Potential effects of air pollutants on epidemics of plant diseases

Agriculture, Ecosystems and Environment, 18 (1987) 251-262 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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Views and Ideas The section Views and Ideas is intended for short contributions, within the scope of the journal, which are not research papers or full-bodied review articles. These may be brief reports on current trends, ideas for research topics, critical notes, discussions of published works (other than book reviews), background information to understanding problems in the relationship between agriculture and environment, etc. Submission of manuscripts by readers of the journal is welcomed.

Potential Effects of Air Pollutants on Epidemics of Plant Diseases ABSTRACT Madden, L.V. and Campbell, C.L., 1987. Potential effects of air pollutants on epidemics of plant diseases. Agric. Ecosystems Environ., 18: 251-262. Air pollutants potentially can affect plant disease epidemics in numerous ways. The initial disease level (yO) and the apparent infection rate (r, a parameter measuring the rate of disease increase) can be altered by pollutants. For compound interest diseases, final disease intensity is more sensitive to changes in r than toy,,. The effective multiplication factor (R), the latent (p) and infectious (i) periods determine r. These values, however, are not equally important in affecting r. One can use fairly simple equations to relate constant values of R, p, and i to r during the early stages of an epidemic. Nonconstancy of these characteristics, due either to changing environment or inherent variability of the population, generally requires computer simulation for a thorough understanding. Spatial variability and pathogen dispersal further complicate the effect of pollutants on plant disease epidemics. Some reported examples of the effects of O,, SOS, and acid deposition on epidemic characteristics are discussed.

INTRODUCTION

An epidemic is a change in disease over time in a population. Usually, plant epidemics consist of an increase in disease intensity with time in a population of plants (i.e., crop) in a greenhouse, field or forest. This definition does not agree with the common lay-person’s concept of an epidemic, being the rapid development of a large amount of disease over large areas or in large populations. Occasionally, plant disease epidemics will reach such a high level, but this is the exception rather than the rule; plant epidemics usually develop over an entire growing season for field crops or over a period of years in a stand of trees. Disease levels can stay relatively low, but even low levels of many crop diseases result in substantial yield losses and are important economically (James and Teng, 1979). A plant disease epidemic will not occur unless there is a susceptible host, a

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virulent pathogen, and a favorable environment. This is known as the disease triangle or triad concept of disease. Air pollutants could be considered pathogens, but for our purposes, only biotic pathogens (e.g., fungi, viruses, bacteria, nematodes) are considered. Pollutants will be considered as part of the environment, which also includes weather and all other biotic and abiotic factors that influence the dynamic interaction of host and pathogen. With epidemics, time must also be considered; conceptually, the disease triangle can be expanded to a disease pyramid. Laurence et al. (1983) have summarized the known effects of pollutants on pathogen-host interactions. As indicated in their review, little work has been done on determining the effects of pollutants on disease progression. To understand the potential effect of pollutants or other environmental variables on epidemics, a description of an epidemic more quantitative than the disease pyramid is necessary. A theoretical description of an epidemic using mathematics, based on published results, is given below to represent an epidemic with well-defined parameters and variables. A discussion of how pollutants can affect epidemics is then given in the context of the mathematical treatment. MODEL OF AN EPIDEMIC

The dynamic process of an epidemic is defined by its rate of change with time. This absolute rate of disease increase is written as dy/dt, i.e., the change in disease (dy ) with infinitesimal change in time (dt) . Vanderplank (1963) proposed a family of models for the absolute rate as a function of time from the beginning of the epidemic ( t) and disease intensity (y ) , the proportion of plants infected in a population or the proportion of host tissue which is infected. The equations used here are for ‘compound interest’ diseases, in which there is production of secondary cycles of inoculum (e.g., spores) which spread from plant to plant, with subsequent disease development. The absolute rate of disease increase can be represented as: dyldt=ry(l--y)

(1)

in which r is a rate parameter with units of l/t, 1 represents the maximum disease proportion, and all other terms are as defined above. dy/dt is then jointly proportional to the level of infected plants or diseased tissue (y) and to the level of healthy tissue of healthy plants (1 - y ) . Eqn. 1 is known as the logistic model and r is commonly called the apparent infection rate; r measures the rate of disease increase. As y increases, more inoculum (e.g., spores) is available for greater disease increase and, thus, y will determine dy/dt. As y increases, however, there is a decrease in healthy plants that limits further disease increase; therefore, 1 -y also determines dy/dt. Although conceptually important, absolute rates are not directly measured

