Exploring how ecological and epidemiological processes shape multi-host disease dynamics using global sensitivity analysis.

We use global sensitivity analysis (specifically, Partial Rank Correlation Coefficients) to explore the roles of ecological and epidemiological processes in shaping the temporal dynamics of a parameterized SIR-type model of two host species and an environmentally transmitted pathogen. We compute the sensitivities of disease prevalence in each host species to model parameters. Sensitivity rankings are calculated, interpreted biologically, and contrasted for cases where the pathogen is introduced into a disease-free community and cases where a second host species is introduced into an endemic single-host community. In some cases the magnitudes and dynamics of the sensitivities can be predicted only by knowing the host species' characteristics (i.e., their competitive abilities and disease competence) whereas in other cases they can be predicted by factors independent of the species' characteristics (specifically, intraspecific versus interspecific processes or a species' roles of invader versus resident). For example, when a pathogen is initially introduced into a disease-free community, disease prevalence in both hosts is more sensitive to the burst size of the first host than the second host. In comparison, disease prevalence in each host is more sensitive to its own infection rate than the infection rate of the other host species. In total, this study illustrates that global sensitivity analysis can provide useful insight into how ecological and epidemiological processes shape disease dynamics and how those effects vary across time and system conditions. Our results show that sensitivity analysis can provide quantification and direction when exploring biological hypotheses.

Exploring How a Generalist Pathogen and Within-Host Priority Effects Alter the Risk of Being Infected by a Specialist Pathogen.

AbstractIn multihost-multipathogen communities, a focal host's risk of being infected by a particular pathogen can be influenced by the presence of other host and pathogen species. We explore how indirect interactions between pathogens at the within-host level (through coinfecting the same individual) and the between-host level (through altered susceptible host densities) affect the focal host's risk of infection. We use an SI-type epidemiological model of two host species and two environmentally transmitted pathogens where one pathogen is a specialist on the focal host and the other pathogen is a generalist. We show that monotonic, unimodal, and U-shaped relationships between the specialist and generalist infectious propagule densities (proxies of the focal host's risk of infection) are driven by the way within-host priority effects alter the production of specialist infectious propagules by infected focal host individuals. Interestingly, within-host priority effects can also lead to overcompensation in density wherein increased infected host mortality results in greater specialist infectious propagule density. We interpret these results in terms of how the focal host's risk of being infected by a specialist pathogen is affected by the presence of a generalist pathogen, its alternative host, and within-host priority effects.

Evolutionary and Plastic Phenotypic Change Can Be Just as Fast as Changes in Population Densities.

AbstractEvolution and plasticity can drive population-level phenotypic change (e.g., changes in the mean phenotype) on timescales comparable to changes in population densities. However, it is unclear whether phenotypic change has the potential to be just as fast as changes in densities or whether comparable rates of change occur only when densities are changing slow enough for phenotypes to keep pace. Moreover, it is unclear whether this depends on the mode of adaptation. Using scaling theory and fast-slow dynamical systems theory, we develop a method for comparing maximum rates of density and phenotypic change estimated from population-level time-series data. We apply our method to 30 published empirical studies where changes in morphological traits are caused by evolution, plasticity, or an unknown combination. For every study, the maximum rate of phenotypic change was between 0.5 and 2.5 times faster than the maximum rate of change in density. Moreover, there were no systematic differences between systems with different modes of adaptation. Our results show that plasticity and evolution can drive phenotypic change just as fast as changes in densities. We discuss the implications of our results in terms of the strengths of feedbacks between population densities and traits.

The Context-Dependent Effects of Host Competence, Competition, and Pathogen Transmission Mode on Disease Prevalence.

AbstractBiodiversity in communities is changing globally, including the gain and loss of host species in host-pathogen communities. Increased host diversity can cause infection prevalence in a focal host to increase (amplification) or decrease (dilution). However, it is unclear what general rules govern the context-dependent effects, in part because theories for pathogens with different transmission modes have developed largely independently. Using a two-host model, we explore how the pathogen transmission mode and characteristics of a second host (disease competence and competitive ability) influence disease prevalence in a focal host. Our work shows how the theories for pathogens with environmental transmission, density-dependent direct transmission, and frequency-dependent direct transmission can be unified. Our work also identifies general rules about how host and pathogen characteristics affect amplification/dilution. For example, higher-competence hosts promote amplification, unless they are strong interspecific competitors; strong interspecific competitors promote dilution, unless they are large sources of new infections; and dilution occurs under frequency-dependent direct transmission more than density-dependent direct transmission, unless interspecific host competition is sufficiently strong. Our work helps explain how the characteristics of the pathogen and a second host affect disease prevalence in a focal host.

