Lethal pathogens, non-lethal synergists and the evolutionary ecology of resistance

Mixed pathogenic infections are known to have profound effects on the ecological and evolutionary diversity of both hosts and parasites. Although a variety of mechanisms have been proposed by which hosts can withstand parasitic infections, the role of multiple infections and the trade-off in multiple defence strategies remain relatively unexplored. We develop a stage-structured host-pathogen model to explore the ecological and evolutionary dynamics of host resistance to different modes of infection. In particular, we investigate how the evolution of resistance is influenced through infection by a lethal pathogen and a non-lethal synergist (that only acts to enhance the infectivity of the pathogen). We extend our theoretical framework to explore how trade-offs in the ability to withstand infection by the lethal pathogen and the ability to tolerate the synergist affect the likelihood of coexistence and the evolution of polymorphic host strategies. We show how the underlying structure of the trade-off surface is crucial in the maintenance of resistance polymorphisms. Further, depending on the shape of the trade-off surface, we predict that different levels of host resistance will show individual responses to the presence of non-lethal synergists. Our results are discussed in the wider context of recent developments in understanding the evolution of resistance to pathogen infections and resistance management.     

Mathematical modeling of bacterial virulence and host-pathogen interactions in the Dictyostelium/Pseudomonas system

We present some studies on the mechanisms of pathogenesis based on experimental work and on its interpretation through a mathematical model. Using a collection of clinical strains of the opportunistic human pathogen Pseudomonas aeruginosa, we performed co-culture experiments with Dictyostelium amoebae, to investigate the two organisms’ interaction, characterized by a cross action between amoeba, feeding on bacteria, and bacteria exerting their pathogenic action against amoeba. In order to classify bacteria virulence, independently of this cross interaction, we have also performed killing experiments of bacteria against the nematode Caenorhabditis elegans.A mathematical model was developed to infer how the populations of the amoeba-bacteria system evolve according to a number of parameters, taking into account the specific features underlying the interaction. The model does not fall within the class of traditional prey-predator models because not only does an amoeba feed on bacteria, but also it is in turn attacked by them; thus the model must include a feedback term modeling this further interaction aspect. The model shows the existence of multiple steady states and the resulting behavior of the solutions, showing bi-stability of the system, gives a qualitative explanation of the co-culture experiments.     

The influence of habitat heterogeneity on host-pathogen population dynamics

The influence of spatial heterogeneity on the population dynamics of a naturally occurring invertebrate host-pathogen system was experimentally investigated. At ten week intervals over a two year period, I quantified the spatial distribution of natural populations of the terrestrial isopod crustacean Porcellio scaber infected with the isopod iridescent virus (IIV). During the seasonally dry periods of summer and early fall in central California, isopod populations were highly aggregated and the degree of patchiness and distance between inhabited patches was greatest. Coincident with increased patchiness and patch spacing was an increase in isopod density within patches. During the wet seasons of winter and spring, isopod population patchiness, inter-patch spacing, and within-patch density was low. Seasonal changes in virus prevalence were negatively correlated with within-patch density, patchiness, and inter-patch spacing. The influence of the spatial distribution of isopods on virus prevalence was also tested in field experiments. The virus was introduced into arrays of artificial habitat patches colonized by isopods in which interpatch distance was varied. The prevalence of resulting infections was monitored at weekly intervals. In addition, dispersal rates between artificial patches and natural patches were quantified and compared. The results showed that isopods in treatments with the smallest inter-patch spacing had the highest virus prevalence, with generally lower prevalence among isopods in more widely spaced patches. The spacing of experimental patches significantly affected virus prevalence, although the experiments did not resolve a clear relationship between patch spacing and virus prevalence. Rates of dispersal between patches decreased with increased patch spacing, and these rates did not differ significantly from dispersal between natural patches. The results suggest that rates of dispersal between isopod subpopulations may be an important component of the infection dynamics in this system. I discuss the consequences of these findings for host-pathogen dynamics in fragmented habitats, and for other ecological interactions in spatially heterogeneous habitats.     

