- Email: [email protected]
Stability of a two-locus ‘coacting’ cline in Silene latifolia: A model study
0305-1975/57 $3.00+0.00 0 1987 PergamonJournals Ltd.
Biohtii Systematicsand Ecology,Vol. 15, No. 2, pp. 217-224.1987. Printed in Great Britain.
Stability of a Two-locus ‘Coacting’ Cline in S/‘lene lathbha: A Model Study JAAP HERINGA*t, PAULINE HOGEWEGt and JAN VAN BREDERODE* *Population and Evolutionary Biology, Section Genome Evolution, Padualaan 8, 3584 CH Utrecht, Netherlands;
tBioinformatics Group, Padualaan 8, 3584 CH Utrecht, Netherlands
Index-Silene lattiiia; S. alba; S. pratensis; Cwyvphyllaceae; geographic variation; two-locus cline; F2 hybrid selection; flavone glycosylationgenes; coacting loci; chemical races, model study. Key Word
Abstract-A gene oriented model was used to study a transition zone between two chemical races of Silene lathMa in western Europe, in which a two-locus cline of ‘coacting’ flavone glycosylation loci occurs: i.e. each locus contributes to this glycosylation. In the F2 generation of crosses between these two chemical races, each homozygous dominant for one of these loci, plants arise which are homozygous recessive for both of these loci. These plants are inactive in flavone glycosylation and hence have a reduced fitness. We show that this F2 hybrid unfitness, unlike a single locus Fl hybrid unfitness, is not able to generate a stable cline. Adding a very small selection against the recombinant which is homozygous dominant on both loci, however, gives rise to stability. Biological implicationsare discussed.
Introduction The geographical distribution of the white campion, Silene latifoiia (- Silene alba, Melandrium album), has thoroughly been studied using pattern recognition techniques on a number of character sets. Mastenbroek [l] and Mastenbroek et al. [2] described the broad scale congruence between the geographical trends in flavone glycosylating genes, seed morphology, pollen morphology and capsule morphology. In this paper we re-examine the flavone glycosylation genes distribution which was reported by him [2-51 using data of 384 European populations of S. btWia. The flavone glycosylation complex is governed by three independent loci g, gland fg in Silene /atirMa [6-8]. Three alleles have been observed for both the g and the gf locus, while two alleles have been found for the third locus [email protected] alleles gG and gX control the binding of glucose and xylose respectively to the free 7-OH group of the basic flavone isovitexin (B-Cglucosylapigenin). The alleles g/R and gkl, of the g/ locus, control the binding of rhamnose and arabinose respectively to the free 2”-OH group of isovitexin. The dominant allele Fg of (Rer&mi
16 April 1888)
the fg locus takes care of the binding of glucose to the 2”-OH group. The recessive genes, g, gl and fg, are inactive in binding. The presence of the genes gX, gA and Fg, which all have low frequencies in most European populations, is most probably the result of introgression with Silene dioica. These genes will not be considered in this paper. Mastenbroek et al. 131 distinguished three different geographical races of European S. IattYolia on the basis of flavone-glycosylation gene frequencies. The first race contains the populations in western and southern Europe with frequencies of value 1.0 for gG and g/ The frequencies of g and g/R are high in the second race present in central Europe, whereas the third chemical race which can be found in the USSR, Scandinavia and eastern Poland has very high frequencies of both gGand SIR. A narrow transition zone, located in the Netherlands, ‘Belgium and parts of western Germany occurs between race-l and race-2. In this zone a cline formed by the two loci g and g/ each with two alleles can be distinguished with high frequencies of gG and g! west of this zone and high frequencies of g and g/R east of it No sharp transition zones exist in eastern Europe between race-2 and race-3.
217
218
Mastenbroek [l, 91 presented a possible scenario for the present-day distribution of S. latifolia, which is, being a weed, closely associated to agriculture [IO]. Agricultural history documents an eastern and western route of spread over Europe which resulted in migration of the plant along these same lines. The transition zones should therefore be interpreted as a result of secondary intergradation [II] of the main races. Contact should have started about 5000 years ago. The maintenance of the distribution does not seem to coincide with environmental gradients, as Mastenbroek et a/. [5] could not find a concordant pattern in climate or soil differences. In the centre of the western European transition zone, an overrepresentation of homozygous dominant plants for the two loci occurs. Also homozygous recessive plants for both loci can be observed in this area. Of this last type of plants it is known that they are weak and have a damaged petal upper epidermis which prevents normal flower opening and therefore successful pollination [6, 121. In all other genotypes a normal formed epidermis has been observed. In this paper we investigate whether a model based upon selection against the herefore mentioned homozygous recessive plants, arising in the F2 generation of crosses between the two races, can explain the occurrence of the narrow transition zone in western Europe. The theory of clines maintained by a balance between dispersal and selection has received much attention. Endler [II] summarised the types of selection that can affect clines. Environmental selection, for instance, can lead to sympatrical divergence of populations, while hybrid selection can give rise to a stable cline of formerly diverged populations, even if the environmental selection gradient is lost in time. As has been mentioned already, environmental gradients (or steps) could not be detected in the transition zones of the S. latifolia populations. Therefore, hybrid selection seems to be involved in the maintenance of the western European two-locus cline. Although a vast majority of cline theory deals with one-locus clines, work has been done as well on the theory of clines in which more than one locus is involved. Slatkin [I31 treated two-
JAAP
HERINGA,
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
locus clines and studied the effect of linkage disequilibrium, which usually steepens a cline. Barton [14] generalised the theory to systems involving any number of loci. He showed that cline width is greatly reduced when more loci are involved. The situation in S latifolia departs from these studies in two ways: (a) selection does not act on each locus separately, but acts only on a combination of the alleles of the loci involved which we therefore call ‘coacting loci’; and (b) the loci segregate independently.