Using sensitivity analysis to identify factors promoting higher versus lower infection prevalence in multi-host communities.

Relationships between host species richness and levels of disease in a focal host are likely to be context-dependent, depending on the characteristics of which particular host species are present in a community. I use a multi-host epidemiological model with environmental transmission to explore how the characteristics of the host species (e.g., competence and competitive ability), host density, and the pathogen transmission mechanism affect the proportion of infected individuals (i.e., infection prevalence) in a focal host. My sensitivity-based approach identifies the indirect pathways through which specific ecological and epidemiological processes affect focal host infection prevalence. This in turn yields predictions about the context-dependent rules governing whether increased host species richness increases (amplifies) or decreases (dilutes) infection prevalence in a focal host. For example, in many cases, amplification and dilution are predicted to occur when added host species are sources or sinks of infectious propagules, respectively. However, if the added host species have strong and asymmetric competitive effects on resident host species, then amplification and dilution are predicted to occur when the added host species have stronger competitive effects on resident host species that are sources or sinks of infectious propagules, respectively. My results also predict that greater dilution and less amplification is more likely to occur under frequency-dependent direct transmission than density-dependent direct transmission when (i) the added hosts have lower competence than resident host species and (ii) interspecific competition between the added host species and resident host species is lower; the opposite conditions promote greater amplification and less dilution under frequency-dependent direct transmission. This work helps identify and explain the mechanisms shaping the context-dependent relationships between host species richness and disease in multi-host communities.

Comparing the Indirect Effects between Exploiters in Predator-Prey and Host-Pathogen Systems.

AbstractIn multipredator and multipathogen systems, exploiters interact indirectly via shared victim species. Interspecific prey competition and the degree of predator specialization are known to influence whether predators have competitive (i.e., (-,-)) or noncompetitive (i.e., (-,+) or (+,+)) indirect interactions. Much less is known about the population-level indirect interactions between pathogens that infect the same populations of host species. In this study, we use two-predator-two-prey and two-host-two-pathogen models to compare the indirect effects between predators with the indirect effects between pathogens. We focus on how the indirect interactions between pathogens are affected by the competitive abilities of susceptible and infected hosts, whether the pathogens are specialists or generalists, and the transmission pathway (direct vs. environmental transmission). In many cases, indirect effects between pathogens and predators follow similar patterns, for example, more positive indirect effects with increased interspecific competition between victim species. However, the indirect effects between pathogens can qualitatively differ, for example, more negative indirect effects with increased interspecific host competition. These contrasting patterns show that an important mechanistic difference between predatory and parasitic interactions (specifically, whether interactions are immediately lethal) can have important population-level effects on the indirect interactions between exploiters.

Destabilizing evolutionary and eco-evolutionary feedbacks drive empirical eco-evolutionary cycles.

We develop a method to identify how ecological, evolutionary, and eco-evolutionary feedbacks influence system stability. We apply our method to nine empirically parametrized eco-evolutionary models of exploiter-victim systems from the literature and identify which particular feedbacks cause some systems to converge to a steady state or to exhibit sustained oscillations. We find that ecological feedbacks involving the interactions between all species and evolutionary and eco-evolutionary feedbacks involving only the interactions between exploiter species (predators or pathogens) are typically stabilizing. In contrast, evolutionary and eco-evolutionary feedbacks involving the interactions between victim species (prey or hosts) are destabilizing more often than not. We also find that while eco-evolutionary feedbacks rarely altered system stability from what would be predicted from just ecological and evolutionary feedbacks, eco-evolutionary feedbacks have the potential to alter system stability at faster or slower speeds of evolution. As the number of empirical studies demonstrating eco-evolutionary feedbacks increases, we can continue to apply these methods to determine whether the patterns we observe are common in other empirical communities.

