a slight differential in fitness. This would be an acceptable frequency for a recessive diploid monogenic resistant biotype.
ADAPTIVE
-4
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11111’11111 0 4
8 I2 YeOrs repeated
HERBICIDE
16 20L treotnwt
RESISTANCE
/,I, 24
28
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32
FIG. 3. The effect of soil seed reservoir on the appearance of herbicide resistance. In this example, an initial steady state frequency of resistance is less than 10-l”. For other initial frequencies the origin should be moved to the appropriate value to show the number of orders of magnitude increase. Different average ages of the seed reservoir (A) are given on the slopes.
The lines in Figs. 3-5 are inaccurate after reaching 10-r when the proportion of resistants ceases to be small. It is clear that the curvature which would be exhibited in graphs obtained by a more exact theory would represent only a small quantitative effect on the appearance of resistance. By noting when the straight lines approach the top of the graph, we can see that under these conditions resistance will become noticeable in about 11 years without a seed bank, while with a seed bank duration ii of 3, 5 and 10 years, resistance will appear in about 17, 24 and 37 years respectiveiy. In considering this and succeeding graphs it should be borne in mind that aR and as enter formula (18) only in the ratio a,/~+. If differential tolerance occurs, the rate of increase can also be calculated. Thus the same a = 10 would be obtained if 80 % of the resistants survived spraying in contrast with 8 % of the susceptibles. The interaction between selection pressure and seed longevity is depicted in Fig. 4. It is obvious that the effects of these two factors, within ranges expected in the field, are important. Their effects are not additive, they are compounded giving a spread of values from 5 years (E = 1 with 99% kill) to 37 years (ii = 10,90x kill) until a resistance of 30% can be expected to be observed. As the range of expected fitnesses is not numerically as great as the possibilities of selection pressure and seed bank longevity, fitness has relatively less effect on the rate of resistance spread throughout the population (Fig. 5). Figure 5 can also be regarded as showing the effect of a differential sensitivity to herbicide of susceptibles and resistants. One can think off always being approximately unity and the various numbers Iabelling each line as describing the fractions of resistants that survive the herbicide treatment. 14
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A- L-i$e d& Years
repeated
ll-Ld-2 20 24
28
32
treatment
FIG. 4. The effect of selection pressure on the appearance of herbicide resistance. Various permutations of selection pressure a, (proportion surviving a herbicide treatment) and seed bank duration are plotted.
It is useful to derive an explicit formula for the time to resistance. To this end, suppose that resistance is observable in the season n1; when the number of resistant seeds is some fraction Q of the total. Virtually the same result will be obtained if we assume that resistants will be noticeable when they comprise a fraction Q of the susceptibles.It is true that in the year that resistance becomes noticeable our assumption that resistants form a negligible portion of the total is no longer a good one, but the resulting error of a year or so is certainly permissible in the face of expected biological variability. Similarly, our results for rrz would differ very little if we adopted the criterion that resistance is observable when a fraction Q of the plants that remain after spraying are resistants.
-4
0
4
8 Years
12 repeated
16 20 24 28
32
treatment
FIG. 5. The effect of fitness on the appearance of herbicide resistance. Different fitnesses are plotted at two average durations of seed life in the soil reservoir.
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Since Nis) B a&N we can use formula (18) to obtain the following formula for n(r (where we explicitly take note of the dependence on ii):
n*tk) = log Q + log______CwhW%R)I Q log 1+$
i 1
(19)
In formula (19) the expression a,&N/NbR’ is the ratio of the essentially constant number of seeds that are deposited each year (per unit area) to the number of resistant seeds deposited just before the onset of herbicide treatment. This ratio can be regarded as a parameter but its measurement does not seem feasible. It is preferable to recognize that conditions at the onset of herbicide treatment should normally be obtainable from the steady-state conditions in the non-herbicide case. Thus, from the conclusion of Part Cwe see that NhR’ = t#$‘Np/( 1 -f’“‘). (20) It remains to relate @) andf’“) to their counterparts when herbicide is being applied. We shall assume that with spraying the total number of seeds per established weed plant increases by a factor of i&..u,, i.e. that
Here the factor I/cl, describes the expanded space available to each established plant while 6, quantifies the degree to which the susceptibles increase their seed production in response to the increased area available. To allow for possible escape from the action of contact and low persistence herbicides we write&/flp’ = L,. With the definition R& - ys it follows from equations (21) and (7) that -4s = Ys _I#$)
(22)
as ’
As the factor a, describes thinning for both susceptibles and resistants we assume, in analogy with equation (22), that 4R
YR
so
that
4R -=--.
YR d$’
(23)
4%
Thus, from equation (9),
f = yf(")
(24) where y = yRIys is a correction factor to the fitness that describes the relative ability of susceptibles and resistants to expand seed production in response to thinning. We expect that y < 1.
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From equations (20), (22) and (24) we obtain the following alternative to equation (19) :
n*(zj = log Q + 1%O-‘1 + 1%CrsV--f/r>1 Q log [l + fafsi]
(25)
The rationale for taking Q = 0.3 is that it is most unlikely that resistance would be noticed until the year when about 30% of the plants would be resistant. In most instances, < 10% would be resistant in the previous year. Values obtained from equation (25) in the absence of a seed bank are plotted in Fig. 6. These values could well be in error by one or two years, as the
FIO. 6. Years to resistance (figf,g)as a function of mutation frequency p for various values of the product of the fitness f and the selection pressure (a= an/as), according to equation (25) with ii = 1 (no seed bank). The last factor in the numerator has been ignored, as is justified, for example, when ~+(l--fy-~) = O-8 so that log y&--A-‘) = -O+J!% If yS(l -h-l) = 0.1, so that log yS(l --F/-l) = -1.0, then 3,2, 1 and half years should be subtracted from Afo.a when f = 1.1, 2, 10 and 100 respectively.
calculations are increasingly innacurate when the number of resistants becomes an appreciable fraction. To display the effect of the seed bank, we plot in Fig. 7 the duration multiple M which is defined as follows : M
_
n;tis>
- -ni$(l>
1% iI1+&I = log [l-t-fcl/ii]
’
where
a = aR/as.
(26)
That is, to calculate the effect of the seed bank on the time for resistance to appear, we first determine the value in the absence of a seed bank (perhaps from Fig. 6) and then multiply by the appropriate factor M determined from Fig. 7. We see from Fig.,7, for example, that at 95 % killwith perfect resistance
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15
FIG. 7. Duration multiple as function of average seed life fi, for various values of fitness (f) and selection pressure a = O$Q. This multiple gives the factor by which the presence of a seed bank increases the number of years to the appearance of resistance.