The evolutionary consequences of plasticity in host-pathogen interactions

Interactions between individuals such as hosts and pathogens are often characterized by substantial phenotypic plasticity. Pathogens sometimes alter their exploitation strategies in response to defensive strategies adopted by their host and vice versa. Nevertheless, most game-theoretic models developed to explain the evolution of pathogen and host characteristics assume that no such plasticity occurs. Allowing for phenotypic plasticity in these models is difficult because one must focus on the evolution of pathogen and host reaction norms, and then allow for the potentially indefinite reciprocal changes in pathogen and host behaviour that occur during an infection as a result of their interacting reaction norms. Here, we begin to address these issues for a simple host-pathogen system in which the pathogen exhibits a level of virulence and the host exhibits a level of immune clearance. We find, quite generally, that plasticity promotes the evolution of higher levels of cooperation, in this case leading to reduced levels of both virulence and clearance.     

Effects of predation on host-pathogen dynamics in SIR models

The integration of infectious disease epidemiology with community ecology is an active area of research. Recent studies using SI models without acquired immunity have demonstrated that predation can suppress infectious disease levels. The authors recently showed that incorporating immunity (SIR models) can produce a “hump”-shaped relationship between disease prevalence and predation pressure; thus, low to moderate levels of predation can boost prevalence in hosts with acquired immunity. Here we examine the robustness of this pattern to realistic extensions of a basic SIR model, including density-dependent host regulation, predator saturation, interference, frequency-dependent transmission, predator numerical responses, and explicit resource dynamics. A non-monotonic relationship between disease prevalence and predation pressure holds across all these scenarios. With saturation, there can also be complex responses of mean host abundance to increasing predation, as well as bifurcations leading to unstable cycles (epidemics) and pathogen extinction at larger predator numbers. Firm predictions about the relationship between prevalence and predation thus require one to consider the complex interplay of acquired immunity, host regulation, and foraging behavior of the predator.     

Phenotypic variation,sexual reproduction and evolutionary population dynamics

I studied the effects of introducing phenotypic variation into a well-known single species model for a population with discrete, non-overlapping generations. The phenotypes differed in their dynamic behaviour. The analysis was made under the assumption that the population was in an evolutionary stable state. Differences in the timing of the competitive impacts of the phenotypes on each other had a strong simplifying effect on the dynamics. This result could also be applied to competition between species. The effect of sexual reproduction on the dynamics of the population was analysed by assuming the simplest genetic model of one locus with two alleles. Sexual reproduction made the system much more stable in the (mathematical) sense that the number of attractors was reduced and their basins of attraction enlarged. In a dominant system sex tended to increase the frequency of the recessive allele, and in an overdominant system it induced gene frequencies of 1/2. Whether the attractors in the dominant system tended to be simpler or more complex than the attractors in the asexual system depended on the phenotype of the recessive homozygote. The overdominant sexual system tended to have simpler dynamics than the corresponding asexual population. A 2-locus model was used to study whether sexuals can invade an asexual population and vice versa. One locus coded for sexual and asexual reproduction, while the other coded for the dynamics. Enhanced stability through sexual reproduction seemed to be the reason why there was a clear asymmetry favouring sex in this evolutionary context.     

The stability of host-pathogen interactions of plant disease in relation to biological weed control

A theoretical analysis was conducted to investigate the dynamics of plant-pathogen interactions for biological weed control. Computer simulation showed that the dynamics of plant-pathogen interactions can be determined by the properties of the pathogen. Pathogens with high levels of virulence may exist in nature in low frequencies due to high extinction rates. Pathogens of this type are suitable for the mycoherbicide strategy. Pathogens with a low level of virulence are frequent and may coexist stably with their host. Good candidates for the classical strategy may be the pathogens with intermediate pathogenicity, which maintain a stable interaction and a high control efficiency. The probability of extinction of a pathogen increases when pathogenicity is greater than a critical value at the intermediate range. The regulation of plant populations through reducing host reproductivity and increasing host mortality has similar results.     

The form of host density-dependence and the likelihood of host-pathogen cycles in forest-insect systems

Forest-insect systems frequently show cyclic dynamics which has been of considerable interest to both experimental and theoretical ecologists. One important issue has been the manner in which density-dependence acting on the host population through resource competition influences the likelihood of population cycles. Existing models make contradictory predictions. Here, we explore two models that allow different forms of density-dependence to be examined. We find that host density-dependence can influence the persistence of the host-pathogen interaction, the likelihood of population cycles and the stability of the host-pathogen interaction. In particular, over-compensatory density-dependence is likely to lead to host-pathogen cycles while under-compensatory density-dependence can promote stability. We discuss these differences with reference to the different forms of intraspecific competition and recent developments in insect population ecology.     