Predator-Prey Coevolution Drives Productivity-Richness Relationships in Planktonic Systems.

The relationship between environmental productivity and species richness often varies among empirical studies, and despite much research, simple explanations for this phenomenon remain elusive. We investigated how phytoplankton and zooplankton coevolution shapes productivity-richness relationships in both phytoplankton and zooplankton, using a simple nutrient-phytoplankton-zooplankton model that incorporates size-dependent metabolic rates summarized from empirical studies. The model allowed comparisons of evolved species richness across productivity levels and at different evolutionary times. Our results show that disruptive selection leads to evolutionary branching of phytoplankton and zooplankton. Both the time required for evolutionary branching and the number of evolved species in phytoplankton and zooplankton tend to increase with productivity, producing a transient unimodal or positive productivity-richness relationship but followed by a positive productivity-richness relationship for both groups over long enough evolutionary time. Our findings suggest that coevolution between phytoplankton and zooplankton can drive the two common forms (unimodal and positive) of productivity-richness relationships in nature.

The Effects of Predator Evolution and Genetic Variation on Predator-Prey Population-Level Dynamics.

This paper explores how predator evolution and the magnitude of predator genetic variation alter the population-level dynamics of predator-prey systems. We do this by analyzing a general eco-evolutionary predator-prey model using four methods: Method 1 identifies how eco-evolutionary feedbacks alter system stability in the fast and slow evolution limits; Method 2 identifies how the amount of standing predator genetic variation alters system stability; Method 3 identifies how the phase lags in predator-prey cycles depend on the amount of genetic variation; and Method 4 determines conditions for different cycle shapes in the fast and slow evolution limits using geometric singular perturbation theory. With these four methods, we identify the conditions under which predator evolution alters system stability and shapes of predator-prey cycles, and how those effect depend on the amount of genetic variation in the predator population. We discuss the advantages and disadvantages of each method and the relations between the four methods. This work shows how the four methods can be used in tandem to make general predictions about eco-evolutionary dynamics and feedbacks.

Coevolution can reverse predator-prey cycles.

A hallmark of Lotka-Volterra models, and other ecological models of predator-prey interactions, is that in predator-prey cycles, peaks in prey abundance precede peaks in predator abundance. Such models typically assume that species life history traits are fixed over ecologically relevant time scales. However, the coevolution of predator and prey traits has been shown to alter the community dynamics of natural systems, leading to novel dynamics including antiphase and cryptic cycles. Here, using an eco-coevolutionary model, we show that predator-prey coevolution can also drive population cycles where the opposite of canonical Lotka-Volterra oscillations occurs: predator peaks precede prey peaks. These reversed cycles arise when selection favors extreme phenotypes, predator offense is costly, and prey defense is effective against low-offense predators. We present multiple datasets from phage-cholera, mink-muskrat, and gyrfalcon-rock ptarmigan systems that exhibit reversed-peak ordering. Our results suggest that such cycles are a potential signature of predator-prey coevolution and reveal unique ways in which predator-prey coevolution can shape, and possibly reverse, community dynamics.

How the Magnitude of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics.

Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary subsystems as well as the interactions between those subsystems. My results show that with low genetic variation, the cyclic dynamics and stability of the system are determined by the ecological subsystem. With increased genetic variation, disruptive selection always destabilizes stable communities, stabilizing selection can stabilize or destabilize communities, and prey evolution can alter predator-prey phase lags. Stability changes occur approximately when the magnitude of genetic variation balances the (in)stabilities of the ecological and evolutionary subsystems. I discuss the connections between my stability results and prior results from the theory of adaptive dynamics.

Population Density, Not Host Competence, Drives Patterns of Disease in an Invaded Community.

Generalist parasites can strongly influence interactions between native and invasive species. Host competence can be used to predict how an invasive species will affect community disease dynamics; the addition of a highly competent, invasive host is predicted to increase disease. However, densities of invasive and native species can also influence the impacts of invasive species on community disease dynamics. We examined whether information on host competence alone could be used to accurately predict the effects of an invasive host on disease in native hosts. We first characterized the relative competence of an invasive species and a native host species to a native parasite. Next, we manipulated species composition in mesocosms and found that host competence results did not accurately predict community dynamics. While the invasive host was more competent than the native, the presence of the native (lower competence) host increased disease in the invasive (higher competence) host. To identify potential mechanisms driving these patterns, we analyzed a two-host, one-parasite model parameterized for our system. Our results demonstrate that patterns of disease were primarily driven by relative population densities, mediated by asymmetry in intra- and interspecific competition. Thus, information on host competence alone may not accurately predict how an invasive species will influence disease in native species.