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0

2.0

40

60

80

Tima

Fig. 1. Logit of y (In [y/(1 -y) ] ) versus time for the logistic model with constant value of the apparent infection rate r (see eqn. 2).

in the field. In practice, it is easier to work with y than dy/dt; this is done by integration eqn. 1. A linear representation of this integration is:

lnb/(l--y)l

=lnbo/(l-yo)l

+rt

(2)

in which In ( - ) is the natural log transformation, In [y/ (1 -y ) ] is known as the logit of y, and y. is a constant of integration and can represent the initial level of disease in an epidemic. Examples of y. are the incidence of seed infection or the amount of overwintering inoculum. This equation has two unknown parameters, ln[y,/(l -yo)] and r. Both can be estimated from a given set of data; estimation approaches and problems are presented elsewhere (Madden, 1986; Madden and Campbell, 1986). The two parameters represent the combined effe& of host, pathogen, and environment, including pollutants, on plant disease epidemics. If an environmental factor such as acid deposition has an effect on some aspect of a given epidemic, it may be quantified through one or both of these parameters. If r is constant, eqn. 2 represents a straight line with intercept ln(y,/( l-y,)) and slope r (Fig. 1, line a). Reducing y. without changing r will produce a lower but parallel line (Fig. 1, line b ) and it will take longer to reach a given level of disease. Reducing r without altering y. slows the rate of disease increase (reduces the slope) and also delays reaching a certain level of y (Fig. 1, line c) . Reducing both parameters has a combined effect of reducing the slope and intercept (Fig. 1, line d) . The two parameters do not have an equivalent influence in determining disease progress, e.g., it takes a logarithmic change in y. (e.g., lo-fold) to equal a linear change in r. The logistic model (eqns. 1 and 2) and variations of it have been shown to describe accurately many plant epidemics (Madden 1980; Berger, 1982; Campbell et al., 1984). A review of the other common models for disease progression and how they relate to the logistic can be found in Madden (1980). For conceptual purposes here, it is sufficient to deal only with the logistic model.

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The initial disease level (yO) is a measure of the amount of inoculum initially present and the efficiency of this inoculum in producing disease (E) . E, the number of infections which occur for a given number of propagules, can be quantified and will influence yO.E is affected by the environment, pathogen virulence or aggressiveness, and host plant resistance. If inoculum level is sufficiently high, even with a low E, y. will be sufficient for epidemic onset. If, however, inoculum level is low and a factor such as a gaseous pollutant or acid deposition reduces E, y. may be reduced and epidemic development will be affected. The apparent infection rate (r) measures the increase in disease intensity over time. The rate is affected by the environment, pathogen virulence or aggressiveness, and host plant resistance. In epidemiological terms, these factors influence r through the latent period (time elapsed from the initiation of infection until the production of infective propagules [e.g., spores] ); infectious period (the time period in which propagules are produced) ; number of spores produced; and effectiveness of these spores in reaching a new healthy infection site and causing an infection. It is convenient to summarize all of the above effects into a single parameter r for data analysis and comparison of treatments. Such a summary parameter, by itself, does not, however, allow one to evaluate the relative importance of these effects in making up r. A theoretical evaluation is possible, however, based on an extension of the logistic model (eqn. 1). Eqn. 1 is based on the assumption that total disease (y) influences dy/dt. This can never be completely true because not all diseased plants or diseased tissues are producing new spores for subsequent infections. Likewise, not all lesions are constantly expanding. Eqn. 1 can be expanded to represent an epidemic more realistically. Through such an expansion, the model is made more mechanetic. Let yt represent y at time t, p the latent period, and i the infectious period. Then yt+ is the level of disease that has passed through the latent period and is capable of producing spores. yt_i._p is the level of disease that has passed through both the latent and infectious period and no longer produces spores; yt_ i__pis said to be ‘removed’ from the epidemic. The new logistic model can be written as: dy,ldt=~(y,-p-Y,-i-p)

(l-Y,)