The impact of diffusion and stirring on the dynamics of interacting populations

We investigate the combined effects of diffusion and stirring on the dynamics of interacting populations which have spatial structure. Specifically we consider the marine phytoplankton and zooplankton populations, and model them as an excitable medium. The results are applicable to other biological and chemical systems. Under certain conditions the combination of diffusion and stirring is found to enhance the excitability, and hence population growth of the system. Diffusion is found to play an important role: too much and initial perturbations are smoothed away, too little and insufficient mixing takes place before the reaction is over. A key time-scale is the mix-down time, the time it takes for the spatial scale of a population to be reduced to that of a diffusively controlled filament. If the mix-down time is short compared to the reaction time-scale, then excitation of the system is suppressed. For intermediate values of the mix-down time the peak population can attain values many times that of a population without spatial structure. We highlight the importance of the spatial scale of the initial disturbance to the system.     

Realistic population dynamics in epidemiological models: the impact of population decline on the dynamics of childhood infectious diseases. Measles in Italy as an example

Most contributions in the field of mathematical modelling of childhood infectious diseases transmission dynamics have focused on stationary or exponentially growing populations. In this paper an epidemiological model with realistic demography is used to investigate the impact of the non-equilibrium conditions typical of the transition to sustained below replacement fertility (BRF) recently observed in a number of western countries, upon the transmission dynamics of measles. The results depend on the manner we model the relation between the (changing) age distribution of the population and contacts. Under some circumstances the transitional ageing phase typical of BRF populations might complexly interact with epidemiological variables leading to (i) a substantial reduction in the amount of vaccination effort required for eliminating the disease; (ii) a significant magnification of the perverse impact of vaccination in terms of the burden of severe age related morbidity.     

The impact of host-cell dynamics on the fixation probability for lytic viruses

Lytic viruses are obligate parasites whose population dynamics are necessarily coupled to the dynamics of their host-cell population. The adaptation rate of these viruses has attracted considerable scientific interest, as they are a key model organism in experimental evolution. Nevertheless, to date mathematical models of experimental evolution have largely ignored the host-cell population. In this paper we incorporate two important features of host-cell dynamics—the possibility of clearance or death of an infected cell before lysis, and the possibility of changing host-cell density—into previous models for the fixation probability of lytic viruses. We compute the fixation probabilities of rare alleles that confer reproductive benefit through either an increase in attachment rate or burst size, or a reduction in lysis time. We find that host-cell clearance significantly reduces the fixation probabilities of all types of beneficial mutations, having the largest impact on mutations which reduce the lysis time, but has only modest effects on the pattern of fixation probabilities previously observed. We further predict that exponential growth of the host-cell population preferentially selects for mutations that affect burst size or lysis time, and exacerbates the sensitive dependence of fixation probabilities on the time between population bottlenecks. Even when burst size and lysis time are constrained to vary together, our results suggest that lytic viruses should readily adapt to optimize these traits to the timing between population bottlenecks.     

The impact of mortality on predator population size and stability in systems with stage-structured prey

The relationships between a predator population's mortality rate and its population size and stability are investigated for several simple predator-prey models with stage-structured prey populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's population growth; the nature of stage-transitions; and the stage-selectivity of the predator. Instability occurs at high, rather than low predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable predator population to increase in abundance as its own mortality rate increases in stable systems, provided that the predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in predator population size with increasing predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.     

Observations on the population dynamics of Globodera pallida under single and double cropping conditions

The population dynamics of Globodera pallida were studied on susceptible potato plants. Oxamyl treated and untreated plots were planted with a G. pallida susceptible crop, from the first early maturity class, under polythene at the end of February and immediately followed, after harvest in June, by a susceptible second crop. Other nematicide treated and untreated plots were sown in April with a G. pallida susceptible cultivar. The results were variable but showed that reproduction of G. pallida under double cropping conditions was greater than on a single main crop.     