The Model The gene-oriented model implements selection against certain recombinants in a number of demes, between which migration is described by a stepping stone model [15]. Populations perform logistic growth in order to keep population size under control. The model is set up using BIOSIM [16]. The spatial distribution of the demes can be implemented in BIOSIM by defining a rectangular or hexagonal array, in which the definitions of the model with its variables and parameters is strictly local to each gridcell. A gridcell will be considered as a deme in which no spatial variation occurs. In every deme the parameters can be set independently. Immigration and emigration of a deme only takes place between adjacent demes. In the model we consider a deme to be a gene pool of the various alleles. The various recombinants can be calculated as products of frequencies of the composing alleles: the loci are completely independent of each other [7]. The model is outlined in Table 1. The number of homozygous recessive plants for the two loci (variable: SELRES) containing only gRES and SIRES alleles, has a negative effect on the gRES and gIRES pools because these plants have reduced fitness, as has been mentioned already. The numbers of gRES and g/RES alleles which are selected against, are subtracted from the gRES and g/RES allele pools. Also the number of homozygous dominant plants for both loci (variable: SELDOM) is implemented in the model as selectable, for reasons which will be shown later. As mentioned above S. latifolia is an annual weed. Therefore, a timestep in the model maps to a year or a generation. In the difference
STABILITY
OF A TWO-LOCUS
COACTING
219
CLINE IN SILENE LATIFOLIA
TABLE 1. GENE MODEL Number
-
(gDOM + gRES + glDOM
NN
-
max (ZERO, NUMBER)
SELRES
- SRES*
(gRES/
SELDOM
-
SDOM
* (gDOM/
d(gDOW
-
R * (gDOM
d(gRES)
- R * (gRES -
-
d(g/DOrW
-
R * (g/DO,%4 -
-
R * (SIRES -
gDOMFR0
= gDOM 1 NN
g/DOMFRO
= glDOM
emi
-u*x = (U /A)
imm(X) hexagonal
-
square grid
grid: A -
:A
-
SELDOM)
* (1 -
SELDOM)
NUMBER
NUMBER
* (1 -
SELRES) * (1 -
* NN
NN)**2
I K) -
NUMBER
NUMBER
* NN
/ K) -
emi(gD0M)
/ K) -
emi(glDDM)
emi(glRES1
sum of six neighbours sum of four neighbours
+ imm(glDOM)
+ imm(glRES1
~ gDOM gRES -
glWM
~ SIRES
: total number of alleles : number of homozygous recessive plants : number of homozygous dominant plants : number of gDOM, ., glRES alleles
SELDOM glRES
SRES
= [0.02. 0.51
(1): selection
SDOM
-
[O.O. 0.01)
(1): selection value against homozygous
U
-
[O.c4, 0.201
(1): dispersion
value against homozygous
R
-
2.0
: intrinsic
= 200
(2): carrying
ZERO
-
(2): lowest value of NUMBER
0.000001
recessive plants dominant
plants
value
K
(2): parameters
-
* NEIGHBOURS
4, NEIGHBOURS(X):
(1): range of parameters
+ imm(gDOM1
emi(gRES1 + imm(gRES)
/ KI -
6, NEIGHBOURS(X):
SELRES
gRES, glDOM,
NN)**2
* (glDOM/
/ NN
NUMBER
gDOM,
* (g/RE.S/
NN)**2
SELRES) * (1 -
d(glRES)
-
NN)**2
+ gIRE.9 I2
growth-rate capacity (to avoid zerodivide)
tested
kept at listed value
equations the annuality is expressed by old portion of alleles subtracting the independent of the growth term. A linear array of 12 demes (echoing at the boundaries) was used. Each deme has dynamics as described in the model (Table I), and is initialised with 100 plants. The first six demes were initialised.with race-l plants (gDOM = 200, gRES = 0, glDOM = 0, gIRES = 200), while the last six demes started with race-2 plants (gDOM = 0, gRES - 200, glDOM = 200, g/RES = 0). Thus, initially, in every deme the allele pool contained 400 alleles. Model Behaviour Selection Against Homozygous Recessive Plants
In Fig. l(a) are depicted cumulatively the clines of the gGfrequency and the glRfrequency after 2000 generations under selection of value 0.5 against homozygous recessive plants which occur in the F2 generation of crosses between the two chemical races. The figure shows an overrepresentation of active alleles in the centre of the clines. This finding is in agreement with the results of Mastenbroek et al. [4], who also
found an overrepresentation of active alleles in the centre of the clines. However, after 5500 generations the cline has been wiped out entirely: fixation of the active alleles (at gDOMFRQ - 0.95 and giDOMFRQ = 0.95) in the entire area has been reached. This is because the active alleles are not inhibited in any way to spread throughout the area, i.e. these alleles never pass through stages of negative selection. Note that in a single cline all alleles pass through such a stage (as hybrids). We conclude that selection on homozygous recessive plants only is not adequate for the formation of a stable 2-10~~s cline and therefore does not contribute to the maintenance of the distribution of race-l and race-2. The cline is not stable because the active genes are not constrained in any way. Therefore they are initially overrepresented in the centre but finally spread throughout the area. Selection Against Homozygous Homozygous Dominant Plants
Recessive
and
Selection against recessive hybrids is not a sufficient condition to get stability in this two-
220
JAAP
HERINGA,
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
I_/
(b)
lcl
(d)
l--rI
FIG. 1. CUMULATIVE 1); lb) SRES -
1
DIAGRAM
0.5; SDOM
-
OF THE gDOM-FREQUENCY 0.01; (c) SRES -
0.5;
SDOM
-
(DARK) AND THE g/DO&+FREQUENCY -
0.001;
(d) SRES -
locus coactjng cline situation. In a one-locus cline a hybrid always contains two different atleles of the locus under consideration, and selection against such hybrids leads to the loss of both of these two different alleles. Therefore, hybrid selection in a one-locus case (with two
0.1; SDOM
-
(LIGHT)
(a) SRES = 0 5 SDOM
= 0 0 (see Table
0.01.
