Bret D. Elderd

Uncertainty in predictions of disease spread and public health responses to bioterrorism and emerging diseases

Concerns over bioterrorism and emerging diseases have led to the widespread use of epidemic models for evaluating public health strategies. Partly because epidemic models often capture the dynamics of prior epidemics remarkably well, little attention has been paid to how uncertainty in parameter estimates might affect model predictions. To understand such effects, we used Bayesian statistics to rigorously estimate the uncertainty in the parameters of an epidemic model, focusing on smallpox bioterrorism. We then used a vaccination model to translate the uncertainty in the model parameters into uncertainty in which of two vaccination strategies would provide a better response to bioterrorism, mass vaccination, or vaccination of social contacts, so-called “trace vaccination.” Our results show that the uncertainty in the model parameters is remarkably high and that this uncertainty has important implications for vaccination strategies. For example, under one plausible scenario, the most likely outcome is that mass vaccination would save ≈100,000 more lives than trace vaccination. Because of the high uncertainty in the parameters, however, there is also a substantial probability that mass vaccination would save 200,000 or more lives than trace vaccination. In addition to providing the best response to the most likely outcome, mass vaccination thus has the advantage of preventing outcomes that are only slightly less likely but that are substantially more horrific. Rigorous estimates of uncertainty thus can reveal hidden advantages of public health strategies, suggesting that formal uncertainty estimation should play a key role in planning for epidemics.

Host‐Pathogen Interactions, Insect Outbreaks, and Natural Selection for Disease Resistance

The theory of insect population dynamics has shown that heterogeneity in natural‐enemy attack rates is strongly stabilizing. We tested the usefulness of this theory for outbreaking insects, many of which are attacked by infectious pathogens. We measured heterogeneity among gypsy moth larvae in their risk of infection with a nucleopolyhedrovirus, which is effectively heterogeneity in the pathogen’s attack rate. Our data show that heterogeneity in infection risk in this insect is so high that it leads to a stable equilibrium in the models, which is inconsistent with the outbreaks seen in North American gypsy moth populations. Our data further suggest that infection risk declines after epidemics, in turn suggesting that the model assumption of constant infection risk is incorrect. We therefore constructed an alternative model in which natural selection drives fluctuations in infection risk, leading to reductions after epidemics because of selection for resistance and increases after epidemics because of a cost of resistance. This model shows cycles even for high heterogeneity, and experiments confirm that infection risk is indeed heritable. The model is very general, and so we argue that natural selection for disease resistance may play a role in many insect outbreaks.

Host behaviour and exposure risk in an insect–pathogen interaction

1. Studies of variability in host resistance to disease generally emphasize variability in susceptibility given exposure, neglecting the possibility that hosts may vary in behaviours that affect the risk of exposure. 2. In many insects, horizontal transmission of baculoviruses occurs when larvae consume foliage contaminated by the cadavers of virus-infected conspecific larvae; so, host behaviour may have a strong effect on the risk of infection. 3. We studied variability in the behaviour of gypsy moth (Lymantria dispar) larvae, which are able to detect and avoid virus-contaminated foliage. 4. Our results show that detection ability can be affected by the family line that larvae originate from, even at some distance from a virus-infected cadaver, and suggest that cadaver-detection ability may be heritable. 5. There is thus the potential for natural selection to act on cadaver-detection ability, and thereby to affect the dynamics of pathogen-driven cycles in gypsy moth populations. 6. We argue that host behaviour is a neglected component in studies of variability in disease resistance.

Pathogen Persistence in the Environment and Insect-Baculovirus Interactions: Disease-Density Thresholds, Epidemic Burnout, and Insect Outbreaks

Classical epidemic theory focuses on directly transmitted pathogens, but many pathogens are instead transmitted when hosts encounter infectious particles. Theory has shown that for such diseases pathogen persistence time in the environment can strongly affect disease dynamics, but estimates of persistence time, and consequently tests of the theory, are extremely rare. We consider the consequences of persistence time for the dynamics of the gypsy moth baculovirus, a pathogen transmitted when larvae consume foliage contaminated with particles released from infectious cadavers. Using field-transmission experiments, we are able to estimate persistence time under natural conditions, and inserting our estimates into a standard epidemic model suggests that epidemics are often terminated by a combination of pupation and burnout rather than by burnout alone, as predicted by theory. Extending our models to allow for multiple generations, and including environmental transmission over the winter, suggests that the virus may survive over the long term even in the absence of complex persistence mechanisms, such as environmental reservoirs or covert infections. Our work suggests that estimates of persistence times can lead to a deeper understanding of environmentally transmitted pathogens and illustrates the usefulness of experiments that are closely tied to mathematical models.