(3)

in which R is a new rate parameter termed the basic infection rate and [Yt_p-3/t-i-p] is the amount of disease that directly influences dy,/dt (infectious disease). R is also called the ‘effective multiplication factor’ and, with diseases that result in non-expanding lesions, has the direct and biologically meaningful definition of ‘the number of daughter lesions per mother lesion per time period’. Unless indicated otherwise, we assume that the time unit is days. R equals the product of the number of spores produced per lesion per time period (N) and the effectiveness of these spores in reaching unoccupied infec-

tion sites and causing infection (E, as discussed above, a proportion between 0 and 1) (Zadoks and Schein, 1978). E is the product of the probability of a propagule of landing on a susceptible host plant into germinating, penetrating and successfully resulting in infection. Although many epidemics progress approximately according to eqn. 1 with constant r, it is not known if eqn. 3 describes real epidemics. Eqn. 3 cannot be integrated to yield an equation to represent yt as a function of t and the parameters R and yo. The equation only represents a logical extension of eqn. 1 to account for meaningful characteristics of an epidemic. To evaluate the effect of R (IV and E ) , p and i on disease progress, one can relate these parameters to the apparent infection rate r. This can be done if r is constant (Vanderpland, 1963; Jeger, 1984) ; such an assumption is reasonable, at least for portions of an epidemic. For our purposes, we will only consider the early stages of an epidemic (y < 0.05) to show how R, p and i affect r. Jeger (1984) explored the relationship among these parameters when y > 0.05 but these complications are not necessary here. If r is constant over time during the early stage of an epidemic, it can be shown (Vanderplank, 1963) that: r=R[exp(

-pr)

-exp(

- (i+p)r)]

(4)

This equation cannot be explicitly used to estimate r because the parameter appears on both sides of the equal sign; r can, however, be estimated numerically. Figure 2 shows the relationship between r and R at i = 10 and three values of the latent period p. The doubling time is also given on the figure. (The doubling time simply is the time required for disease intensity to double. When y < 0.05 and the logistic model represents the epidemic, it is approximately equal to 0.693/r.) The apparent infection rate increases as R increases: the greatest increase is when R < 100. The increase in r slows down as R increases: when R = 200, changes in R of 3 100 have little effect on r. When R < 25, slight changes in R have a large effect on r, especially whenp is short. Although there is no limit to R, values of > 100 are unlikely. This means that values of r > 0.6 are unlikely except for very short latent periods (p N 5). An increase inp results in a decrease in r. The change in r, however, depends on the levels of p and R involved. The curves diverge more as R increases; i.e., changes in p have a greater effect at high R than at low R. A decline of p from 10 to 5 has a greater effect on r than a decline from 15 to 10. The infectious period has only a slight effect on R during the early stage of an epidemic. EXAMPLES OF POLLUTANT EFFECTS ON EPIDEMIC CHARACTERISTICS

A review of the literature reveals that pollutants increase, decrease, or have no effect on epidemic characteristics (Laurence et al., 1983). Some relevant examples are presented here. There is useful information on the effects of O3

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and SO, on the germination and penetration components of E, probably because it is easily studied. Ozone, for example, has been shown to either inhibit or stimulate fungal spore germination (Hibben and Stotzky, 1969; Krause and Weidensaul, 1978; James et al., 1982). Likewise, SO, inhibits (Weinstein et al., 1975) or has no effect (Hibben, 1966) on fungal spore germination. In an example involving acid deposition, infection of potato plants by Phytophthoru infestans was inhibited when sporangia were carried in simulated rain solutions with pH < 3.1, even though germination occurred in solutions of pH 2.8 ( Martin et al., 1985 ) . Other components making up E have been little studied. Surprisingly, there is very little information on the effects of pollutants on N. It has been found, however, that O3 can decrease (Krause and Weidensaul, 1978; Heagle, 1977) or increase (Heagle, 1977; Heagle and Strickland, 1972) N. Many investigators have studied the effects of pollutants on colonization, which influences p and N. As with the other characteristics, O3 and SO, have been shown to increase, decrease, or have no discernable effeet on colonization (e.g., Heagle, 1970; Heagle and Key, 1973; Weinstein et al., 1975; Weidensaul and Darling, 1979; Laurence et al., 1983). Given the wide range of reported results, it is not surprising that there is no clear understanding of air pollutant effects on plant disease epidemics. Even the directional effect of a pollutant or acid deposition (i.e., positive or negative) is not consistent for a given pathogen-host system. For instance, O3 inhibits colonization and propagule formation of the fungus Fomes annosus. Ozone, however, also increases the susceptibility of trees to infection (James et al., 1980a,b, 1982). Using epidemiological principles, one can at least determine the potential effect of various pollutants. Consider the data of James et al. (1982) : assume that N= 200 and E, which includes the proportion of spores germinating, equals 0.9 without O3 exposure. R therefore equals 180. A 25% reduction in germination rate when spores were exposed to O3 was highly significant (see Table II in James et al., 1982), and R was reduced to 135. As can be seen in Fig. 2 for values of p 2 10 (reasonable), the apparent infection rate would only be slightly reduced. This type of analysis can be carried out for many of the reported studies. CONCLUSIONS BASED ON THE LOGISTIC MODEL

In epidemiologic terms, five values describe an epidemic. These are yo, p, i, N and E. The product of N and E comprises R, whereas p, i and R, determine r, and, at least initially, E influences yo. Air pollutants can potentially affect disease progress through one or more of these values. Using the known relationships between these parameters, one can rationally assess a pollutant’s impact on at least the early stages of an epidemic. Changes in one or more of the five values may or may not have a substantial effect on disease progress.