different alleles) always results in forces on both alleles pools. In hybrids situation, however, homozygous for both loci can selection against such hybrids asymmetrical forces on each
symmetrical a two-locus which are arise, and results in locus. The
STABILITY OF A TWO-LOCUS COACTING CLINE IN SILENELATIFOLIA
stabilizing effect of hybrid selection in a single locus can therefore be lost in a two-locus cline situation. When we subject heterozygous and homozygous dominant plants for both loci to selection, stability is reached with even very small selection values against these dominant plants. In this ease, almost all hybrids are subjected to selection, except for the ‘homozygous and heterozygous’ race-l and race-2 plants, and selection is not restricted to F2 offspring anymore. This reduces the problem to a one-locus situation, because the constraints for stability in such a situation are met. Selecting only against homozygous dominant plants and homozygous recessive plants is therefore a more minimal assumption. Figure l(b) represents the result for a selection of value 0.5 against homozygous recessive plants and a selection of value 0.01 against homozygous dominant plants. With these selection values, the model iterated to a stable equilibrium after about 2200 generations. Figure l(b) shows that overrepresentation of active genes remains a feature of the centre of the transition zone. As the initial populations (i.e. the races 1 and 2) have been founded about 5000 years ago in western Europe, this stable two-locus cline will probably have been reached already. Even smaller amounts of selection on homozygous dominant plants give rise to stability. Figure l(c) shows the clines cumulatively for selection of value 0.5 on homozygous recessive plants, and 0.001 on homozygous dominant plants. In this case, however, the overrepresentation of dominant alleles is more spread over the entire cline and the lower tails of the clines are lifted substantially. The selection against homozygous recessive plants seems to be rather strong in nature, but is not known quantitatively [Mastenbroek, personal communication]. Therefore, we tested also a lower selection value of 0.1 against homozygous recessive plants, keeping selection against homozygous dominant plants at value 0.01. This is depicted in Fig. l(d). It can be noticed that the clines become steeper with greater selection values on homozygous recessive plants, and the ranges of the gene frequencies (i.e. the differences between the
221
highest and lowest points of the clines) become larger. Moreover, the overrepresentation of dominant alleles in the cline centre becomes more pronounced when higher selection values are used. The amount of dispersion of p = 0.01 (to each neighbour) seems to be reasonable, if we look at the distances of the investigated populations in Mastenbroek et alf-[4] and the dispersion ability of Silene latifolia,which seems to be rather weak [Mastenbroek, personal communication]. The threshold for stability is about u = 0.05 (to each neighbour): higher values give fading clines. Boundary Elects As has been mentioned earlier, the demes are echoed at the boundaries. Therefore, the most left and most right deme only get input from their right and left neighbour respectively. These border demes can only reach stability if the selective forces match the one-sided dispersion. Because of this, the gene frequencies in these demes cannot deviate much from their neighbour, as can occur in demes with twosided dispersion (e.g. in the cline centre). As a result of this boundary effect the higher tail of a cline tends to go down, whereas the lower end is lifted. These abberations become more pronounced when greater dispersion values are used. So, we used the most disadvantageous condition for clines to maintain their range. This is illustrated in Fig. 2, where the cline of Fig. 1(b) is set out against a cline, generated by the same model implemented in an array containing 24 demes (the g/DOM cline has been left out of this figure for reasons of clarity). Notice that the cline range becomes larger in the longer array. However, the maximal slope in the cline centre is not, affected. Thus, if we measure cline width by calculating the inverse of the maximal slope, as is often done, this width is not affected by boundary effects. Density Gradients Mastenbroek et al. [4] showed that the distribution of race-l is more widespread than is the distribution of race-2. This is reflected in the transition zone between these two races, where the gG allele (gDOM in the model) has spread more in eastern direction than has the g/R allele (g/DOM in the model) in western direction. In
JAAP
222
FIG
2. BOUNDARY
simulations1
EFFECT. The gOOM-frequencies
are depicted
for an array of 24 demes
(light). In the first and last six demes the gOOM-frequencies
deme has two bars (a dark and a light one). The g/OOMcline
are not defined
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
(dark) and an array of 12 demes
for the 12 demes
simulation.
(as I” the other
In the 12 central demes:
We simulated this in the model by incorporating a carrying capacity gradient: population density descending linearly from west to east. Figure 3 presents the result for K-values from 244 in the west to 200 in the east with a step of four per deme. The selection values used were 0.5 against homozygous recessive plants for both loci, and 0.01 against homozygous dominant plants for both loci. The clines have moved in eastern direction, which makes that the gGallele b)
(al
GRADIENT.
Cumulative
diagram
of the gOOM- and the g/OOM-frequencies.
K-values
(see Table 1) from left to right: 244; 240; 236;
232; 228; 224; 220; 216; 212; 208; 204; 200. SRES -
one
has been left out for reasons of clarity.
fact, few populations of race-2 in central Europe are of the proper race-2 type, i.e. with g/R frequency = 1.0 and gGfrequency = 0.0. In most of these race-2 populations the gG frequency has values up to 0.20. If we consider history, we see that deforestation has proceeded from western Europe in eastern direction. As Sdene pratensis is restricted to open land, the number of populations should have decreased from west to east.