(ol = 20) if f = 0.5 it will take twice as long to reach resistance if the seed longevity is four years and four times as long if it is twelve years. The slopes in Figs. 3-6 are based on information gleaned from various different literature sources. The actual number of seasons till the appearance of resistance will be a function of the initial frequency of the resistant genotype in the population, which (as has been pointed out above) is a function of mutation frequency and fitness. Thus the scale of proportionate resistance should be viewed as a “sliding scale” in so far as the 100 can be “moved’” to fit the difference between the initial frequency of resistance and full resistance (see also Fig. 7). In Figs. 3-6 an initial frequency of slightly less than 10-l’ was chosen as it may well represent a diploid monogenic recessive allele. Obviously, this initial frequency is a function of dominance, number of genes involved and ploidy. We have described herein the reasons for the paucity of resistance to herbicides. Because mutation frequency is so difficult to estimate, it will be exceedingly hard to get a direct measure of the initial frequency of the resistant phenotype. In the rare cases where resistance has appeared and fitness has been measured (as in Conard & Radosevich, 1978) by doing accurate measurements of the selection pressure, it would be possible using a rearrangement of equation (25) to calculate the initial phenotypic frequency, as follows (27) What are the effects of stopping herbicide treatment? Let us tirst assume that there is no seed bank. The counterpart of equation (1) shows that with spraying, the resistants increase annually by a factor of fa. (Typicallyf = O-8
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and c1= 10 so this factor is 8.) When spraying is stopped [equation (l)] shows that resistants increase by a factor of ffu), f(“’ < l- i.e. there is an actual decrease. From equation (24) we recall thatf’“) will generally be greater thanf sayf’“’ = 0.9, so that the decrease in resistants is comparatively small. The n;merical values we have mentioned illustrate the general trend; generally, a cessation of spraying for one season far from cancels the enhancement in the proportion of resistants that comes about from a single year’s herbicide treatment. In the presence of a seed bank with a reasonable value of E, the approximation equation (15) is still valid for a period after spraying is stopped. But the factor a should be deleted and the untreated fitness used, so that equation ( 16) becomes
That is, there is a “momentum” with a seed bank, and the number of resistants still increases for a fraction of fi years but at the slower rate of a factor of (1 +f(“)/%) per year, not (1 tf/- na ) as was the case with herbicide treatment. 5. Agronomic Implications:
Weeds
From the above we can understand the essential stability achieved in the field. Usually weed populations only decrease during the agronomic season while a herbicide is persistent, but do not decrease over a period of years; the frequency of the resistant genotypes would not noticeably increase over the years. From the data in the literature (cf. review of Gressel, 1979), it can be seen that the only well substantiated deviations from this thesis concern the S-triazine herbicides. The S-triazines are more persistent in the soil than most herbicides; they persist for months to years depending on soil and climate (cf. Libik & Romanowski, 1976, & Burnside & Schultz, 1978) and in maize and nurseries are often applied twice a year (cf. Fryer & Makepeace, 1972). Thus they exert a much higher selection pressure than foliar contact herbicides and herbicides that are rapidly degraded. If our reasons for the paucity of appearance of herbicide resistance are correct, then the original warnings to rotate herbicides should be modified. It is not to be expected that resistance to low selection pressure herbicides will appear and it is questionable whether they will often appear to the few herbicides which apply high selection pressures. From the mathematical interpretation, it is clear that herbicide rotation will not be too helpful in stopping the appearance of herbicide resistance. Whereas resistance increases as a function of selection pressure and fitness, it will decrease at a much slower rate upon removal of the selection pressure (Fig. 8).
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FIG. 8. The effect of stopping and restarting herbicide treatment. The ratio of resistant seeds deposited in year A to those deposited in reference year 1 (logarithmic scale) is plotted, giving curves similar to Figs. 3-5. Continual herbicide application is shown with fitnesses of 0.8 and 0.6. Other curves show the decline in resistance as expected when treatment is stopped after year 5 and the reappearance of resistance when herbicide treatment is restarted after 1,3 and 5 years after stoppage. These graphs are drawn for the case where 90% of the susceptibles are destroyed by the herbicide and none of the resistants, and where the average seed longevity is five years.
A few things become apparent when Fig. 8 is considered. (1) After stoppage, because of the seed bank, the proportion of resistants may rise for a period after a drop during the first year. (2) Upon reuse of the herbicide, after a year the graph of frequency will again rise parallel to the line denoting continued usage. (3) To an adequate approximation, for each year that a herbicide is not used the appearance of resistance will be delayed for about a year. Thus, if resistance under continued use would appear in 10 years and a herbicide is then used one out of every three years in rotation, resistance would now appear in about 30 years. (3) Once resistance had appeared and treatment with the selecting herbicide stopped, the initial decay in the resistant strain would seem likely to be moderately rapid. Conard & Radosevich (1978) have shown that the triazine resistance found in three species would decrease to 2 % (fi = 1) in 6-9 years when grown with 2% susceptible plants without the presence of herbicide. But this is not decisive, for if herbicide were reintroduced then resistance would rapidly reappear, as now the resistants are starting from a frequency many orders of magnitude higher than one would find in a natural situation. With fitnesses of 0.6-0.8, it would take very long to return to the initial resistance frequency as can be seen from the slope in Fig. 8. This may be part of the reason that resistance to insecticides has not returned to the initial frequency, though genetic reasons have been offered
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for this; i.e. a fitness increase of the resistant strains owing to insect interbreeding (Kelding, 1967). If this happens with plants, it maytake even longer to return to the pretreatment steady-state than shown in Fig. 8. 6. Agronomic Implications:
Crops
The number of selective herbicides available is both finite and small, especially when compared to the number of crops. All too often there is not a good match between a crop, the weeds attacking it, and an economic selective herbicide. For this reason it would be useful to select for herbicide resistant strains in many crops. Differential tolerance to pesticides has been noted in crops (cf. Gressel, 1979) and is often a factor in choosing varieties for use with some herbicides. Karim & Bradshaw (1968) have noted “there is no good reason why the improvement of herbicide resistance of crop plants should not be undertaken”. Because of the slowness imposed by the fitness and selection pressure, one may arrive at different conclusions, With crops the problem of “fitness” should be marginal; crop species have been so heavily selected for, for so long and are thus usually so homozygous that they are already quite naturally “unfit” except in the highly artificial “cultural” environments where they are grown. Herbicide resistance should hardly decrease this lack of fitness in a crop species, in its crop environment. Conversely, the homozygosity of crops may pose a problem if we can extrapolate from insects; there was a relative ineffectiveness of selection for insecticide resistance within inbred lines (cf. Crow, 1960). This would be especially severe when resistance is a multigenic quantitative effect. It is a greater problem to find ways to exert sufficient selection pressure to obtain resistance, and this is probably the reason for the fact that there are no reports of successful selection for herbicide resistance in crops, although there has been a modicum of success in a crop that was already partially tolerant (Faulkner, 1976). It should be easier to select resistance to the more persistent herbicides, but there are pervading agronomic and ecological reasons (described above) not to use this type of compound. Even with high selection pressures, no loss of fitness and no seed bank, it will still take a considerable length of time (Fig. 5) and large populations of plants to test, and large areas in which to grow them. These problems may be obviated by using cell culture techniques as reviewed in Gressel, Zilkah & Ezra 1978 and Gressel, 1979. The first author deeply acknowledges the mentorship of L. G. Holm who 18 years ago described this problem to him. Stimulating discussions or correspondences with J. Antonovics, A. D. Bradshaw, A. Dafni, W. Ewens, E. Galun, S. Kevin and A. Radosevich were quite helpful and encouraging. The second author’s research was supported in part by a grant from the United States-Israel Binational Science Foundation (BSF 5777).
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REFERENCES A. L. (1954). Proc. 1st Weed Control Conf. pp. 249-255. (1967). Report of the First Session of the FAO Working Party of Experts on Resistance of Pests to Pesticides, FAO Public. PL/1965/18, 127 pp. ANON. (1974). Report of the 10th Session of the FAO Working Party of Experts on Pest Resistance to Pesticides, 28 pp.. FAO Public. AGP:1974/M/9, Rome. ANTONOMCS, J. (1971). Amer. Sci. 59, 593. ANTONOVICS, J. & BRADSHAW, A. D. (1970). Heredity 25, 349. ASHTON, F. M. & CRAFIS, A. S. (1973). Mode of Action of Herbicides, 504 pp. New York:
ABEL, ANON.
Wiley. BAKER, H. G. (1974). Ann. Rev. Ecol. Systemat. 5, 1. BANDEEN, J. D. & MCLAREN, R. D. (1976). Can. J. Plant Sci. 56,411. BLEASDALE, J. K. A. (1960). In The Biology of Weeds, (J. L. Harper, ed.), pp. 133-142. London: Blackwell. BRADSHAW, A. D. (197.5). In Symposium Proceedings; International Conf: on Heavy Metals in the Environment, (T. C. Hut&son, ed.), pp. 599-622. Univ. Toronto Press. BURNSJDE, 0. C. & SCHULTZ, M. E. (1978). Weed Sci. 26, 108. CHANCELWR, R. J. (1960). Proc. 7th Brit. Weed Control Conf. pp. 599-606. CHEPIL, W. S. (1946). Scient. Agric. 26, 307. COMSTOCK, V. E. & ANDERSEN, R. N. (1968). Crop. Sci. 8, 508. CONARD, S. G. & RADOSEVICH, S. R. (1978). J. Ecol, submitted. CROW, J. F. (1960). In Research Progress on insect Resistance, Misc. Public Entom. Sot.