The effects of the evolution of stoichiometry-related traits on population dynamics in plankton communities

Both ecological stoichiometry and the evolution of traits for energetic interactions such as prey protection and predatory efficiency are considered to be important aspects affecting population dynamics. However, no attempt has been made to examine the effect of the evolution of traits relating to stoichiometry. This study first examined the effects of the evolution of nutrient utilization traits (i.e., the minimum nutrient content of prey, the maximum nutrient uptake affinity of prey and the nutrient contents of predators) on population dynamics in a plankton community. When the evolution of these traits was assumed, the range of the nutrient loading conditions where the system became unstable was smaller than when the evolution was not assumed, but the range of the conditions for zooplankton extinction became larger. Furthermore, when the trade-offs (i.e. genetic correlation between the traits) were assumed, the system rarely became extinct and the range of the nutrient loading conditions where the system became stable became larger through evolution. Stable dynamics were caused by increasing uptake affinity through evolution, and zooplankton extinction was caused by decreasing the minimum content of limiting nutrients. Thus, our results suggest that the evolution of traits relating to stoichiometry can affect the dynamics of the systems, and the outcomes the dynamics change greatly depend on which traits can evolve.     

The macroecology of population dynamics: taxonomic and biogeographic patterns in population cycles

Regular cycles in population abundance are fascinating phenomena, but are they common in natural populations? How are they distributed among taxa? Are there differences between different regions of the world, or along latitudinal gradients? Using the new Global Population Dynamics Database we analysed nearly 700 long (25 + years) time series of animal field populations, looking for large-scale patterns in cycles. Nearly 30% of the time series were cyclic. Cycle incidence varied among taxonomic classes, being most common in mammal and fish populations, but only in fish did cycle incidence vary among orders. Cycles were equally common in European and North American populations, but were more common in Atlantic fish than Pacific fish. The incidence of cycles increased with latitude in mammals only. There was no latitudinal gradient in cycle period, but cycle amplitude declined with latitude in some groups of fish. Even after considering the biases in the data source and expected type I error, population cycles seem common enough to warrant ecological attention.     

Effect of the shape of forest fragments on tree population dynamics

A lattice model is used to study the influence of the shape of forest fragments on the augmentation process of a tree population following clear-cutting. Two fragments of different shapes, squarish and linear, were studied without seed immigration from the outside. Both fragments consisted initially of two patches, a 4-ha clear-cut area and a 1-ha remnant forest, mimicking a common forest management regime in Japan. Stochastic simulations using the model reveal several differences in the dynamics and equilibrium structure of the tree population between the fragments. In the squarish fragment, the forest structure reached an equilibrium state in 500–600 years, but the linear fragment took 2100–2400 years. At equilibrium, the proportion of treeless area was significantly larger in the linear fragment than in the squarish fragment. The mean area of gaps was also larger in the linear fragment. The population expansion rate from the remnant forest into the cleared area differed significantly between the two fragments: 0.63 m year^–1 in the squarish fragment, and 0.43 m year^–1 in the linear fragment. These differences are explained as arising from the spatial configuration of seed dispersal: in the linear fragment, the density of seedlings was lower by half than in the squarish fragment, because a greater proportion of seeds produced within the linear fragment were deposited outside the fragment and were lost. However, the density effect (i.e., one-sided competition among trees) mitigates the negative impact of dispersal loss on the adult population density at equilibrium. Forest fragments with linear shapes should be preferred by fugitive light-demanding species in forested landscapes.     

The effect of delayed host self-regulation on host-pathogen population cycles in forest insects

Delayed host self-regulation using a Beverton-Holt function and delayed logistic self-regulation are included in a host-pathogen model with free-living infective stages (Anderson and May's model G) with the purpose of investigating whether adding the relatively complex self-regulations decrease the likelihood of population cycles. The main results indicate that adding delayed self-regulation to the baseline model increases the likelihood of population cycles. The dynamics display some of the key features seen in the field, such as cycle peak density exceeding the carrying capacity and a locally stable equilibrium coexisting with a stable cycle (bistability). Numerical studies show that the model with more complex forms of self-regulation can generate cycles which match most aspects of the cycles observed in nature.     

The effects of spatial heterogeneity in population dynamics

The dynamics of a population inhabiting a heterogeneous environment are modelled by a diffusive logistic equation with spatially varying growth rate. The overall suitability of an environment is characterized by the principal eigenvalue of the corresponding linearized equation. The dependence of the eigenvalue on the spatial arrangement of regions of favorable and unfavorable habitat and on boundary conditions is analyzed in a number of cases.Research supported by National Science Foundation grant #DMS 88-02346