FIG. 3. DENSITY
HERINGA,
0.5; SDOM
-
0.01. (a) gOOM-frequencies
dark; g/OOA+frequencies
light; (b) g/OOM-frequencies
dark; gOOM-frequencies
light
223
STABILITY OF A TWO-LOCUS COACTING CUNE IN SlLENELATlFOLlA
has penetrated more in the east than has the g/R allele in the west; the gG frequency is raised substantially in the eastern demes. Second Generation Effect In concordance with the finding that selection on homozygous recessive F2 recombinants only is not a sufficient condition for stability of our twolocus cline, we studied second generation effects by using an individual oriented model. In this model, homozygous recombinants for both loci occur in the second generation at first. This is not the case in the gene model. However, the effects of this delay in hybrid formation are negligible: the individual-oriented model generates almost exactly the same clines as the gene frequency model for the same parameters.
Discussion Implications of Model Results for the Evolution of the Silene latifolia Distribution Over Europe In a two-locus situation, clines formed under selection against homozygous recessive plants only, are not stable and gradually smooth out (Fig. la). If the effective dispersion of Silene populations in the empirical world is lower than the dispersion rate used in the model, the argument that the observed two locus cline is just a stage in the process of fading out, cannot be excluded. To get an impression of the timescale, one may look at the eastern Europe transition zone between race-2 (gDOMFR0 = 0, gIDOMFR0 = 1) and race-3 (gDOMFRQ = 1, glDOMFRQ = 1). Recombinants, homozygous for the recessive alleles cannot occur in this area, as all plants possess at least the active gene g/DOM. In fact, in this case we are dealing with a single-locus cline (of the g locus) which will fade out unhampered by selection. The model showed that the rate of fading out of a two-locus cline under selection against homozygous recessive recombinants for both loci hardly deviates from this rate under neutral selection. The eastern transition zone, however, is much broader than the western transition zone (see ref. [41, fig. 5). So, either the time of formation differed appreciably between the two clines, or in the western cline stabilizing
selection has taken observed steepness.
place
to
maintain
the
Stability of Flavone-glycosylationGenes Distributionand Other Characters The large-scale congruence between the flavone-glycosylation genes distribution and the distribution of other character sets of Silene /atifi$ia is explained by sampling drift and migration in Mastenbroek [l]. Therefore, genetic linkage between these character distributions is not needed. However, if the flavone-glycosylation genes distribution is maintained by hybrid selection and the other characters are selectively neutral, stability of these other character distributions can only occur when the genes coding for these characters are affected by the flavone-glycosylation barriers. Barton and Hewitt [17] stated that neutral loci can be considerably impeded by strong hybrid zones. This appeared not to be the case in our two-locus cline, in which no selection against Fl hybrids takes place. A third unlinked neutral locus incorporated in the gene model with selection value 0.5 on homozygous recessive plants and a selection value of 0.01 on homozygous dominant plants turned out to spread as easily as does a neutral locus in the absence of a hybrid zone of other loci. So, it seems that the distribution of other character sets cannot be stabilized by the stable barrier of flavone glycosylation genes. Conclusions (a) Selection against recombinants lacking dominant flavone-glycosylation alleles which have known decreased fertility cannot explain the formation of a stable two-locus coacting cline. (b) Adding a very small selection (of value 0.01 or smaller) against homozygous plants for both loci gives rise to a stable two-locus coacting cline. (c) This cline has an overrepresentation in its centre of dominant flavone-glycosylation genes, which is also observed in nature [4]. (d) Stability and the mentioned overrepresentation of dominant alleles is preserved for a wide range of selection values used. (e) The observed small area of race-2 can be a result of deforestation in the past: implementing
JAAP
224
a density gradient in the modet leads to the penetration of gG alleles in race-2 which can be observed in the flavone-glycosylation data [I, 91.
Acknowledgement-We thank Dr. 0. Mastenbroek an early stage of this research.
for
his
supportat
References 1. Mastenbroek, 0. (1983) Patterns of variation in European Silene pratensis. Thesis, R. U. Utrecht. 2. Mastenbroek, O., Prentice, H. C., Heringa, J. and Hogeweg, P. (1984) Plant Sysf. Evol. 145, 227. 3. Mastenbroek, O., Maas, J. W., Brederode, J. van, Niemann, G. J. and Nigtevecht, G. van (1982) Genetica 59, 139. 4. Mastenbroek, O., Hogeweg, P., Brederode, J. van and Nigtevecht, G. van (1983) Biochem. Sysf. Ecol. 11, 91. 5. Mastenbroek, O., Prentice, H. C., Kamps-Heinsbroek, R., Brederode, J. van, Niemann, G. J. and Nigtevecht, G. van (1983) Plant Syst. Evol. 141, 257.
HERINGA,
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
6. Brederode, J. van and Nigtevecht, G. van (1972) Molec. Gen. Genet. 118, 247. 7. Brederode, J. van and Nigtevecht, G. van (1975) Theor. Appl. Genet. 48, 353. 8. Besson, E., Besset, A., Bouillant, M. L., Chopin, J., Brederode, J. van and Nigtevecht, G. van (1979) Phy?ochemistry 18,657. 9. Mastenbroek, 0. and Brederode, J. van (1985) Biochem. Syst. Ecol. 14, 165. 10. Suominen, J. (1979) Acta Bot Fenn. II, 1. 11. Endler, J. A. (1977) Geographic Variation, Speciation and Clines. Princeton University Press, Princeton, NJ. 12. Brederode, J. van, Genderen, H. H. van and Berendsen, W. (1982) Experientia 38, 929. 13. Slatkin, M. (1975) Genetics 81, 787. 14. Barton, N. H. (1983) Evolution 37,454. 15. Kimura, M. (1953) Ann. Rept. Nat Inst. GeneticsJapan 3,62. 16. Hogeweg, P. and Hesper, B. (1984) UKSC-84 Conference on Computer Simulation, p. 102, Butterworths, London. 17. Barton, N. H. and Hewitt, G. M. (1981) in Evolution and Speciation (Atchley, W. R. and Woodruff, D. S., eds), pp. 109-145. Essays in honor of M. J. D. White. Cambridge University Press, London.