Hydra effects in stable communities and their implications for system dynamics.

A hydra effect occurs when the mean density of a species increases in response to greater mortality. We show that, in a stable multispecies system, a species exhibits a hydra effect only if maintaining that species at its equilibrium density destabilizes the system. The stability of the original system is due to the responses of the hydra-effect species to changes in the other species' densities. If that dynamical feedback is removed by fixing the density of the hydra-effect species, large changes in the community make-up (including the possibility of species extinction) can occur. This general result has several implications: (1) Hydra effects occur in a much wider variety of species and interaction webs than has previously been described, and may occur for multiple species, even in small webs; (2) conditions for hydra effects caused by predators (or diseases) often differ from those caused by other mortality factors; (3) introducing a specialist or a switching predator of a hydra-effect species often causes large changes in the community, which frequently involve extinction of other species; (4) harvest policies that attempt to maintain a constant density of a hydra-effect species may be difficult to implement, and, if successful, are likely to cause large changes in the densities of other species; and (5) trophic cascades and other indirect effects caused by predators of hydra-effect species can exhibit amplification of effects or unexpected directions of change. Although we concentrate on systems that are originally stable and models with no stage-structure or trait variation, the generality of our result suggests that similar responses to mortality will occur in many systems without these simplifying assumptions. In addition, while hydra effects are defined as responses to altered mortality, they also imply counterintuitive responses to changes in immigration and other parameters affecting population growth.

Hydra effects in discrete-time models of stable communities.

A species exhibits a hydra effect when, counter-intuitively, increased mortality of the species causes an increase in its abundance. Hydra effects have been studied in many continuous time (differential equation) multispecies models, but only rarely have hydra effects been observed in or studied with discrete time (difference equation) multispecies models. In addition most discrete time theory focuses on single-species models. Thus, it is unclear what unifying characteristics determine when hydra effects arise in discrete time models. Here, using discrete time multispecies models (where total abundance is the single variable describing each population), I show that a species exhibits a hydra effect in a stable system only when fixing that species' density at its equilibrium density destabilizes the system. This general characteristic is referred to as subsystem instability. I apply this result to two-species models and identify specific mechanisms that cause hydra effects in stable communities, e.g., in host--parasitoid models, host Allee effects and saturating parasitoid functional responses can cause parasitoid hydra effects. I discuss how the general characteristic can be used to identify mechanisms causing hydra effects in communities with three or more species. I also show that the condition for hydra effects at stable equilibria implies the system is reactive (i.e., density perturbations can grow before ultimately declining). This study extends previous work on conditions for hydra effects in single-species models by identifying necessary conditions for stable systems and sufficient conditions for cyclic systems. In total, these results show that hydra effects can arise in many more communities than previously appreciated and that hydra effects were present, but unrecognized, in previously studied discrete time models.

The virus of my virus is my friend: ecological effects of virophage with alternative modes of coinfection.

Virophages are viruses that rely on the replication machinery of other viruses to reproduce within eukaryotic hosts. Two different modes of coinfection have been posited based on experimental observation. In one mode, the virophage and the virus enter the host independently. In the other mode, the virophage adheres to the virus so both virophage and virus enter the host together. Here we ask: what are the ecological effects of these different modes of coinfection? In particular, what ecological effects are common to both infection modes, and what are the differences particular to each mode? We develop a pair of biophysically motivated ODE models of viral-host population dynamics, corresponding to dynamics arising from each mode of infection. We find that both modes of coinfection allow for the coexistence of the virophage, virus, and host either at a stable fixed point or through cyclical dynamics. In both models, virophage tends to be the most abundant population and their presence always reduces the viral abundance and increases the host abundance. However, we do find qualitative differences between models. For example, via extensive sampling of biologically relevant parameter space, we only observe bistability when the virophage and the virus enter the host together. We discuss how such differences may be leveraged to help identify modes of infection in natural environments from population level data.