Amer. 2(l), 69. CROW, J. F. (1966). Natl. Acad. Sci.-N.R.C. Public. 1402, pp. 261-275. FAULKNER, J. S. (1976). Brit. Crop Protection Conf. Vol. 2, pp. 485-490. FRYER, J. D. & MAKEPEACE, R. J. (eds) (1972). Weed Control Handbook, Vol. II Recommendations 7th edit., 424 pp. Oxford: Blackwell Sci. Public. G-EL, J. (1979). In Plant Regulation and World Agriculture (T. K. Scott, ed.). Plenum Press (in press). G-EL, J. & HOLM, L. G. (1964). Weed Res. 4,44. GRESSEL, J., ZILKAH, S. & EZRA, G. (1978). Proc. Fourth Intl. Gong. PIant Tissue Culture, (T. Thorpe, ed.). Univ. Calgary Press (in press). GROOAN, C. O., EA~TIN, E. F. & PALMER, R. D. (1963). Crop Sci. 3,451. HAHN, F. E. (ed.) (1976). Acquired Resistance of Microorganisms to Chemotherapeutic Drugs (Vol. 20 of Antibiotics & Chemotheraphy), 272 pp.Basel: S. Karger. HALDANE, J. B. S. (1960). J. Genet. 57, 351. HARPER, J. L. (1956). Proc. 3rd Brit. Weed Control Conf. Vol. 1, pp. 179-188. HARPER, J. L. (1957). Outlook in Agric. l(5), 197. HARPER, J. L. (1960). Iu The Biology of Weeds, (J. L. Harper, ed.), pp. 119-132. Oxford: Blackwell Scientific Public. HARPER, J. L. & GAJIC, D. (1961). Weed Res. 1, 91. HAYES, R. M. &WAX, L. M. (1975). Weed Sci. 23, 516. HOLLIDAY, R. J. & PUTWAIN, P. D. (1977). Weed Res. 17, 291. HOLLJDAY, R. J., PUTWAIN, P. D. & DAFNI, A. (1976). Proc. 1976 Brit. Crop Protection Conf. Weeds, pp. 937-946. HOLM, L. G. (1977). Weed Sci. 25, 338. INWANG, E. E., I&AN, M. A. Q. &BROWN, A. W. A. (1967). Bull. Wid. Hlth. Org. 36,409. ISEN~E, A. R., SHAW, W. C., GENTER, W. A., SWANSON, C. R., TURNER. B. C. & WOOLSON, E. A. (1973). Weed Sci. 21, 409. KARIM, A. & BRADSHAW, A. D. (1968). Weed Res. 8,283. KELDING, J. (1967). World Rev. Pest Control 6, 115. LIBIK, A. W. & ROMANOWSKI, R. R. (1976). Weed Sci. 24, 627. MCNEILLY, T. (1968). Heredity 23, 99. MILES, C. D. (1976). PIant Physiol. 57,284.
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NEWMAN, J. F. (1957). Outlook in Agric. l(6), 235. PARKINSON, C. N. (1957). Purkinsons Law. Boston: Houghton-MilXlin. PTLE, D. W. (1976). Nature 263, 317. RADOSEVICH, S. R. & CONARD, S. G. (1977). Abstract Weed Sci. ROBERTS, H. A. & DAWSON, P. A. (1967). Weed Res. 7,290. RYAN, G. F. (1970). Weed Sci. 18, 614. SCHOOLER, A. B., BELL, A. R. & NALAWAJA, J. D. (1972). Weed SEGEL, L. A. (1978). In press. VANVALEN, L. (1965). Evolution 13, 514.
Sot. Amer. p. 77. Sci. 20, 167.
APPENDIX
Following a suggestion by S. Rubinow we outline here an approach to our problem that makes somewhat different and probably more realistic assumptions about the seed bank. An advantage of this approach is that depletion of the seed bank by germination is easily accounted for. When this effect is not important, however, the results will be seen to be virtually equivalent to those obtained with our principal model-which testifies to the robustness of our conclusions. Let GLR)(Gis)) be the number of viable resistant (susceptible) seeds that are found in a unit area at the beginning of the nth season. The germination probabilities IJ,, and pn are now given by g = G’S’/[G’S’ + xG’~‘]
p,, = xG:~)/[G$~‘+xG:~)].
(Al)
[Equation (Al)“replaLs Eiuation;b):] In considering how GkR’ changes, we subtract the number of seeds that germinate at the beginning of the nth season, subtract a portion dR of the remaining seeds that lose their viability during this season, and add the resistant seeds that are deposited at the end of the season. This gives G$,
= GcR)Np, - 6, (GiR’ - NpJ + NiR’. n
WI
The present model is completed with an analogous equation for G$ 1, plus equations (1 la) and (11 b) as before. Let us immediately make two simplifying assumptions, that the resistant population is small compared to the susceptible, and (for the moment) that germination can be neglected in monitoring the seed bank. These assumptions imply that equations (Al) and (A2) can be simplified to cTn= 1,
pn = xG;~)/G’~’n 7
G;$
= GiR’ (1 - 6,) + NiR).
(A3a,b,c)
We expect G,(‘) to maintain a constant value, which we denote by G. By the analog of equation (A3c) we find that G(‘) n = G where
G = Na&6,.
Thus p n = xG’~‘/G. n
644)
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Combining equation (A4) with equation (1 lb) we obtain G$r = AGiRP’+B or alternatively, NLt), = A NiR’+B 6,, (A% b) where A = I-6,+@f6,, B = N CL&us, We wish to compare equation (A5b) with the corresponding equation (16) obtained in our previous model. But equation (16) was made under the assumption that uf was rather large compared to unity. Making the corresponding assumption here we find that in the present case the number of resistant seeds deposited, NiR’, grows by an annual factor of 1 +ccf6,. In the earlier model the corresponding factor was 1 +olf/ii. These results are the same if E = 6,-l, but this is just the relationship mandated by the equation displayed after equation (4). We conclude that when the resistant population is growing rather rapidly and when germination may be neglected in tallying changes in the seed bank, then it makes virtually no difference whether one asumes (i) that each seed remains viable for e years, or (ii) that each year a fraction of seeds in the bank dies at a rate which gives an average seed lifetime of fi years. Under other circumstances there are differences. When germination is not neglected, appropriate alterations in our calculations lead to a final result of the same form as equation (A5) but with different constants. In particular when all terms are retained the growth rate A is given by A = (l-6,) (1 -N xG- ‘)+ N xG-‘$,u, where now G = 6,’ [Na,&-1+&i.