Biohtii Systematicsand Ecology,Vol. 15, No. 2, pp. 217-224.1987. Printed in Great Britain.
Stability of a Two-locus ‘Coacting’ Cline in S/‘lene lathbha: A Model Study JAAP HERINGA*t, PAULINE HOGEWEGt and JAN VAN BREDERODE* *Population and Evolutionary Biology, Section Genome Evolution, Padualaan 8, 3584 CH Utrecht, Netherlands;
tBioinformatics Group, Padualaan 8, 3584 CH Utrecht, Netherlands
Index-Silene lattiiia; S. alba; S. pratensis; Cwyvphyllaceae; geographic variation; two-locus cline; F2 hybrid selection; flavone glycosylationgenes; coacting loci; chemical races, model study. Key Word
Abstract-A gene oriented model was used to study a transition zone between two chemical races of Silene lathMa in western Europe, in which a two-locus cline of ‘coacting’ flavone glycosylation loci occurs: i.e. each locus contributes to this glycosylation. In the F2 generation of crosses between these two chemical races, each homozygous dominant for one of these loci, plants arise which are homozygous recessive for both of these loci. These plants are inactive in flavone glycosylation and hence have a reduced fitness. We show that this F2 hybrid unfitness, unlike a single locus Fl hybrid unfitness, is not able to generate a stable cline. Adding a very small selection against the recombinant which is homozygous dominant on both loci, however, gives rise to stability. Biological implicationsare discussed.
Introduction The geographical distribution of the white campion, Silene latifoiia (- Silene alba, Melandrium album), has thoroughly been studied using pattern recognition techniques on a number of character sets. Mastenbroek [l] and Mastenbroek et al. [2] described the broad scale congruence between the geographical trends in flavone glycosylating genes, seed morphology, pollen morphology and capsule morphology. In this paper we re-examine the flavone glycosylation genes distribution which was reported by him [2-51 using data of 384 European populations of S. btWia. The flavone glycosylation complex is governed by three independent loci g, gland fg in Silene /atirMa [6-8]. Three alleles have been observed for both the g and the gf locus, while two alleles have been found for the third locus [email protected] alleles gG and gX control the binding of glucose and xylose respectively to the free 7-OH group of the basic flavone isovitexin (B-Cglucosylapigenin). The alleles g/R and gkl, of the g/ locus, control the binding of rhamnose and arabinose respectively to the free 2”-OH group of isovitexin. The dominant allele Fg of (Rer&mi
16 April 1888)
the fg locus takes care of the binding of glucose to the 2”-OH group. The recessive genes, g, gl and fg, are inactive in binding. The presence of the genes gX, gA and Fg, which all have low frequencies in most European populations, is most probably the result of introgression with Silene dioica. These genes will not be considered in this paper. Mastenbroek et al. 131 distinguished three different geographical races of European S. IattYolia on the basis of flavone-glycosylation gene frequencies. The first race contains the populations in western and southern Europe with frequencies of value 1.0 for gG and g/ The frequencies of g and g/R are high in the second race present in central Europe, whereas the third chemical race which can be found in the USSR, Scandinavia and eastern Poland has very high frequencies of both gGand SIR. A narrow transition zone, located in the Netherlands, ‘Belgium and parts of western Germany occurs between race-l and race-2. In this zone a cline formed by the two loci g and g/ each with two alleles can be distinguished with high frequencies of gG and g! west of this zone and high frequencies of g and g/R east of it No sharp transition zones exist in eastern Europe between race-2 and race-3.
217
218
Mastenbroek [l, 91 presented a possible scenario for the present-day distribution of S. latifolia, which is, being a weed, closely associated to agriculture [IO]. Agricultural history documents an eastern and western route of spread over Europe which resulted in migration of the plant along these same lines. The transition zones should therefore be interpreted as a result of secondary intergradation [II] of the main races. Contact should have started about 5000 years ago. The maintenance of the distribution does not seem to coincide with environmental gradients, as Mastenbroek et a/. [5] could not find a concordant pattern in climate or soil differences. In the centre of the western European transition zone, an overrepresentation of homozygous dominant plants for the two loci occurs. Also homozygous recessive plants for both loci can be observed in this area. Of this last type of plants it is known that they are weak and have a damaged petal upper epidermis which prevents normal flower opening and therefore successful pollination [6, 121. In all other genotypes a normal formed epidermis has been observed. In this paper we investigate whether a model based upon selection against the herefore mentioned homozygous recessive plants, arising in the F2 generation of crosses between the two races, can explain the occurrence of the narrow transition zone in western Europe. The theory of clines maintained by a balance between dispersal and selection has received much attention. Endler [II] summarised the types of selection that can affect clines. Environmental selection, for instance, can lead to sympatrical divergence of populations, while hybrid selection can give rise to a stable cline of formerly diverged populations, even if the environmental selection gradient is lost in time. As has been mentioned already, environmental gradients (or steps) could not be detected in the transition zones of the S. latifolia populations. Therefore, hybrid selection seems to be involved in the maintenance of the western European two-locus cline. Although a vast majority of cline theory deals with one-locus clines, work has been done as well on the theory of clines in which more than one locus is involved. Slatkin [I31 treated two-
JAAP
HERINGA,
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
locus clines and studied the effect of linkage disequilibrium, which usually steepens a cline. Barton [14] generalised the theory to systems involving any number of loci. He showed that cline width is greatly reduced when more loci are involved. The situation in S latifolia departs from these studies in two ways: (a) selection does not act on each locus separately, but acts only on a combination of the alleles of the loci involved which we therefore call ‘coacting loci’; and (b) the loci segregate independently.