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50

100

Basic

150

Infection

200

250

300

Rate (RI

Fig. 2. Relationship between the apparent infection rate three levels of the latent period p (see eqn. 4).

(F)

and the basic infection rate (R) at

For example, sometimes a large change in R or p will have a small effect, and at other times a small change in R orp will have a large effect on the epidemic. LIMITATIONS

IN USING THE LOGISTIC MODEL

One generally assumes that p, i, r or R are constant. Although not theoretically necessary, a constant value permits a more thorough mathematical development of the models and easier estimation of the parameters. In reality, all of the parameters may actually vary. It is often possible to use mean values for estimated parameters but large errors will sometimes result. A further complication is the fact that all five epidemic characteristics are dependent on the natural and man-made components of the environment. In particular, temperature, atmospheric and soil moisture, radiation, air movement, gaseous and solid pollutants, wet and dry deposition, and other p_hysical factors can influence disease progression. Pollutants could alter the coverage and breakdown of pesticides on plant surfaces (Troiano and Butterfield, 1984)) further complicating epidemic development. The changing environment during the course of an epidemic suggests that R, p and i will vary throughout an epidemic. A general assumption is that the host area to be infected is uniform and constant. Host area may be nearly constant in time when pathogen populations increase rapidly, especially after most host growth is completed. Other pathogen populations increase slowly over an extended period of time while host area is changing. In these situations, one could model the absolute area of disease plants or host tissue instead of proportions (Berger and Jones, 1985 1,

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or use a still unproven approach suggested by Kushalappa and Ludwig (1982 ) to correct for host growth. Although host plants are often fairly close to being uniform, this is not always the case. In forest systems, host plants can vary drastically in age, vigor, and susceptibility. In annual crops, mixtures of cultivars (occasionally used with grain crops) can result in multiple levels of susceptibility to a given pathogen. Dealing with non-uniformity with mathematics is necessarily complex compared to the models presented here. As shown by Jeger et al. (1981) for mixtures of cultivars, one can model these epidemics by combining separate logistic equations for each susceptibility class. COMPUTER SIMULATION

One approach to handling variability and environmental effects is computer simulation. Each component of a disease cycle, e.g., sporulation or latent period, is modeled as a function of time, host resistance, pathogen aggressiveness, and/or environment. Models for the components are implemented into a computer program which is used to simulate disease progression under a specified set of conditions (Waggoner, 1978). Dozens to hundreds of equations might be necessary and the development of such simulation models requires many years of data collection and analysis. The final program can become very complicated and cumbersone. Once developed, however, a simulator permits testing of many combinations of inputs (e.g., environmental factors) on disease progress. An example of where a plant disease simulator might be useful would be in the stripe rust of wheat pathosystem. A plant disease simulator, EPIDEMIC, was developed by Shrum (1975) which includes most of the epidemic characteristics identified in this article. Now that the simulator has been validated (Shrum ,1975), one can evaluate the effect of changes in important variables on resulting epidemic development. For instance, one can ascertain the effect of N (a variable function of a changing environment in EPIDEMIC) on epidemics of stripe rust. A pollutant that reduces N to N/2 may or may not have a substantial effect (Fig. 3). When environmental conditions favor a rapid rate of disease increase, halving N has little effect on y (Fig. 3B). When conditions are less favorable, halving N has a much greater impact ( Fig. 3A). This is in basic agreement with the conclusions drawn from the theoretical relationship between r and R based on a simple equation (Fig. 2). Other experimentation with this simulator can be done. Lateblight of potatoes represents another pathosystem where plant disease simulation would be useful. The simulator, LATEBLIGHT, was developed by Bruhn et al. (1979) and also includes most of the epidemic characteristics identified previously. The simulator also incorporates fungicide coverage and redistribution, as well as disease management procedures. If information on