The Paucity of Plants Evolving Genetic Resistance to Herbicides : Possible Reasons and Implications J. GRESSEL Department of Plant Genetics AND
L. A. SEGEL Department of Applied Mathematics The Weizmann Institute of Science, Rehovot, Israel (Received 12 January 1978, and in revised form 19 July 1978) Resistances to antibiotics and pesticides except herbicides rapidly developed following their introduction. Despite repeated use of herbicides only a few cases of acquired genetic resistance have been reported. By extrapolation from analogous situations, it is suggested that this is due to a combination of low selection pressure of most herbicides, lower fitness of resistant weed strains in the absence of herbicide, the ability of herbicide thinned strands of susceptible weeds to produce relatively more seeds, as well as to the large soil reservoir of susceptible weed seeds. The few reported cases of resistance are to persistent, high selection pressure herbicides supporting our contentions. 1. Introduction
Shortly after the introduction of herbicides into commercial use thirty years ago, there were predictions that repeated use would select for resistance (Abel, 1954; Harper, 1956) as had happened with all other groups of pesticides from antibiotic drugs through rodenticides. These views remain ingrained (Anon, 1974a). From similar considerations, it was suggested that both herbicides and crops be rotated (Abel, 1954). Yet there are many areas where “heretical” agriculturists have successfully used the same herbicide annually on the same crop in the same field repeatedly without apparent selection for resistant mutants in the susceptible weed species. For example, 2,4-D,? a widely used selective herbicide, has been used to control annual i The WSSA or IUPAC common names of pesticides are used throughout ; their chemical names are as follows : atrazine = 2--chloro4-(ethylamino>d-(isopropylamino)-s-triazine ; diquat = 6,7--dihydrodipyrido DDT =: ]I]-trichlor+2, 2-bis(p
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dicotyledonous weeds in grains, yearly, in many places without crop rotation for more than 25 years. To our knowledge, no substantial cases of genetic resistance to this herbicide have been reported. There are a few isolated reports of such selections occurring to S-triazine herbicides (see later). It appears then that predicted resistance seldom appears. The analysis of possible reasons for the non-appearance of resistance is the main topic of this paper. After remarking on the nature of herbicide resistance, we shall consider the various factors affecting the appearance of such resistance: mutation, selection pressure, fitness, and the particular “plasticity” of weed growth and especially the reservoir of seeds in the soil. To obtain an idea of how all these factors interact we present some mathematical models. Our paper concludes with a discussion of the agronomic implications of our findings. The discussion herein will be devoted to the appearance of resistance in species that were heretofore susceptible. We shall not consider well known changes of weed populations due to changes in agronomic procedures including the use of herbicides for species which are naturally insensitive, as discussed by Harper (1957), Harper, ed. (1960), Baker (1974) and Holm (1977). 2. The Nature of Resistance Resistances to phytotoxic compounds such as herbicides are known to occur at a multiplicity of levels (as is well reviewed in Ashton & Crafts, 1973). Selective permeation, for example, can occur at various levels, e.g. uptake into the root, through the cuticle, or uptake into target organelles. Prevention of toxicity by lack of translocation is also known, especially in the root endodermis. Selectivity can be based on the differential ability to detoxify a compound enzymatically. Phenological modes of resistance occur, for example, by germination after the normal time of application of contact herbicides or after degradation of mildly persistent herbicides. Thus the modes of selective resistance are quite varied, making it all the more surprising that there has been little selection for genetic resistance. Some ecological and genetic aspects of this problem have been recently reviewed by Holliday, Putwain & Dafni (1976). Resistance is often lumped with natural strain differences in tolerance. They are best differentiated by the effective dose. Intraspecific differential tolerance is known, i.e. small variations in dose affect biotypes differently. Further on the continuum is “resistance” (as herein defined) : resistant plants completely survive a dose, that is essentially completely toxic to the susceptible type. Our definitions of resistance and differential tolerance conform to those of the FAO (Anon., 1967).
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Known cases of resistance and differential tolerance are summarized in Gressel(l979). Of the many reports in the appearance of differential tolerance and the few on resistance, only those using S triazines claim that the more resistant strains occurred in the field as a result of herbicide treatment (Bandeen & McLaren, 1976; Ryan, 1970; Holliday & Putwain, 1977). Cases of phenological resistance would not be found by the methods used by the experimenters until now. We know of no ecological assessment of selection for this type of resistance. 3. Factors Affecting the Appearance of Resistance (A)
GENERATION
TIME
Antibiotics, chlorinated insecticides, dicoumarol rodenticides and herbicides were introduced into usage at about the same time. Acquired genetic resistance appeared rapidly for all these pesticides, except herbicides. Various arguments have been raised that it is premature to expect selection for herbicide resistance; the major one being that not enough generations have gone by (e.g. Crow, 1966). It is true that the generation time of higher plants is less than houseflies or mosquitoes, but the first field resistance of both these insects was noted within the first year DDT was used (reviewed by Newman, 1957; Crow, 1966). Moreover, some weed species (e.g. Amaranthus retroJlexus and Chenopodium album) are capable of more than one generation during an agricultural season. Even with one plant generation per year, as many generations have passed since herbicides were introduced as it took to achieve field resistance to insecticides. There are various reasons for the delay in appearance of resistance to herbicides by plants. Our contribution is to pinpoint the major factors involved and to combine them into a mathematical model that provides experimentally testable predictions of how long it would take resistance to appear under various conditions and allows the importance of each factor to be evaluated. To this end, we first discuss the various factors that affect the evolution of resistance. (B)
MUTATION
FREQUENCY
In untreated crops, the proportion of resistant individuals is governed by the mutation rate. There may be a particularly low mutation rate to herbicide resistance. This occurs with DDT resistance in the East African strains of the Yellow Fever Mosquito (vs. the Asian strains which can interbreed with it) which may account for the possible continual control of this problem in East Africa with DDT (Inwang, Khan & Brown, 1969). There is also the remote possibility that a gene for a particular herbicide resistance does not
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exist, in analogy to the case of continued control of streptococci by penicillin. The streptococci seem to lack both the gene for penicillinase and the ability to acquire a plasmid for penicillinase. Bacterial resistances are reviewed in Hahn (1976). Whereas it may be possible that some plant species lack genes for resistance (or have a low mutation frequency for resistance) to a given herbicide, it would appear to be highly unlikely that most plants could not genetically adapt to most herbicides. This would he highly dissimilar from the bacterial, fungal and animal situations. (C)
SELECTION
PRESSURE
Another factor that affects the evolution of resistant strains is selection pressure. In considering this factor, we begin by taking note of a series of ecological studies of plant succession on mine tailings in which Bradshaw’s group showed the selection of ecotypes of various species that are resistant to much higher levels of copper, zinc and lead than the normal ecotypes can survive. The frequency of such types in the normal population is low and yet it only takes a few seasons for such areas to become revegetated by resistant strains (Antonovics, 1970; Antonovics & Bradshaw, 1970; McNeilly, 1968, Bradshaw, 1975). There is a basic difference between the field phytotoxicities of heavy metals and herbicides, the degree of selection pressure. The metals are in such high concentrations (i.e. “overkill”) that only l&20% of the species can evolve resistance (cf. Bradshaw, 1975). Because of various agronomic/ economic considerations, herbicides are usually applied at rates predetermined to give 90-95x kill of the susceptible species. Heavy metals are at higher phytotoxicity levels and may be leached quite slowly from the soil, whereas many herbicides are rapidly leached or degraded, lessening their persistence. Thus there is a stronger pressure for selection of heavy metal tolerance than for resistance to most herbicides. Yet different levels of selection pressure alone cannot account for the nonappearance of herbicide resistance. Assuming even 90% kill and a natural frequency of one resistant plant in lOi repeated annual treatment would lead to a tenfold increase per year in the frequency of resistant strains. In ten years resistance will be apparent. But the effective selection pressure of the rapidly degraded herbicides is even less than the initial kill would suggest because of non-uniform germination of weed seeds throughout the crop year. Some seeds of a given weed species may germinate sufficiently late to be unaffected by the treatment and at a time when they do not greatly affect crop yield (see e.g. Chepil, 1946; Chancellor, 1960; Roberts & Dawson, 1967). Thus one expects a relatively slow increase in herbicide resistance compared to the almost immediate jump seen with heavy metal tolerance.
