Greg Dwyer

Dynamics of disease resistance polymorphism at the Rpm1 locus of Arabidopsis

The co-evolutionary ‘arms race’ is a widely accepted model for the evolution of host–pathogen interactions. This model predicts that variation for disease resistance will be transient, and that host populations generally will be monomorphic at disease-resistance (R -gene) loci. However, plant populations show considerable polymorphism at R -gene loci involved in pathogen recognition. Here we have tested the arms-race model in Arabidopsis thaliana by analysing sequences flanking Rpm1, a gene conferring the ability to recognize Pseudomonas pathogens carrying AvrRpm1 orAvrB (ref. 3). We reject the arms-race hypothesis: resistance andsusceptibility alleles at this locus have co-existed for millions of years. To account for the age of alleles and the relative levels ofpolymorphism within allelic classes, we use coalescence theory to model the long-term accumulation of nucleotide polymorphism in the context of the short-term ecological dynamics of disease resistance. This analysis supports a ‘trench warfare’ hypothesis, inwhich advances and retreats of resistance-allele frequency maintain variation for disease resistance as a dynamic polymorphism,.

The combined effects of pathogens and predators on insect outbreaks.

The economic damage caused by episodic outbreaks of forest-defoliating insects has spurred much research, yet why such outbreaks occur remains unclear. Theoretical biologists argue that outbreaks are driven by specialist pathogens or parasitoids, because host–pathogen and host–parasitoid models show large-amplitude, long-period cycles resembling time series of outbreaks. Field biologists counter that outbreaks occur when generalist predators fail, because predation in low-density defoliator populations is usually high enough to prevent outbreaks. Neither explanation is sufficient, however, because the time between outbreaks in the data is far more variable than in host–pathogen and host–parasitoid models, and far shorter than in generalist-predator models. Here we show that insect outbreaks can be explained by a model that includes both a generalist predator and a specialist pathogen. In this host–pathogen–predator model, stochasticity causes defoliator densities to fluctuate erratically between an equilibrium maintained by the predator, and cycles driven by the pathogen. Outbreaks in this model occur at long but irregular intervals, matching the data. Our results suggest that explanations of insect outbreaks must go beyond classical models to consider interactions among multiple species.

HOST HETEROGENEITY IN SUSCEPTIBILITY AND DISEASE DYNAMICS: TESTS OF A MATHEMATICAL MODEL

Most mathematical models of disease assume that transmission is linearly dependent on the densities of host and pathogen. Recent data for animal diseases, however, have cast doubt on this assumption, without assessing the usefulness of alternative models. In this article, we use a combination of laboratory dose‐response experiments, field transmission experiments, and observations of naturally occurring populations to show that virus transmission in gypsy moths is a nonlinear function of virus density, apparently because of heterogeneity among individual gypsy moth larvae in their susceptibility to the virus. Dose‐response experiments showed that larvae from a laboratory colony of gypsy moths are substantially less heterogeneous in their susceptibility to the virus than are larvae from feral populations, and field experiments showed that there is a more strongly nonlinear relationship between transmission and virus density for feral larvae than for lab larvae. This nonlinearity in transmission changes the dynamics of the virus in natural populations so that a model incorporating host heterogeneity in susceptibility to the virus gives a much better fit to data on virus dynamics from large‐scale field plots than does a classical model that ignores host heterogeneity. Our results suggest that heterogeneity among individuals has important effects on the dynamics of disease in insects at several spatial and temporal scales and that heterogeneity in susceptibility may be of general importance in the ecology of disease.