Distinguishing between indirect and direct modes of transmission using epidemiological time series.

Pathogen transmission can involve direct and/or indirect pathways. Using theoretical models, in this study we ask, "do directly and indirectly transmitted pathogens yield different population-level epidemiological dynamics?" and "can the transmission pathway be inferred from population-level epidemiological data?" Our approach involves comparing the continuous-time dynamics of a class of compartmental epidemiological models with direct versus environmentally mediated indirect transmission pathways. Combing analytical theory and numerical simulations we show that models with direct and indirect transmission can produce quantitatively similar time series when the pathogen cannot reproduce in the environment, particularly when the environmental pathogen dynamics are fast. We apply these results to a previous study on chronic wasting disease and show that identifying the transmission pathway is more difficult than previously acknowledged. Our analysis and simulations also yield conditions under which numerical differences can potentially identify the transmission route in oscillating endemic systems and systems where the environmental pathogen dynamics are not fast. This work begins to identify how differences in the transmission pathway can result in quantitatively different epidemiological dynamics and how those differences can be used to identify the transmission pathway from population level time series.

Mechanisms of multi-strain coexistence in host-phage systems with nested infection networks.

Bacteria and their viruses (bacteriophages) coexist in natural environments forming complex infection networks. Recent empirical findings suggest that phage-bacteria infection networks often possess a nested structure such that there is a hierarchical relationship among who can infect whom. Here we consider how nested infection networks may affect phage and bacteria dynamics using a multi-type Lotka-Volterra framework with cross-infection. Analysis of similar models has, in the past, assumed simpler interaction structures as a first step towards tractability. We solve the proposed model, finding trade-off conditions on the life-history traits of both bacteria and viruses that allow coexistence in communities with nested infection networks. First, we find that bacterial growth rate should decrease with increasing defense against infection. Second, we find that the efficiency of viral infection should decrease with host range. Next, we establish a relationship between relative densities and the curvature of life history trade-offs. We compare and contrast the current findings to the "Kill-the-Winner" model of multi-species phage-bacteria communities. Finally, we discuss a suite of testable hypotheses stemming from the current model concerning relationships between infection range, life history traits and coexistence in complex phage-bacteria communities.

When does pathogen evolution maximize the basic reproductive number in well-mixed host-pathogen systems?

Pathogen evolution towards the largest basic reproductive number, R0, has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host-pathogen systems have defined general conditions under which R0 maximization occurs in terms of R0 itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host-pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes R0. Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when R0 maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent R0 maximization.

A healthy but depleted herd: Predators decrease prey disease and density.

The healthy herds hypothesis proposes that predators can reduce parasite prevalence and thereby increase the density of their prey. However, evidence for such predator-driven reductions in the prevalence of prey remains mixed. Furthermore, even less evidence supports increases in prey density during epidemics. Here, we used a planktonic predator-prey-parasite system to experimentally test the healthy herds hypothesis. We manipulated density of a predator (the phantom midge, Chaoborus punctipennis) and parasitism (the virulent fungus Metschnikowia bicuspidata) in experimental assemblages. Because we know natural populations of the prey (Daphnia dentifera) vary in susceptibility to both predator and parasite, we stocked experimental populations with nine genotypes spanning a broad range of susceptibility to both enemies. Predation significantly reduced infection prevalence, eliminating infection at the highest predation level. However, lower parasitism did not increase densities of prey; instead, prey density decreased substantially at the highest predation levels (a major density cost of healthy herds predation). This density result was predicted by a model parameterized for this system. The model specifies three conditions for predation to increase prey density during epidemics: (i) predators selectively feed on infected prey, (ii) consumed infected prey release fewer infectious propagules than unconsumed prey, and (iii) sufficiently low infection prevalence. While the system satisfied the first two conditions, prevalence remained too high to see an increase in prey density with predation. Low prey densities caused by high predation drove increases in algal resources of the prey, fueling greater reproduction, indicating that consumer-resource interactions can complicate predator-prey-parasite dynamics. Overall, in our experiment, predation reduced the prevalence of a virulent parasite but, at the highest levels, also reduced prey density. Hence, while healthy herds predation is possible under some conditions, our empirical results make it clear that the manipulation of predators to reduce parasite prevalence may harm prey density.