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FITNESS
Another major factor is fitness, the ability to compete and reproduce in non selective conditions. Important here is the much discussed “cost” of natural selection (see for example Haldane, 1960; van Valen, 1965). Pyle (1976) recently described an example of the lowering of fitness in Drosophila by artificial selection, together with a review of the pertinent genetic literature for insects. It had been claimed that the homozygosity required for recessive genes for resistance to occur is the cause for the decrease in fitness. This would not pertain to dominant resistant types (Crow, 1960, 1966; Kelding, 1967) yet resistant bacterial strains are also less fit (Hahn, 1976). To our knowledge little has been reported on the genetics of resistance in the few known cases. Differential tolerance of flax to atrazine was found to be quantitative (Comstock & Anderson, 1968), although in maize atrazine resistance is dominant and monogenic (Grogan, Eastin 8z Palmer, 1963). The inheritance of siduron tolerance in Hordeum jubatum is dominant and trigenic (Schooler, Bell & Nalawaja, 1972). DDT resistance in barleyis monogenic recessive(cf. Hayes & Wax, 1975); thus most forms of genetic inheritance have been observed. In the case of metal tolerance, it was shown that this “cost” is charged against “fitness”. When the metal tolerant genotypes were interseeded with the wild type plants on a normal non-selective soil, the metal tolerant type genetically “disappeared” back towards its normal frequency. The tolerant type was less fit to compete with the wild type (McNeilly, 1968). In this case, it was calculated that the coefficient of selection against tolerance on normal soils is 0.53. A preliminary report on the “lowered fitness” of S-triazine resistant Amaranthus was presented by Radosevich & Conard (1977) and this lesser fitness may be about a level of 0.5 (calculated from Conard & Radosevich, 1978). Similarly, S-triazine resistant Chenopodium germinated 2-3 days after the sensitive wild type (Bandeen & McLaren, 1976). That this can be a strong disadvantage has been discussed previously (Gressel & Holm, 1964). An example of a resistant mutant with an extremely high cost is an artificially selected mutant of maize resistant to diquat. This mutant is viable in the presence of diquat as it is blocked on the oxidizing side of photosystem 11 and thus is also defective in normal photosynthesis (Miles, 1976). Similarly, white (achlorophyllous) tissue cultures of higher plants are phenotypically resistant to herbicides working at the level of photosynthesis (Gressel, Zilkah & Ezra, 1978), but these are hardly able to exist outside of the test tube. (E)
PARKINSONIAN
PLASTICITY
A final set of factors that affect the appearance of resistance to herbicides is the “plastic” property of many plant species. Weed populations can often
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follow aspects of the expanded “Parkinson’s Law” (Parkinson, 1957), insofar as they often “expand to fill the space available”. This is well described by Harper (1960) and Harper & Gajic (1961), in a case where they adjusted seedling density; a 90% reduction of the seedling population of Agrostema githugo gave rise to larger plants and utimately less than a 10% reduction in seed yield. This “plasticity” of the population means that seed yield (within a certain range) is not a direct function of plant number, but a function of the space. Similar findings have been reported with crops (cf. Bleasdale, 1960). The “space available” is considerably increased by herbicide thinning of a population. This was demonstrated for many species and herbicides in the work of Isenee et al. (1973). They applied massive doses of 13 herbicides and followed the revegetation of 19 species. The herbicide levels were so high that the first effect was a contact killing of all plants, followed later by revegetation. The herbicides had varying selectivities, thus various numbers of plants germinated and grew to maturity in the first two years. We plotted their data on resulting plant numbers and area covered. It is apparent that even under these conditions of massive herbicide “overkill”, the plants that managed to grow followed Parkinson’s edict and “expanded to fill the space available”, by “expanding” in their seed yield to a level approaching that of a dense population. Unfortunately, Isenee et al. (1973) did not check any of the regrowth for herbicide resistance.
b.~LA
I
0 ,0203040~0660~080~0 Reduction of plant number
IOC by herblcldes
FIG. 1. An example of plasticity; revegetation following massive herbicide treatment (calculated and plotted from Table 1 in Isenee et al., 1973). Plots were treated with 2400 times the recommended agricultural doses of 13 herbicides. Revegetation occurring or reinfesting propagules was measured 1 and 2 years after treatment. Each point represents the effect of one herbicide (in three plots) on plant number and area covered for either the first or second year. The dashed line represents a linear proportionality between plant number and area covered and the deviation represents Parkinsonian plasticity.
LACK
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If after herbicide treatment we are left with a mixed population of lessvigorous resistant plants and fit susceptible plants that were for some reason untreated, it is apparent that the fit plants will “expand” much better to fill the gap than the resistant plants. Even without herbicides, there is a considerable amount of thinning. As more seeds germinate than reach maturity, fitness is a factor under natural conditions in governing which plants mature. A variety of factors govern fitness at this early stage, as described by Harper (1960) and Gressel & Holm (1964). The potential for “expanding” is much better realized under thinned conditions of herbicide treatment and the “normal” plants should realize this potential better than the less fit resistants. With contact herbicides or those rapidly degraded, the selection pressure is ephemeral, which would then allow the expression of fitness of the susceptible. (F)
SOIL
SEED RESERVOIR
Another important source helping to keep the resistant weed population constant is the “buffering action” of buried viable weed seeds, which have greater fitness (being susceptible strains). As these germinate over a period of years, they would be another factor which would delay the appearance of resistance. To the soil weed seed reservoir must also be added weed seed blown, dropped, washed or mistakenly planted in a treated field. Holm (1977) has clearly stated that “in a list of things about which weed science is ignorant, the source of resupply of weed seeds must rank near the top.” These latter are more a factor in smaller fields and irrigated fields. Other factors stabilizing weed populations which we will not consider herein are discussed in Harper (1957) and in Harper, ed. (1960) but are of interest when considered in the context of differential fitness. 4. Mathematical
Description of the Interrelated Affecting Resistance
Phenomena
The interrelation of selection pressure, fitness, Parkinsonian “plasticity” and the buffer capacity of the soil seed bank can be developed mathematically. We shall present such a development in a sequence of models of increasing complexity. A discussion of some of the mathematical aspects of the problem can be found in Segel (1978). Our goal is to illustrate the major factors that operate in typical situations. Only when specific data are available for particular systems does it appear worthwhile to consider all of the modifying influences involved. The first three sections describe the situation prior to herbicide treatment. In a repeatedly cropped field in which some method of cultivation other than
356
J.
GRESSEL
AND
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A.
SEGEL
herbicides is used to suppress weeds, a miniscule part of the weed population of a given species will be resistant to any given herbicide. The seed yields of the two types, “susceptible” and “resistant” in the nth generation are denoted by N$” and NiR’ respectively. For simplicity, we onlyconsider the case of one generation per year. (A)
NO SEED BANK
IN THE SOIL,
$1 = fW!!$ ll+t
II
NO MUTATIONS
, n = 0, 1,2, 3,4, . . .
Heref’“’ is a constant, the relative fitness. The superscript “u” denotes that we are considering the untreated situation, where no herbicide is being applied. IfJ’“’ < 1, the fraction of resistants will decrease until the resistants have effectively disappeared altogether. (B)
NO SEED BANK, WITH
Ignoring back mutation
MUTATION
TO RESISTANCE
A FREQUENCY
/l
the situation is governed by the equation (2)
As can be verified straightforwardly, NiR) P N(s) ” - ----@ 1-s
the solution of this equation is
1cm”*
+
(3)
When n = 0 the ratio of resistant to susceptible seeds has the initial value N’,R)/NbS’. Becausef’“’ < 1, the second term in equation (3) will decrease each year and the ratio will approach the steady-state value p/(1 -f’“‘). (C)
MUTATION.
SOIL
SEED BANK
WHOSE
DURATION
IS fi YEARS
(4)
In this model it is assumed that the seeds in (where E varies from species to species) and As illustrated in Fig. 2, such an assumption tive results even though it may be more
the soil are fully viable for C years then cease altogether to be viable. should give satisfactory qualitarealistic to assume that viability
LACK
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RESISTANCE
357
declines exponentially over a period of years which is different for different species (e.g. Chepil, 1946; Chancellor, 1960; Roberts & Dawson, 1967). The value of fi can reflect to some extent a gradual loss of vigor in the viable seeds; but of course this feature could be accurately represented in a more detailed model.
FIG. 2. A typical case in which a fixed portion of seeds from a given year germinate in the succeeding year and the same proportion of the remaining seeds germinate the next year, etc., giving an exponential loss. The average viability as de&-d in the text is such that the area under the dashed half rectangle is equal to the area under the broken line. This criterion can be used to select R from field data (cf. Chepil, 1946; Chancellor, 1960; Roberts & Dawson, 1967). A will typically not be too different from the half life r,-log 2/logI of seeds in the soil bank. See also discussion in the appendix.
If 1 is the probability (assumed constant) that a seed which is viable in one season is also viable in the next then the average duration of viability in years is l+~+%2+;13+...
= &,
and this value should be taken for Fi. Empirical data can also be used to establish the average duration of viability and hence the appropriate value of ii. An appendix shows a somewhat different and more complete model of the seed reservoir. That model leads to essentially the same results as the approach taken here. In general, equation (4) is not sufficient to describe the situation, as in any given year only one relation is provided for the two unknowns NiR) and Ni”. In the previous cases we were nonetheless able to solve for the ratio of these two unknowns, but this is no longer possible. To describe a complete model, let us denote by a,, and pn the percentages of the N seeds that germinate each year that are respectively susceptibles and
3%
J.