Combining Population-Dynamic and Ecophysiological Models to Predict Climate-Induced Insect Range Shifts

Hundreds of species are shifting their ranges in response to recent climate warming. To predict how continued climate warming will affect the potential, or “bioclimatic range,” of a skipper butterfly, we present a population‐dynamic model of range shift in which population growth is a function of temperature. We estimate the parameters of this model using previously published data for Atalopedes campestris. Summer and winter temperatures affect population growth rate independently in this species and therefore interact as potential range‐limiting factors. Our model predicts a two‐phase response to climate change; one range‐limiting factor gradually becomes dominant, even if warming occurs steadily along a thermally linear landscape. Whether the range shift accelerates or decelerates and whether the number of generations per year at the range edge increases or decreases depend on whether summer or winter warms faster. To estimate the uncertainty in our predictions of range shift, we use a parametric bootstrap of biological parameter values. Our results show that even modest amounts of data yield predictions with reasonably small confidence intervals, indicating that ecophysiological models can be useful in predicting range changes. Nevertheless, the confidence intervals are sensitive to regional differences in the underlying thermal landscape and the warming scenario.

Using simple models to predict virus epizootics in gypsy moth populations

1. Biologists have made little use of recent advances in the mathematical theory of the dynamics of insect pathogens, because of difficulties with parameter estimation and misgivings about the simplicity of the models in question. 2. We use an existing simple model for the dynamics of insect pathogens, slightly modified both to provide greater accuracy and to allow for more straightforward parameter estimation. 3. Focusing on the nuclear polyhedrosis virus (NPV) of gypsy moth (Lymantria dispar (L.)), we estimated each of the model parameters independently, estimating three of the four model parameters from the literature

HYBRID ZONE DYNAMICS AND SPECIES REPLACEMENT BETWEEN ORCONECTES CRAYFISHES IN A NORTHERN WISCONSIN LAKE

Abstract.— Hybrid zones that result in the genetic assimilation (replacement) of one species by another are underrepresented in the animal literature, most likely due to their transient nature. One such zone involves the rusty crayfish, Orconectes rusticus, and its congener O. propinquus. Orconectes rusticus was recently introduced into northern Wisconsin and Michigan lakes and streams, where it is hybridizing with and displacing resident O. propinquus. Here we report on a study investigating the dynamics of a hybrid zone between the two crayfish in Trout Lake, Wisconsin, where both the time (circa 1979) and location of the initial introduction are known. Our prediction was that hybridization should hasten the demise of O. propinquus because we expected that male O. rusticus (which are larger than congeners) would outcompete male O. propinquus for mates of both species. If hybrid progeny are unfit, then the result would be decreased reproductive output of O. propinquus females. However, we found a pattern of cytonuclear disequilibrium between allozymes and mtDNA suggesting that a majority (94.5%) of F1 hybrids resulted from matings between O. rusticus females and O. propinquus males. Also contrary to expectations, fecundity (O. rusticus and O. propinquus) and early hybrid survivorship did not differ significantly from nonhybrids. Moreover, adults of mixed ancestry were superior to both O. rusticus and O. propinquus in competition for a limiting food resource. Using a single‐locus model, we estimated that hybridization increases the advance of O. rusticus genes in Trout Lake between 4.8% and 36.3% above that due to the previously documented ecological interactions. Consequently, whereas hybridization may be hastening the elimination of genetically pure O. propinquus, introgression is nevertheless slowing the loss of O. propinquus nuclear genes. Although our results suggest that O. rusticus and O. propinquus may not be true species under the biological concept, their ecological differences are of great conservation importance.

Pathogen‐Driven Outbreaks in Forest Defoliators Revisited: Building Models from Experimental Data

Models of outbreaks in forest‐defoliating insects are typically built from a priori considerations and tested only with long time series of abundances. We instead present a model built from experimental data on the gypsy moth and its nuclear polyhedrosis virus, which has been extensively tested with epidemic data. These data have identified key details of the gypsy moth–virus interaction that are missing from earlier models, including seasonality in host reproduction, delays between host infection and death, and heterogeneity among hosts in their susceptibility to the virus. Allowing for these details produces models in which annual epidemics are followed by bouts of reproduction among surviving hosts and leads to quite different conclusions than earlier models. First, these models suggest that pathogen‐driven outbreaks in forest defoliators occur partly because newly hatched insect larvae have higher average susceptibility than do older larvae. Second, the models show that a combination of seasonality and delays between infection and death can lead to unstable cycles in the absence of a stabilizing mechanism; these cycles, however, are stabilized by the levels of heterogeneity in susceptibility that we have observed in our experimental data. Moreover, our experimental estimates of virus transmission rates and levels of heterogeneity in susceptibility in gypsy moth populations give model dynamics that closely approximate the dynamics of real gypsy moth populations. Although we built our models from data for gypsy moth, our models are, nevertheless, quite general. Our conclusions are therefore likely to be true, not just for other defoliator‐pathogen interactions, but for many host‐pathogen interactions in which seasonality plays an important role. Our models thus give qualitative insight into the dynamics of host‐pathogen interactions, while providing a quantitative interpretation of our gypsy moth–virus data.