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L

IS

I

1 35

1

I 55

I 75

Time
the effects of acidic deposition on attributes of the pathogen, Phytophthora infestczm (Martin et al., 1985; Campbell et al., 1985)) and on retention of pesticides on leaf surfaces (Troiano and Butterfield, 1984) could be incorporated into the model, potential effects of acidic deposition on management of late blight could be examined. PROBLEMS

IN THE INTERPRETATION

OF POLLUTANT

AND DEPOSITION

EFFECTS ON EPIDEMICS

Alterations in epidemic characteristics are dependent upon the complex interaction of numerous environmental and pathosystem components. The observed amount of disease is the ‘integration’ of these many effects. Due to the integration, specific causes of pollutant and deposition effects may not be apparent. Three specific examples may be used to illustrate possible problems

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in interpretation. Two examples involve the specific characteristics of acid deposition and the third illustrates an effect on host characteristics. During a rain event, if initial washing-out of the atmosphere occurs, the initial rainfall may be more acidic than rainfall during the remainder of the event. Thus, exposed pathogen propagules may be subjected to more acidic deposition for a brief time than would be apparent from the average acidity level for the entire event. If the pathogen propagules are sensitive to level of acidity in rain, N or E may be substantially reduced by the initially high level of acidity in the rainfall; however, if average acidity for the entire event were considered, it would appear that a much lower (average) acidity level was responsible for the reduction in N or E. Thus, there is a definite need for dose-response studies in chronic and acute exposures to acid deposition and to other types of pollutants. The proportion of various acids in rain may also affect epidemic characteristics. Because sulfur or sulfur compounds may be fungicidal to certain plant, pathogens, the proportion of acidity due to sulfuric acid may play a major role in the effects of acidic deposition on epidemics. Effects of pollutants on host plants may also confound interpretation of epidemics. Subtle, but significant changes in host resistance or susceptibility may occur under pollutant and deposition pressure. A small erosion of waxes or leaching of nutrients due to acid deposition may have profound effects on N or E. Whether direct effects occur to the host and pathogen (or both) will have to be ascertained before causal relationships can be suggested to account for differences in epidemics. ACKNOWLEDGEMENTS

L.V.M. thanks the Ecosystem Research Center, Boyce Thompson Institute, and Yale University for the invitation to speak at the workshop on “The effects of air pollutants on plant-pest interactions” held in New York from 2 to 5 June, 1985. We both thank these organizations for the invitation to write this paper so that our ideas will reach a wider audience. Salaries and research support provided by State and Federal Funds appropriated to the Ohio Agricultural Research and Development Center (OARDC ) , the Ohio State University, for the first author, and by State and Federal Funds appropriated to the School of Agriculture and Life Sciences and the North Carolina Agricultural Research Service, North Carolina State University, for the second. OARDC Journal Article 45-85.

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262 Martin, S.B., Jr., Campbell, C.L. and Bruck, R.I., 1985. Infectivity of Phytophthora infestuns in simulated acid rain solutions. (Abstr.) Phytopathology, 75: 501-502. Shrum, R.D., 1975. Simulation of wheat stripe rust (Puccinia striiformis West.) using EPIDEMIC, a flexible plant disease simulator. Progress Report 347. Pennsylvania State University, College of Agriculture, University Park, PA, 81 pp. Troiano, J. and Butterfield, E.J., 1984. Effects of simulated acidic rain on retention of pesticides on leaf surfaces. Phytopathology, 74: 1377-1380. Vanderplank, J.E., 1963. Plant Diseases: Epidemics and Control. Academic Press, New York, 349 PP. Waggoner, P.E., 1978. Computer simulation of epidemics. In: J.G. Horsfall and E.B. Cowling (Editors), Plant Disease; An Advanced Treatise, Vol. II. Academic Press, New York, pp. 203-222. Weidensaul, T.C. and Darling, S.L., 1979. Effectsof ozoneand sulfur dioxide on the host-pathogen 69: 939-941. relationship of Scotch pine Scirrhia acicola. Phytopathology, Weinstein, L.H., McCune, D.C., Aluisio, A.L. and van Leuken, 1975. The effect of sulfur dioxide on the incidence and severity of bean rust and early blight of tomato. Environ. Pollut., 9: 145-155. Zadoks, J.C. and Schein, R.D., 1978. Epidemiology and Plant Disease Management. Oxford University Press, New York, 427 pp. L.V. MADDEN Department of Plant Pathology Ohio Agricultural Research and The Ohio State University Development Center Wooster, OH 44691 U.S.A. C. LEE CAMPBELL Department of Plant Pathology North Carolina State University Raleigh, NC 27695 U.S.A.