GRESSEL
AND
I,.
A.
SEGEL
resistants. (That N can be regarded as constant is one aspect of Parkinsonism.) We shall assume that only a small proportion of seeds in the seed bank will germinate. In the simplest instance, o;, and P,, can then be computed by counting the seeds that have deposited in the last 6 years (neglecting “withdrawals”) and determining what percentage of these are susceptible and what resistant. To be somewhat more precise, we shall take into account relative germination ability by a factor x < I that describes how the probability of finding a germinating resistant is less than one would expect from counting the viable resistant seeds in the seed bank. That is n-t i=$+ NR’ Pn -=x,i--. (5) a;2 i=FM, *IS’ Given that the probabilities (T,~and P,, must add to unity, we deduce from equation (5) that n- 1 II- 1 x 1 NiR’ i=gm, W’ i=n-fi ----. (6) fJ!l = 1,- 1 i=g,
[N,!“‘+xNjl’l
’
“I =
“-I i=;‘+ C*?‘+x*iR’I
Let /I$‘) (/3$“) be the proportion of germinating susceptibles (resistants) that become established, $$‘)(I,@) the proportion of established plants that survive to the end of the season, and v$@(v$‘))the number of seeds per survivor. (Again, a superscript “u” is used in anticipation that parameters may change when herbicide is applied). Let us introduce the abbreviations (#p E ~~)~~)vp, (j$’ s p$0@$$0, (7) i.e. C& and +n are fitness parameters for each type. We have as the governing equations N@’ NCR’ ” = p,,N &” +/.m,N &“. (8% b) ” = g ” N &‘, We have neglected back mutations as well as the tiny loss of susceptibles from mutation to resistance. The combination of equations (6) and (8) allows the’.successive numbers of susceptibles and resistants to be computed given any initial situation. The quotient of equations (8b) and @a), with (6), gives (4), where the relative fitness is given by f’“’ = x qg+pp (9) The compound fitness f(“) reflects the joint influences of the germination fitness ratio 2 and the ratio &‘)/c#$” that describes the relative fitnesses in the period following germination through seed production.
LACK
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GENETIC
HERBICIDE
RESISTANCE
359
Equation (4) is sufficient to describe the situation if the resistant population is sufficiently low, as we shall now demonstrate. Indeed for our purposes we lose little by confining ourselves to instances where the number of resistants is considerably less than the number of susceptibles. Then each year the number of susceptible seeds germinating per unit area can be approximated by a constant N (i.e. a, x 1) because of the Parkinsonian plasticity described above. From equation (Sa) we see that the number of susceptible seeds deposited each year will be c#$‘N. With this equation (4) simplifies to
Even with the seed bank, it can be shown that iff@) < 1 the ratio of resistant to susceptible seeds will approach the same steady-state value as before, p/( 1 -f’““, ,. (D)
THE EFFECTS
OF HERBICIDE
TREATMENT
If gS(aR) is the fraction of established susceptibles (resistants) that survive spraying then the governing equations (8) must be modified to N@) NCR) n = g nNus~s 9 n = p nNuRc~R+p g ” Nu&, . (lla, b) We have dropped the superscript “u” for “untreated” and will shortly discuss how we expect fitness to change in the presence of spraying. Keeping in mind our assumption that o,, Y 1 and again employing equation (5), the quotient of equations (11 b) and (1 la) is taken to obtain the new governing equation.
Previously, with f(‘) < 1, the proportion of resistant seeds tended to a low value maintained only by mutation. The analogous result can be true here, only the condition is changed by selection pressure to foR& c 1: N(R)
fc? < 1,-J-%W
N(R) =
--f-
j& n
P l-c$f
;a=--.
CfR
%
(13)
But c+ is typically between O*l-O*Ol and CI~is little less than unity. We thus expect that although f < 1, faR/cxs> 1. In this case the proportion of resistants in the population will grow. A further approximation permits an esti-
360
J.
GRESSEL
AND
I,.
A.
SEGEL
mate of the rate of growth. To obtain this, we subtract from equation (12) the corresponding equation when n is replaced by n - 1: (14) If enrichment approximation
for resistants is fast or even moderate,
we can make the
N;!$ - NS;R_‘,mii cz N:?,. In this case our equation simplifies to
(15)
, where CC= ER
as
(16)
with solution (17) or (18)
We note that equation (14) cannot be used in the first year of herbicide application, because N$?r + is not defined. Thus, use of equation (16) cannot be justified in computing the effect of the first year’s application of herbicide. There generally results an underestimate of the rate of resistant growth, which however is counterbalanced by the relatively small overestimate afforded by all future uses of equation (16). These errors, plus errors stemming from the linearization [equation (lo)], will typically result in a misestimate by one to three years in the appearance of resistance. The clarity afforded by the simple formula (18) outweighs gains in precision that would be obtained by more accurate calculations. In a complex situation such as that under investigation it is broad semi-quantitative trends that one should seek in a first attempt at mathematical modelling. We can now generate a sequence of graphs to clarify the influence of the various factors that appear in formula (18) for the annual enrichment in the proportion of resistant seeds deposited in the season of the herbicide treatment. In the first set of graphs (Fig. 3) we depict the effect of the seed bank on the increase of the proportion of resistant seeds in the field when there is a 90 % kill of susceptible plants (0~~= 0.1) and total immunity of the resistants (aR = l), a steady-state resistant frequency prior to spraying of just under 10 -lo, and a slight differential in fitness. This would be an acceptable frequency for a recessive diploid monogenic resistant biotype.
ADAPTIVE
-4
GENETIC
11111’11111 0 4
8 I2 YeOrs repeated
HERBICIDE
16 20L treotnwt
RESISTANCE
/,I, 24
28
361
32
FIG. 3. The effect of soil seed reservoir on the appearance of herbicide resistance. In this example, an initial steady state frequency of resistance is less than 10-l”. For other initial frequencies the origin should be moved to the appropriate value to show the number of orders of magnitude increase. Different average ages of the seed reservoir (A) are given on the slopes.
The lines in Figs. 3-5 are inaccurate after reaching 10-r when the proportion of resistants ceases to be small. It is clear that the curvature which would be exhibited in graphs obtained by a more exact theory would represent only a small quantitative effect on the appearance of resistance. By noting when the straight lines approach the top of the graph, we can see that under these conditions resistance will become noticeable in about 11 years without a seed bank, while with a seed bank duration ii of 3, 5 and 10 years, resistance will appear in about 17, 24 and 37 years respectiveiy. In considering this and succeeding graphs it should be borne in mind that aR and as enter formula (18) only in the ratio a,/~+. If differential tolerance occurs, the rate of increase can also be calculated. Thus the same a = 10 would be obtained if 80 % of the resistants survived spraying in contrast with 8 % of the susceptibles. The interaction between selection pressure and seed longevity is depicted in Fig. 4. It is obvious that the effects of these two factors, within ranges expected in the field, are important. Their effects are not additive, they are compounded giving a spread of values from 5 years (E = 1 with 99% kill) to 37 years (ii = 10,90x kill) until a resistance of 30% can be expected to be observed. As the range of expected fitnesses is not numerically as great as the possibilities of selection pressure and seed bank longevity, fitness has relatively less effect on the rate of resistance spread throughout the population (Fig. 5). Figure 5 can also be regarded as showing the effect of a differential sensitivity to herbicide of susceptibles and resistants. One can think off always being approximately unity and the various numbers Iabelling each line as describing the fractions of resistants that survive the herbicide treatment. 14
362
J. GRESSEL
-4
AND
LLLL1.1. 0 4
L. A. SEGEL
A- L-i$e d& Years
repeated
ll-Ld-2 20 24
28
32
treatment
FIG. 4. The effect of selection pressure on the appearance of herbicide resistance. Various permutations of selection pressure a, (proportion surviving a herbicide treatment) and seed bank duration are plotted.