Induced plant defenses, host–pathogen interactions, and forest insect outbreaks

Significance Many forest insects undergo outbreaks, in which their densities rise from undetectable to extremely high. Outbreaks are widely assumed to be driven by specialist natural enemies such as infectious pathogens, but gypsy moth outbreaks show alternating severe and mild outbreaks in forests with a high percentage of oaks, a pattern that cannot be explained by host-pathogen models. We used an experiment to show that induced defenses in red oak reduce heterogeneity among gypsy moth larvae in the risk of virus infection, and extending standard models to allow for this effect produces alternating outbreaks, matching the data. The ability of our model to reproduce this complex pattern suggests that the role of induced defenses in insect outbreaks has been underestimated. Cyclic outbreaks of defoliating insects devastate forests, but their causes are poorly understood. Outbreak cycles are often assumed to be driven by density-dependent mortality due to natural enemies, because pathogens and predators cause high mortality and because natural-enemy models reproduce fluctuations in defoliation data. The role of induced defenses is in contrast often dismissed, because toxic effects of defenses are often weak and because induced-defense models explain defoliation data no better than natural-enemy models. Natural-enemy models, however, fail to explain gypsy moth outbreaks in North America, in which outbreaks in forests with a higher percentage of oaks have alternated between severe and mild, whereas outbreaks in forests with a lower percentage of oaks have been uniformly moderate. Here we show that this pattern can be explained by an interaction between induced defenses and a natural enemy. We experimentally induced hydrolyzable-tannin defenses in red oak, to show that induction reduces variability in a gypsy moth’s risk of baculovirus infection. Because this effect can modulate outbreak severity and because oaks are the only genus of gypsy moth host tree that can be induced, we extended a natural-enemy model to allow for spatial variability in inducibility. Our model shows alternating outbreaks in forests with a high frequency of oaks, and uniform outbreaks in forests with a low frequency of oaks, matching the data. The complexity of this effect suggests that detecting effects of induced defenses on defoliator cycles requires a combination of experiments and models.

THE IMPACT OF CHANGING FLOW REGIMES ON RIPARIAN VEGETATION AND THE RIPARIAN SPECIES MIMULUS GUTTATUS

Alteration of riparian stream flow through the damming of rivers and streams impacts not only river morphology but also the vegetation communities that exist within the confines of a rivers banks. To examine changes in vegetation community composition and structure resulting from human control of water flow, I conducted a series of surveys on dammed and undammed streams in the Eastern Sierra Nevada Mountains of California. These surveys documented that areas below dams contain increased leaf litter and grass thatch deposition, increased grass species coverage, and an altered community of existing forbs as compared to sites with naturally flowing streams. There was also an increased woody species canopy coverage as distance from the stream increased. To examine the proximal causes of damming on herbaceous plants, I set up a factorial field experiment examining the impact of grass thatch, shading, and herbivory on a common riparian species, Mimulus guttatus, the common monkeyflower. M. guttatus germination was decreased in the thatch augmentation plots and under artificial shading. For seedlings, shading increased final plant height and thatch increased herbivory. In plots where herbivory was not controlled by insecticide, M. guttatus plants grew smaller and had lower reproduction. I also repeated this experiment in a more controlled greenhouse environment using two seed sources and two levels of shading coverage. Results from this experiment largely confirm patterns seen in the field, but also revealed a strong interaction between shading and thatch treatments for both germination and growth. Overall, my results suggest that altering riparian stream flow may impact plant performance through a cascading set of biotic interactions, and that controlled releases from dams that mimic bankfull or greater discharge events may be required to restore these important and diverse communities by resetting disturbance rates.

Disturbance-mediated trophic interactions and plant performance

Disturbances, such as flooding, play important roles in determining community structure. Most studies of disturbances focus on the direct effects and, hence, the indirect effects of disturbances are poorly understood. Within terrestrial riparian areas, annual flooding leads to differences in the arthropod community as compared to non-flooded areas. In turn, these differences are likely to alter the survival, growth, and reproduction of plant species via an indirect effect of flooding (i.e., changes in herbivory patterns). To test for such effects, an experiment was conducted wherein arthropod predators and herbivores were excluded from plots in flooded and non-flooded areas and the impact on a common riparian plant, Mimulus guttatus was examined. In general, the direct effect of flooding on M. guttatus was positive. The indirect effects, however, significantly decreased plant survival for both years of the experiment, regardless of predator presence, because of an increased exposure to grasshoppers, the most abundant herbivore in the non-flooded sites. Leafhoppers, which were more abundant in the flooded sites, had much weaker and varying effects. During 2000, when the leafhopper herbivory was high, arthropod predators did not significantly reduce damage to plants. In 2001, the mean herbivory damage was lower and predators were able to significantly reduce overall leafhopper damage. The effects of predators on leafhoppers, however, did not increase plant survival, final weight, or the reproduction potential and, thus, did not initiate a species-level trophic cascade. Overall, it was the differences in the herbivore community that led to a significant decrease in plant survival. While flooding certainly alters riparian plant survival through direct abiotic effects, it also indirectly affects riparian plants by changing the arthropod community, in particular herbivores, and hence trophic interactions.