The Roles of Density, Stage, and Patchiness in the Transmission of an Insect Virus

Although the importance of insect viruses in the population dynamics of their hosts is widely acknowledged, ecologists are still relatively ignorant of the factors determining the rate of transmission of insect viruses in the field. I performed a series of field experiments in which I investigated the transmission dynamics of the nuclear poly- hedrosis virus (NPV) of Douglas-fir tussock moth, Orgyia pseudotsugata (Lepidoptera: Lymantriidae), in northern Idaho, USA. In these experiments, I reared healthy and infected larvae together on seedling Douglas-fir (Pseudotsuga menziesii), and used the number of healthy larvae that became infected as a measure of transmission. I explored the influences of density, stage structure, and spatial structure on transmission by manipulating the density and stage distribution of healthy and infected hosts, and the spatial distribution of infected hosts. The experiments indicate that transmission is strongly affected by the densities of both healthy and infected hosts, but the effect depends on the instar of each. Late instars are both more infectious and more likely to become infected than are early instars, so that the NPV is more likely to spread in populations of late-instar tussock moth larvae. I also found that transmission is affected by the spatial distribution of infected hosts, and this effect also depends on the instar of healthy hosts. That is, transmission to healthy early instars decreases with increasing patchiness of infected hosts, but transmission to healthy late instars is essentially unaffected by patchiness. I discuss how these results can be in- terpreted in terms of behavioral differences among instars, and relate the results to the mathematical theory of disease and the use of viruses in biological pest control.

Virus transmission in gypsy moths is not a simple mass action process

We used the nuclear polyhedrosis virus (LdNPV) of the gypsy moth, Ly- mantria dispar (Lepidoptera: Lymantriidae), to test one of the basic assumptions of most models of disease dynamics, that the rate of horizontal transmission is directly proportional to the product of the densities of healthy larvae and virus. To do this we made measurements of virus transmission, using small-scale experiments in bags on red oak (Quercus rubra) foliage and field data on naturally occurring populations from a previous study. We observed a decline in the transmission constant as the densities of both healthy larvae and pathogen increased, indicating that the rate of disease transmission is not directly proportional to the product of these variables.

Density dependence and spatial structure in the dynamics of insect pathogens

Many forest-defoliating Lepidoptera exhibit long-term cyclic fluctuations in density that span several orders of magnitude. One hypothesis to explain these fluctuations is that they are driven by pathogens with long-lived infectious stages capable of surviving outside the host. The basis of the argument is that, for realistic parameter values, a mathematical disease model incorporating such an infectious stage is likely to show cycles with the same period as is observed in nature. The mathematical model used to make this argument, however, is so simple that it may not be biologically meaningful. In this article, I extend the original model by including two realistic complications: density-dependent host reproduction and host movement behavior. Including density-dependent host reproduction greatly increases the likelihood of cycles; additional realism thus strengthens the original conclusion. Including host movement behavior makes the model more versatile, as it allows comparison of the model output with literature data on the spatial spread of insect viruses. This comparison suggests that the spatial spread of the viruses of Gilpinia hercyniae and Oryctes rhinoceros can be explained with a very simple model of host movement, without recourse to complicated mechanisms of dispersal. The introduction of host movement behavior also introduces the possibility of cycles of outbreaks in space and time simultaneously-that is, waves of disease that will reappear at regular intervals.