The Model The gene-oriented model implements selection against certain recombinants in a number of demes, between which migration is described by a stepping stone model [15]. Populations perform logistic growth in order to keep population size under control. The model is set up using BIOSIM [16]. The spatial distribution of the demes can be implemented in BIOSIM by defining a rectangular or hexagonal array, in which the definitions of the model with its variables and parameters is strictly local to each gridcell. A gridcell will be considered as a deme in which no spatial variation occurs. In every deme the parameters can be set independently. Immigration and emigration of a deme only takes place between adjacent demes. In the model we consider a deme to be a gene pool of the various alleles. The various recombinants can be calculated as products of frequencies of the composing alleles: the loci are completely independent of each other [7]. The model is outlined in Table 1. The number of homozygous recessive plants for the two loci (variable: SELRES) containing only gRES and SIRES alleles, has a negative effect on the gRES and gIRES pools because these plants have reduced fitness, as has been mentioned already. The numbers of gRES and g/RES alleles which are selected against, are subtracted from the gRES and g/RES allele pools. Also the number of homozygous dominant plants for both loci (variable: SELDOM) is implemented in the model as selectable, for reasons which will be shown later. As mentioned above S. latifolia is an annual weed. Therefore, a timestep in the model maps to a year or a generation. In the difference
STABILITY
OF A TWO-LOCUS
COACTING
219
CLINE IN SILENE LATIFOLIA
TABLE 1. GENE MODEL Number
-
(gDOM + gRES + glDOM
NN
-
max (ZERO, NUMBER)
SELRES
- SRES*
(gRES/
SELDOM
-
SDOM
* (gDOM/
d(gDOW
-
R * (gDOM
d(gRES)
- R * (gRES -
-
d(g/DOrW
-
R * (g/DO,%4 -
-
R * (SIRES -
gDOMFR0
= gDOM 1 NN
g/DOMFRO
= glDOM
emi
-u*x = (U /A)
imm(X) hexagonal
-
square grid
grid: A -
:A
-
SELDOM)
* (1 -
SELDOM)
NUMBER
NUMBER
* (1 -
SELRES) * (1 -
* NN
NN)**2
I K) -
NUMBER
NUMBER
* NN
/ K) -
emi(gD0M)
/ K) -
emi(glDDM)
emi(glRES1
sum of six neighbours sum of four neighbours
+ imm(glDOM)
+ imm(glRES1
~ gDOM gRES -
glWM
~ SIRES
: total number of alleles : number of homozygous recessive plants : number of homozygous dominant plants : number of gDOM, ., glRES alleles
SELDOM glRES
SRES
= [0.02. 0.51
(1): selection
SDOM
-
[O.O. 0.01)
(1): selection value against homozygous
U
-
[O.c4, 0.201
(1): dispersion
value against homozygous
R
-
2.0
: intrinsic
= 200
(2): carrying
ZERO
-
(2): lowest value of NUMBER
0.000001
recessive plants dominant
plants
value
K
(2): parameters
-
* NEIGHBOURS
4, NEIGHBOURS(X):
(1): range of parameters
+ imm(gDOM1
emi(gRES1 + imm(gRES)
/ KI -
6, NEIGHBOURS(X):
SELRES
gRES, glDOM,
NN)**2
* (glDOM/
/ NN
NUMBER
gDOM,
* (g/RE.S/
NN)**2
SELRES) * (1 -
d(glRES)
-
NN)**2
+ gIRE.9 I2
growth-rate capacity (to avoid zerodivide)
tested
kept at listed value
equations the annuality is expressed by old portion of alleles subtracting the independent of the growth term. A linear array of 12 demes (echoing at the boundaries) was used. Each deme has dynamics as described in the model (Table I), and is initialised with 100 plants. The first six demes were initialised.with race-l plants (gDOM = 200, gRES = 0, glDOM = 0, gIRES = 200), while the last six demes started with race-2 plants (gDOM = 0, gRES - 200, glDOM = 200, g/RES = 0). Thus, initially, in every deme the allele pool contained 400 alleles. Model Behaviour Selection Against Homozygous Recessive Plants
In Fig. l(a) are depicted cumulatively the clines of the gGfrequency and the glRfrequency after 2000 generations under selection of value 0.5 against homozygous recessive plants which occur in the F2 generation of crosses between the two chemical races. The figure shows an overrepresentation of active alleles in the centre of the clines. This finding is in agreement with the results of Mastenbroek et al. [4], who also
found an overrepresentation of active alleles in the centre of the clines. However, after 5500 generations the cline has been wiped out entirely: fixation of the active alleles (at gDOMFRQ - 0.95 and giDOMFRQ = 0.95) in the entire area has been reached. This is because the active alleles are not inhibited in any way to spread throughout the area, i.e. these alleles never pass through stages of negative selection. Note that in a single cline all alleles pass through such a stage (as hybrids). We conclude that selection on homozygous recessive plants only is not adequate for the formation of a stable 2-10~~s cline and therefore does not contribute to the maintenance of the distribution of race-l and race-2. The cline is not stable because the active genes are not constrained in any way. Therefore they are initially overrepresented in the centre but finally spread throughout the area. Selection Against Homozygous Homozygous Dominant Plants
Recessive
and
Selection against recessive hybrids is not a sufficient condition to get stability in this two-
220
JAAP
HERINGA,
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
I_/
(b)
lcl
(d)
l--rI
FIG. 1. CUMULATIVE 1); lb) SRES -
1
DIAGRAM
0.5; SDOM
-
OF THE gDOM-FREQUENCY 0.01; (c) SRES -
0.5;
SDOM
-
(DARK) AND THE g/DO&+FREQUENCY -
0.001;
(d) SRES -
locus coactjng cline situation. In a one-locus cline a hybrid always contains two different atleles of the locus under consideration, and selection against such hybrids leads to the loss of both of these two different alleles. Therefore, hybrid selection in a one-locus case (with two
0.1; SDOM
-
(LIGHT)
(a) SRES = 0 5 SDOM
= 0 0 (see Table
0.01.