Warmer temperatures increase disease transmission and outbreak intensity in a host–pathogen system

While rising global temperatures are increasingly affecting both species and their biotic interactions, the debate about whether global warming will increase or decrease disease transmission between individuals remains far from resolved. This may stem from the lack of empirical data. Using a tractable and easily manipulated insect host-pathogen system, we conducted a series of field and laboratory experiments to examine how increased temperatures affect disease transmission using the crop-defoliating pest, the fall armyworm (Spodoptera frugiperda) and its species-specific baculovirus, which causes a fatal infection. To examine the effects of temperature on disease transmission in the field, we manipulated baculovirus density and temperature. As infection occurs when a host consumes leaf tissue on which the pathogen resides, baculovirus density was controlled by placing varying numbers of infected neonate larvae on experimental plants. Temperature was manipulated by using open-top chambers (OTCs). The laboratory experiments examined how increased temperatures affect fall armyworm feeding and development rates, which provide insight into how host feeding behaviour and physiology may affect transmission. Disease transmission and outbreak intensity, measured as the cumulative fraction infected during an epizootic, increased at higher temperatures. However, there was no appreciable change in the mean transmission rate of the disease, which is often the focus of empirical and theoretical research. Instead, the coefficient of variation (CV) associated with the transmission rate shrunk. As the CV decreased, heterogeneity in disease risk across individuals declined, which resulted in an increase in outbreak intensity. In the laboratory, increased temperatures increased feeding rates and decreased developmental times. As the host consumes the virus along with the leaf tissue on which it resides, increased feeding rate is likely to increase the probability of an individual consuming virus-infected leaf tissue. On the other hand, decreased developmental time increases the sloughing of midgut cells, which is predicted to hinder viral infection. Increases in outbreak intensity or epizootic severity, as the climate warms, may lead to changes in the long-term dynamics of pests whose populations are strongly affected by host-pathogen interactions. Overall, this work demonstrates that the usual assumptions governing these effects, via changes in the mean transmission rate alone, may not be correct.

Quantifying demographic uncertainty: Bayesian methods for integral projection models

Integral projection models (IPMs) are a powerful and popular approach to modeling population dynamics. Generalized linear models form the statistical backbone of an IPM. These models are typically fit using a frequentist approach. We suggest that hierarchical Bayesian statistical approaches offer important advantages over frequentist methods for building and interpreting IPMs, especially given the hierarchical nature of most demographic studies. Using a stochastic IPM for a desert cactus based on a 10-year study as a worked example, we highlight the application of a Bayesian approach for translating uncertainty in the vital rates (e.g., growth, survival, fertility) to uncertainty in population-level quantities derived from them (e.g., population growth rate). The best-fit demographic model, which would have been difficult to fit under a frequentist framework, allowed for spatial and temporal variation in vital rates and correlated responses to temporal variation across vital rates. The corresponding poste...

Effects of biological control on long‐term population dynamics: identifying unexpected outcomes

Summary 1. Attempts to control natural systems through management have often met with success but have also led to unexpected and often undesirable outcomes. Unfortunately, the ultimate result of such management programmes may not be apparent until long after the control efforts have begun. This is particularly true for forest-defoliating species that exhibit longperiod cycles such as the invasive gypsy moth Lymantria dispar, which causes widespread damage in some years but is rare in other years. 2. We studied the effects of two commonly employed biocontrol agents on gypsy moth dynamics using a series of field-tested and empirically parameterized mathematical models, which allowed us to examine various potential control strategies and assess long-term effects. 3. In a non-spatial model, addition of either a manufactured version of the same baculovirus involved in natural epizootics, or a general bioinsecticide Bacillus thuringiensis var. kurstaki (Btk), which directly kills a fraction of the population, decreases the amplitude between boom and bust portions of the cycle. 4. However, ill-planned biocontrol applications can result in increased gypsy moth densities over the long term. Thus, control efforts may maintain pest populations at unexpectedly high numbers, which could result in constant forest defoliation. 5. In a spatial two-patch model, where one patch is sprayed and the other is left untreated, there is also considerable danger that migration between patches may drive the unsprayed population to levels that could result in constant forest defoliation. 6. Synthesis and applications: Perturbations to host–pathogen systems may have unexpected results, driving and maintaining populations at multiple levels including those far from desired management goals. It is often assumed that any control strategy that decreases pest populations in the short term is beneficial, but our results show that undesirable outcomes may often occur. The mechanisms we describe apply to many systems that undergo population cycles or outbreaks regulated by density-dependent processes, and in which disease or pesticide application is used for pest control. We suggest that successful management strategies should closely monitor population responses immediately following the control application to ensure that pest populations are not being maintained at artificially high levels compared with historic data.