It is useful to derive an explicit formula for the time to resistance. To this end, suppose that resistance is observable in the season n1; when the number of resistant seeds is some fraction Q of the total. Virtually the same result will be obtained if we assume that resistants will be noticeable when they comprise a fraction Q of the susceptibles.It is true that in the year that resistance becomes noticeable our assumption that resistants form a negligible portion of the total is no longer a good one, but the resulting error of a year or so is certainly permissible in the face of expected biological variability. Similarly, our results for rrz would differ very little if we adopted the criterion that resistance is observable when a fraction Q of the plants that remain after spraying are resistants.
-4
0
4
8 Years
12 repeated
16 20 24 28
32
treatment
FIG. 5. The effect of fitness on the appearance of herbicide resistance. Different fitnesses are plotted at two average durations of seed life in the soil reservoir.
LACK
OF
ADAPTIVE
GENETIC
HERBICIDE
RESISTANCE
363
Since Nis) B a&N we can use formula (18) to obtain the following formula for n(r (where we explicitly take note of the dependence on ii):
n*tk) = log Q + log______CwhW%R)I Q log 1+$
i 1
(19)
In formula (19) the expression a,&N/NbR’ is the ratio of the essentially constant number of seeds that are deposited each year (per unit area) to the number of resistant seeds deposited just before the onset of herbicide treatment. This ratio can be regarded as a parameter but its measurement does not seem feasible. It is preferable to recognize that conditions at the onset of herbicide treatment should normally be obtainable from the steady-state conditions in the non-herbicide case. Thus, from the conclusion of Part Cwe see that NhR’ = t#$‘Np/( 1 -f’“‘). (20) It remains to relate @) andf’“) to their counterparts when herbicide is being applied. We shall assume that with spraying the total number of seeds per established weed plant increases by a factor of i&..u,, i.e. that
Here the factor I/cl, describes the expanded space available to each established plant while 6, quantifies the degree to which the susceptibles increase their seed production in response to the increased area available. To allow for possible escape from the action of contact and low persistence herbicides we write&/flp’ = L,. With the definition R& - ys it follows from equations (21) and (7) that -4s = Ys _I#$)
(22)
as ’
As the factor a, describes thinning for both susceptibles and resistants we assume, in analogy with equation (22), that 4R
YR
so
that
4R -=--.
YR d$’
(23)
4%
Thus, from equation (9),
f = yf(")
(24) where y = yRIys is a correction factor to the fitness that describes the relative ability of susceptibles and resistants to expand seed production in response to thinning. We expect that y < 1.
364
J.
GRESSEL
AND
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A.
SEGEL
From equations (20), (22) and (24) we obtain the following alternative to equation (19) :
n*(zj = log Q + 1%O-‘1 + 1%CrsV--f/r>1 Q log [l + fafsi]
(25)
The rationale for taking Q = 0.3 is that it is most unlikely that resistance would be noticed until the year when about 30% of the plants would be resistant. In most instances, < 10% would be resistant in the previous year. Values obtained from equation (25) in the absence of a seed bank are plotted in Fig. 6. These values could well be in error by one or two years, as the
FIO. 6. Years to resistance (figf,g)as a function of mutation frequency p for various values of the product of the fitness f and the selection pressure (a= an/as), according to equation (25) with ii = 1 (no seed bank). The last factor in the numerator has been ignored, as is justified, for example, when ~+(l--fy-~) = O-8 so that log y&--A-‘) = -O+J!% If yS(l -h-l) = 0.1, so that log yS(l --F/-l) = -1.0, then 3,2, 1 and half years should be subtracted from Afo.a when f = 1.1, 2, 10 and 100 respectively.
calculations are increasingly innacurate when the number of resistants becomes an appreciable fraction. To display the effect of the seed bank, we plot in Fig. 7 the duration multiple M which is defined as follows : M
_
n;tis>
- -ni$(l>
1% iI1+&I = log [l-t-fcl/ii]
’
where
a = aR/as.
(26)
That is, to calculate the effect of the seed bank on the time for resistance to appear, we first determine the value in the absence of a seed bank (perhaps from Fig. 6) and then multiply by the appropriate factor M determined from Fig. 7. We see from Fig.,7, for example, that at 95 % killwith perfect resistance
LACK
OF
ADAPTIVE
GENETIC
2
4
HERBICIDE
6 8 Years in ground
IO (5)
RESISTANCE
12
365
15
FIG. 7. Duration multiple as function of average seed life fi, for various values of fitness (f) and selection pressure a = O$Q. This multiple gives the factor by which the presence of a seed bank increases the number of years to the appearance of resistance.
(ol = 20) if f = 0.5 it will take twice as long to reach resistance if the seed longevity is four years and four times as long if it is twelve years. The slopes in Figs. 3-6 are based on information gleaned from various different literature sources. The actual number of seasons till the appearance of resistance will be a function of the initial frequency of the resistant genotype in the population, which (as has been pointed out above) is a function of mutation frequency and fitness. Thus the scale of proportionate resistance should be viewed as a “sliding scale” in so far as the 100 can be “moved’” to fit the difference between the initial frequency of resistance and full resistance (see also Fig. 7). In Figs. 3-6 an initial frequency of slightly less than 10-l’ was chosen as it may well represent a diploid monogenic recessive allele. Obviously, this initial frequency is a function of dominance, number of genes involved and ploidy. We have described herein the reasons for the paucity of resistance to herbicides. Because mutation frequency is so difficult to estimate, it will be exceedingly hard to get a direct measure of the initial frequency of the resistant phenotype. In the rare cases where resistance has appeared and fitness has been measured (as in Conard & Radosevich, 1978) by doing accurate measurements of the selection pressure, it would be possible using a rearrangement of equation (25) to calculate the initial phenotypic frequency, as follows (27) What are the effects of stopping herbicide treatment? Let us tirst assume that there is no seed bank. The counterpart of equation (1) shows that with spraying, the resistants increase annually by a factor of fa. (Typicallyf = O-8
366
J.
GRESSEL
AND
L.
A.
SEGEL
and c1= 10 so this factor is 8.) When spraying is stopped [equation (l)] shows that resistants increase by a factor of ffu), f(“’ < l- i.e. there is an actual decrease. From equation (24) we recall thatf’“) will generally be greater thanf sayf’“’ = 0.9, so that the decrease in resistants is comparatively small. The n;merical values we have mentioned illustrate the general trend; generally, a cessation of spraying for one season far from cancels the enhancement in the proportion of resistants that comes about from a single year’s herbicide treatment. In the presence of a seed bank with a reasonable value of E, the approximation equation (15) is still valid for a period after spraying is stopped. But the factor a should be deleted and the untreated fitness used, so that equation ( 16) becomes
That is, there is a “momentum” with a seed bank, and the number of resistants still increases for a fraction of fi years but at the slower rate of a factor of (1 +f(“)/%) per year, not (1 tf/- na ) as was the case with herbicide treatment. 5. Agronomic Implications:
Weeds
From the above we can understand the essential stability achieved in the field. Usually weed populations only decrease during the agronomic season while a herbicide is persistent, but do not decrease over a period of years; the frequency of the resistant genotypes would not noticeably increase over the years. From the data in the literature (cf. review of Gressel, 1979), it can be seen that the only well substantiated deviations from this thesis concern the S-triazine herbicides. The S-triazines are more persistent in the soil than most herbicides; they persist for months to years depending on soil and climate (cf. Libik & Romanowski, 1976, & Burnside & Schultz, 1978) and in maize and nurseries are often applied twice a year (cf. Fryer & Makepeace, 1972). Thus they exert a much higher selection pressure than foliar contact herbicides and herbicides that are rapidly degraded. If our reasons for the paucity of appearance of herbicide resistance are correct, then the original warnings to rotate herbicides should be modified. It is not to be expected that resistance to low selection pressure herbicides will appear and it is questionable whether they will often appear to the few herbicides which apply high selection pressures. From the mathematical interpretation, it is clear that herbicide rotation will not be too helpful in stopping the appearance of herbicide resistance. Whereas resistance increases as a function of selection pressure and fitness, it will decrease at a much slower rate upon removal of the selection pressure (Fig. 8).