different alleles) always results in forces on both alleles pools. In hybrids situation, however, homozygous for both loci can selection against such hybrids asymmetrical forces on each
symmetrical a two-locus which are arise, and results in locus. The
STABILITY OF A TWO-LOCUS COACTING CLINE IN SILENELATIFOLIA
stabilizing effect of hybrid selection in a single locus can therefore be lost in a two-locus cline situation. When we subject heterozygous and homozygous dominant plants for both loci to selection, stability is reached with even very small selection values against these dominant plants. In this ease, almost all hybrids are subjected to selection, except for the ‘homozygous and heterozygous’ race-l and race-2 plants, and selection is not restricted to F2 offspring anymore. This reduces the problem to a one-locus situation, because the constraints for stability in such a situation are met. Selecting only against homozygous dominant plants and homozygous recessive plants is therefore a more minimal assumption. Figure l(b) represents the result for a selection of value 0.5 against homozygous recessive plants and a selection of value 0.01 against homozygous dominant plants. With these selection values, the model iterated to a stable equilibrium after about 2200 generations. Figure l(b) shows that overrepresentation of active genes remains a feature of the centre of the transition zone. As the initial populations (i.e. the races 1 and 2) have been founded about 5000 years ago in western Europe, this stable two-locus cline will probably have been reached already. Even smaller amounts of selection on homozygous dominant plants give rise to stability. Figure l(c) shows the clines cumulatively for selection of value 0.5 on homozygous recessive plants, and 0.001 on homozygous dominant plants. In this case, however, the overrepresentation of dominant alleles is more spread over the entire cline and the lower tails of the clines are lifted substantially. The selection against homozygous recessive plants seems to be rather strong in nature, but is not known quantitatively [Mastenbroek, personal communication]. Therefore, we tested also a lower selection value of 0.1 against homozygous recessive plants, keeping selection against homozygous dominant plants at value 0.01. This is depicted in Fig. l(d). It can be noticed that the clines become steeper with greater selection values on homozygous recessive plants, and the ranges of the gene frequencies (i.e. the differences between the
221
highest and lowest points of the clines) become larger. Moreover, the overrepresentation of dominant alleles in the cline centre becomes more pronounced when higher selection values are used. The amount of dispersion of p = 0.01 (to each neighbour) seems to be reasonable, if we look at the distances of the investigated populations in Mastenbroek et alf-[4] and the dispersion ability of Silene latifolia,which seems to be rather weak [Mastenbroek, personal communication]. The threshold for stability is about u = 0.05 (to each neighbour): higher values give fading clines. Boundary Elects As has been mentioned earlier, the demes are echoed at the boundaries. Therefore, the most left and most right deme only get input from their right and left neighbour respectively. These border demes can only reach stability if the selective forces match the one-sided dispersion. Because of this, the gene frequencies in these demes cannot deviate much from their neighbour, as can occur in demes with twosided dispersion (e.g. in the cline centre). As a result of this boundary effect the higher tail of a cline tends to go down, whereas the lower end is lifted. These abberations become more pronounced when greater dispersion values are used. So, we used the most disadvantageous condition for clines to maintain their range. This is illustrated in Fig. 2, where the cline of Fig. 1(b) is set out against a cline, generated by the same model implemented in an array containing 24 demes (the g/DOM cline has been left out of this figure for reasons of clarity). Notice that the cline range becomes larger in the longer array. However, the maximal slope in the cline centre is not, affected. Thus, if we measure cline width by calculating the inverse of the maximal slope, as is often done, this width is not affected by boundary effects. Density Gradients Mastenbroek et al. [4] showed that the distribution of race-l is more widespread than is the distribution of race-2. This is reflected in the transition zone between these two races, where the gG allele (gDOM in the model) has spread more in eastern direction than has the g/R allele (g/DOM in the model) in western direction. In
JAAP
222
FIG
2. BOUNDARY
simulations1
EFFECT. The gOOM-frequencies
are depicted
for an array of 24 demes
(light). In the first and last six demes the gOOM-frequencies
deme has two bars (a dark and a light one). The g/OOMcline
are not defined
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
(dark) and an array of 12 demes
for the 12 demes
simulation.
(as I” the other
In the 12 central demes:
We simulated this in the model by incorporating a carrying capacity gradient: population density descending linearly from west to east. Figure 3 presents the result for K-values from 244 in the west to 200 in the east with a step of four per deme. The selection values used were 0.5 against homozygous recessive plants for both loci, and 0.01 against homozygous dominant plants for both loci. The clines have moved in eastern direction, which makes that the gGallele b)
(al
GRADIENT.
Cumulative
diagram
of the gOOM- and the g/OOM-frequencies.
K-values
(see Table 1) from left to right: 244; 240; 236;
232; 228; 224; 220; 216; 212; 208; 204; 200. SRES -
one
has been left out for reasons of clarity.
fact, few populations of race-2 in central Europe are of the proper race-2 type, i.e. with g/R frequency = 1.0 and gGfrequency = 0.0. In most of these race-2 populations the gG frequency has values up to 0.20. If we consider history, we see that deforestation has proceeded from western Europe in eastern direction. As Sdene pratensis is restricted to open land, the number of populations should have decreased from west to east.
FIG. 3. DENSITY
HERINGA,
0.5; SDOM
-
0.01. (a) gOOM-frequencies
dark; g/OOA+frequencies
light; (b) g/OOM-frequencies
dark; gOOM-frequencies
light
223
STABILITY OF A TWO-LOCUS COACTING CUNE IN SlLENELATlFOLlA
has penetrated more in the east than has the g/R allele in the west; the gG frequency is raised substantially in the eastern demes. Second Generation Effect In concordance with the finding that selection on homozygous recessive F2 recombinants only is not a sufficient condition for stability of our twolocus cline, we studied second generation effects by using an individual oriented model. In this model, homozygous recombinants for both loci occur in the second generation at first. This is not the case in the gene model. However, the effects of this delay in hybrid formation are negligible: the individual-oriented model generates almost exactly the same clines as the gene frequency model for the same parameters.