LACK
OF
ADAPTIVE
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HERBICIDE
RESISTANCE
367
FIG. 8. The effect of stopping and restarting herbicide treatment. The ratio of resistant seeds deposited in year A to those deposited in reference year 1 (logarithmic scale) is plotted, giving curves similar to Figs. 3-5. Continual herbicide application is shown with fitnesses of 0.8 and 0.6. Other curves show the decline in resistance as expected when treatment is stopped after year 5 and the reappearance of resistance when herbicide treatment is restarted after 1,3 and 5 years after stoppage. These graphs are drawn for the case where 90% of the susceptibles are destroyed by the herbicide and none of the resistants, and where the average seed longevity is five years.
A few things become apparent when Fig. 8 is considered. (1) After stoppage, because of the seed bank, the proportion of resistants may rise for a period after a drop during the first year. (2) Upon reuse of the herbicide, after a year the graph of frequency will again rise parallel to the line denoting continued usage. (3) To an adequate approximation, for each year that a herbicide is not used the appearance of resistance will be delayed for about a year. Thus, if resistance under continued use would appear in 10 years and a herbicide is then used one out of every three years in rotation, resistance would now appear in about 30 years. (3) Once resistance had appeared and treatment with the selecting herbicide stopped, the initial decay in the resistant strain would seem likely to be moderately rapid. Conard & Radosevich (1978) have shown that the triazine resistance found in three species would decrease to 2 % (fi = 1) in 6-9 years when grown with 2% susceptible plants without the presence of herbicide. But this is not decisive, for if herbicide were reintroduced then resistance would rapidly reappear, as now the resistants are starting from a frequency many orders of magnitude higher than one would find in a natural situation. With fitnesses of 0.6-0.8, it would take very long to return to the initial resistance frequency as can be seen from the slope in Fig. 8. This may be part of the reason that resistance to insecticides has not returned to the initial frequency, though genetic reasons have been offered
368
J.
GRESSEL
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A.
SEGEL
for this; i.e. a fitness increase of the resistant strains owing to insect interbreeding (Kelding, 1967). If this happens with plants, it maytake even longer to return to the pretreatment steady-state than shown in Fig. 8. 6. Agronomic Implications:
Crops
The number of selective herbicides available is both finite and small, especially when compared to the number of crops. All too often there is not a good match between a crop, the weeds attacking it, and an economic selective herbicide. For this reason it would be useful to select for herbicide resistant strains in many crops. Differential tolerance to pesticides has been noted in crops (cf. Gressel, 1979) and is often a factor in choosing varieties for use with some herbicides. Karim & Bradshaw (1968) have noted “there is no good reason why the improvement of herbicide resistance of crop plants should not be undertaken”. Because of the slowness imposed by the fitness and selection pressure, one may arrive at different conclusions, With crops the problem of “fitness” should be marginal; crop species have been so heavily selected for, for so long and are thus usually so homozygous that they are already quite naturally “unfit” except in the highly artificial “cultural” environments where they are grown. Herbicide resistance should hardly decrease this lack of fitness in a crop species, in its crop environment. Conversely, the homozygosity of crops may pose a problem if we can extrapolate from insects; there was a relative ineffectiveness of selection for insecticide resistance within inbred lines (cf. Crow, 1960). This would be especially severe when resistance is a multigenic quantitative effect. It is a greater problem to find ways to exert sufficient selection pressure to obtain resistance, and this is probably the reason for the fact that there are no reports of successful selection for herbicide resistance in crops, although there has been a modicum of success in a crop that was already partially tolerant (Faulkner, 1976). It should be easier to select resistance to the more persistent herbicides, but there are pervading agronomic and ecological reasons (described above) not to use this type of compound. Even with high selection pressures, no loss of fitness and no seed bank, it will still take a considerable length of time (Fig. 5) and large populations of plants to test, and large areas in which to grow them. These problems may be obviated by using cell culture techniques as reviewed in Gressel, Zilkah & Ezra 1978 and Gressel, 1979. The first author deeply acknowledges the mentorship of L. G. Holm who 18 years ago described this problem to him. Stimulating discussions or correspondences with J. Antonovics, A. D. Bradshaw, A. Dafni, W. Ewens, E. Galun, S. Kevin and A. Radosevich were quite helpful and encouraging. The second author’s research was supported in part by a grant from the United States-Israel Binational Science Foundation (BSF 5777).
LACK
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HERBICIDE
RESISTANCE
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REFERENCES A. L. (1954). Proc. 1st Weed Control Conf. pp. 249-255. (1967). Report of the First Session of the FAO Working Party of Experts on Resistance of Pests to Pesticides, FAO Public. PL/1965/18, 127 pp. ANON. (1974). Report of the 10th Session of the FAO Working Party of Experts on Pest Resistance to Pesticides, 28 pp.. FAO Public. AGP:1974/M/9, Rome. ANTONOMCS, J. (1971). Amer. Sci. 59, 593. ANTONOVICS, J. & BRADSHAW, A. D. (1970). Heredity 25, 349. ASHTON, F. M. & CRAFIS, A. S. (1973). Mode of Action of Herbicides, 504 pp. New York:
ABEL, ANON.
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APPENDIX
Following a suggestion by S. Rubinow we outline here an approach to our problem that makes somewhat different and probably more realistic assumptions about the seed bank. An advantage of this approach is that depletion of the seed bank by germination is easily accounted for. When this effect is not important, however, the results will be seen to be virtually equivalent to those obtained with our principal model-which testifies to the robustness of our conclusions. Let GLR)(Gis)) be the number of viable resistant (susceptible) seeds that are found in a unit area at the beginning of the nth season. The germination probabilities IJ,, and pn are now given by g = G’S’/[G’S’ + xG’~‘]
p,, = xG:~)/[G$~‘+xG:~)].
(Al)
[Equation (Al)“replaLs Eiuation;b):] In considering how GkR’ changes, we subtract the number of seeds that germinate at the beginning of the nth season, subtract a portion dR of the remaining seeds that lose their viability during this season, and add the resistant seeds that are deposited at the end of the season. This gives G$,
= GcR)Np, - 6, (GiR’ - NpJ + NiR’. n
WI
The present model is completed with an analogous equation for G$ 1, plus equations (1 la) and (11 b) as before. Let us immediately make two simplifying assumptions, that the resistant population is small compared to the susceptible, and (for the moment) that germination can be neglected in monitoring the seed bank. These assumptions imply that equations (Al) and (A2) can be simplified to cTn= 1,
pn = xG;~)/G’~’n 7
G;$
= GiR’ (1 - 6,) + NiR).
(A3a,b,c)
We expect G,(‘) to maintain a constant value, which we denote by G. By the analog of equation (A3c) we find that G(‘) n = G where
G = Na&6,.
Thus p n = xG’~‘/G. n
644)
LACK
OF
ADAPTIVE
GENETIC
HERBICID’E
RESISTANCE
371
Combining equation (A4) with equation (1 lb) we obtain G$r = AGiRP’+B or alternatively, NLt), = A NiR’+B 6,, (A% b) where A = I-6,+@f6,, B = N CL&us, We wish to compare equation (A5b) with the corresponding equation (16) obtained in our previous model. But equation (16) was made under the assumption that uf was rather large compared to unity. Making the corresponding assumption here we find that in the present case the number of resistant seeds deposited, NiR’, grows by an annual factor of 1 +ccf6,. In the earlier model the corresponding factor was 1 +olf/ii. These results are the same if E = 6,-l, but this is just the relationship mandated by the equation displayed after equation (4). We conclude that when the resistant population is growing rather rapidly and when germination may be neglected in tallying changes in the seed bank, then it makes virtually no difference whether one asumes (i) that each seed remains viable for e years, or (ii) that each year a fraction of seeds in the bank dies at a rate which gives an average seed lifetime of fi years. Under other circumstances there are differences. When germination is not neglected, appropriate alterations in our calculations lead to a final result of the same form as equation (A5) but with different constants. In particular when all terms are retained the growth rate A is given by A = (l-6,) (1 -N xG- ‘)+ N xG-‘$,u, where now G = 6,’ [Na,&-1+&i.