Discussion Implications of Model Results for the Evolution of the Silene latifolia Distribution Over Europe In a two-locus situation, clines formed under selection against homozygous recessive plants only, are not stable and gradually smooth out (Fig. la). If the effective dispersion of Silene populations in the empirical world is lower than the dispersion rate used in the model, the argument that the observed two locus cline is just a stage in the process of fading out, cannot be excluded. To get an impression of the timescale, one may look at the eastern Europe transition zone between race-2 (gDOMFR0 = 0, gIDOMFR0 = 1) and race-3 (gDOMFRQ = 1, glDOMFRQ = 1). Recombinants, homozygous for the recessive alleles cannot occur in this area, as all plants possess at least the active gene g/DOM. In fact, in this case we are dealing with a single-locus cline (of the g locus) which will fade out unhampered by selection. The model showed that the rate of fading out of a two-locus cline under selection against homozygous recessive recombinants for both loci hardly deviates from this rate under neutral selection. The eastern transition zone, however, is much broader than the western transition zone (see ref. [41, fig. 5). So, either the time of formation differed appreciably between the two clines, or in the western cline stabilizing
selection has taken observed steepness.
place
to
maintain
the
Stability of Flavone-glycosylationGenes Distributionand Other Characters The large-scale congruence between the flavone-glycosylation genes distribution and the distribution of other character sets of Silene /atifi$ia is explained by sampling drift and migration in Mastenbroek [l]. Therefore, genetic linkage between these character distributions is not needed. However, if the flavone-glycosylation genes distribution is maintained by hybrid selection and the other characters are selectively neutral, stability of these other character distributions can only occur when the genes coding for these characters are affected by the flavone-glycosylation barriers. Barton and Hewitt [17] stated that neutral loci can be considerably impeded by strong hybrid zones. This appeared not to be the case in our two-locus cline, in which no selection against Fl hybrids takes place. A third unlinked neutral locus incorporated in the gene model with selection value 0.5 on homozygous recessive plants and a selection value of 0.01 on homozygous dominant plants turned out to spread as easily as does a neutral locus in the absence of a hybrid zone of other loci. So, it seems that the distribution of other character sets cannot be stabilized by the stable barrier of flavone glycosylation genes. Conclusions (a) Selection against recombinants lacking dominant flavone-glycosylation alleles which have known decreased fertility cannot explain the formation of a stable two-locus coacting cline. (b) Adding a very small selection (of value 0.01 or smaller) against homozygous plants for both loci gives rise to a stable two-locus coacting cline. (c) This cline has an overrepresentation in its centre of dominant flavone-glycosylation genes, which is also observed in nature [4]. (d) Stability and the mentioned overrepresentation of dominant alleles is preserved for a wide range of selection values used. (e) The observed small area of race-2 can be a result of deforestation in the past: implementing
JAAP
224
a density gradient in the modet leads to the penetration of gG alleles in race-2 which can be observed in the flavone-glycosylation data [I, 91.
Acknowledgement-We thank Dr. 0. Mastenbroek an early stage of this research.
for
his
supportat
References 1. Mastenbroek, 0. (1983) Patterns of variation in European Silene pratensis. Thesis, R. U. Utrecht. 2. Mastenbroek, O., Prentice, H. C., Heringa, J. and Hogeweg, P. (1984) Plant Sysf. Evol. 145, 227. 3. Mastenbroek, O., Maas, J. W., Brederode, J. van, Niemann, G. J. and Nigtevecht, G. van (1982) Genetica 59, 139. 4. Mastenbroek, O., Hogeweg, P., Brederode, J. van and Nigtevecht, G. van (1983) Biochem. Sysf. Ecol. 11, 91. 5. Mastenbroek, O., Prentice, H. C., Kamps-Heinsbroek, R., Brederode, J. van, Niemann, G. J. and Nigtevecht, G. van (1983) Plant Syst. Evol. 141, 257.
HERINGA,
PAULINE
HOGEWEG
AND
JAN VAN BREDERODE
6. Brederode, J. van and Nigtevecht, G. van (1972) Molec. Gen. Genet. 118, 247. 7. Brederode, J. van and Nigtevecht, G. van (1975) Theor. Appl. Genet. 48, 353. 8. Besson, E., Besset, A., Bouillant, M. L., Chopin, J., Brederode, J. van and Nigtevecht, G. van (1979) Phy?ochemistry 18,657. 9. Mastenbroek, 0. and Brederode, J. van (1985) Biochem. Syst. Ecol. 14, 165. 10. Suominen, J. (1979) Acta Bot Fenn. II, 1. 11. Endler, J. A. (1977) Geographic Variation, Speciation and Clines. Princeton University Press, Princeton, NJ. 12. Brederode, J. van, Genderen, H. H. van and Berendsen, W. (1982) Experientia 38, 929. 13. Slatkin, M. (1975) Genetics 81, 787. 14. Barton, N. H. (1983) Evolution 37,454. 15. Kimura, M. (1953) Ann. Rept. Nat Inst. GeneticsJapan 3,62. 16. Hogeweg, P. and Hesper, B. (1984) UKSC-84 Conference on Computer Simulation, p. 102, Butterworths, London. 17. Barton, N. H. and Hewitt, G. M. (1981) in Evolution and Speciation (Atchley, W. R. and Woodruff, D. S., eds), pp. 109-145. Essays in honor of M. J. D. White. Cambridge University Press, London.