Host-pathogen systems in a spatially patchy environment

Within-Colony Transmission of Microsporidian and Trypanosomatid Parasites in Honey Bee and Bumble Bee Colonies

Parasites are commonly cited as one of the causes of population declines for both managed and wild bees. Epidemiological models sometimes assume that increasing the proportion of infected individuals in a group should increase transmission. However, social insects exhibit behaviors and traits which can dampen the link between parasite pressure and disease spread. Understanding patterns of parasite transmission within colonies of social bees has important implications for how to control diseases within those colonies, and potentially the broader pollinator community. We used bumble bees (Bombus impatiens Cresson) (Hymenoptera: Apidae) and western honey bees (Apis mellifera L.) (Hymenoptera: Apidae) infected with the gut parasites Crithidia bombi (Lipa & Triggiani) (Trypanosomatida: Trypanosomatidae) and Nosema ceranae (Fries et al.) (Dissociodihaplophasida: Nosematidae), respectively, to understand how the initial proportion of infected individuals impacts within-colony spread and intensity of infection of the parasites. In bumble bees, we found that higher initial parasite prevalence increased both the final prevalence and intensity of infection of C. bombi. In honey bees, higher initial prevalence increased the intensity of infection in individual bees, but not the final prevalence of N. ceranae. Measures that reduce the probability of workers bringing parasites back to the nest may have implications for how to control transmission and/or severity of infection and disease outbreaks, which could also have important consequences for controlling disease spread back into the broader bee community.

Dependence of Initial Value on Pattern Formation for a Logistic Coupled Map Lattice

The logistic coupled map lattices (LCML) have been widely investigated as well as their pattern dynamics. The patterns formation may depend on not only fluctuations of system parameters, but variation of the initial conditions. However, the mathematical discussion is quite few for the effect of initial values so far. The present paper is concerned with the pattern formation for a two-dimensional Logistic coupled map lattice, where any initial value can be linear expressed by corresponding eigenvectors, and patterns formation can be determined by selecting the corresponding eigenvectors. A set of simulations are conducted whose results demonstrate the fact. The method utilized in the present paper could be applied to other discrete systems as well.

Parasite-driven extinction in spatially explicit host-parasite systems

General host-parasite theory suggests that parasites may be implicated in the extinction of their hosts by causing instability that leads to increased risk of stochastic extinction. In contrast, spatially explicit models suggest that the parasite may directly drive the host population to extinction. Here we examine the ecological characteristics of host-parasite interactions that favor parasite-driven host extinction. Pair approximations and simulations show that parasites only drive their hosts to extinction when they significantly reduce host reproduction. As a matter of interest, parasites that have a relatively small effect on host death rate are more likely to cause host extinction. Parasite-driven host extinction occurs at any population size, whereas extinction caused by stochastic effects is less likely to occur in large host populations. Populations may therefore be under threat from parasites that stop host reproduction, and this type of parasite may prove to be the most effective biological pesticide.

Transients: the key to long-term ecological understanding?

Ecological theory has been dominated by a focus on long-term or asymptotic behavior as a way to understand natural systems. Yet experiments are done on much shorter timescales, and the relevant timescales for ecological systems can also be relatively short. Thus, there is a mismatch between the timescales of most experiments and the timescales of many theoretical investigations. However, recent work has emphasized the importance of transient dynamics rather than long-term behavior in ecological systems, enabling the examination of forces that allow coexistence on ecological timescales. Through an examination of what leads to transients in ecological systems, a deeper appreciation of the forces leading to persistence or coexistence in ecological systems emerges, as well as a general understanding of how population levels can change through time.

Changes over time in the spatiotemporal dynamics of cyclic populations of field voles (Microtus agrestis L.)

We demonstrate changes over time in the spatial and temporal dynamics of an herbivorous small rodent by analyzing time series of population densities obtained at 21 locations on clear cuts within a coniferous forest in Britain from 1984 to 2004. Changes had taken place in the amplitude, periodicity, and synchrony of cycles and density-dependent feedback on population growth rates. Evidence for the presence of a unidirectional traveling wave in rodent abundance was strong near the beginning of the study but had disappeared near the end. This study provides empirical support for the hypothesis that the temporal (such as delayed density dependence structure) and spatial (such as traveling waves) dynamics of cyclic populations are closely linked. The changes in dynamics were markedly season specific, and changes in overwintering dynamics were most pronounced. Climatic changes, resulting in a less seasonal environment with shorter winters near the end of the study, are likely to have caused the changes in vole dynamics. Similar changes in rodent dynamics and the climate as reported from Fennoscandia indicate the involvement of large-scale climatic variables.

Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations

In this paper we develop a general mathematical model describing the spatio-temporal dynamics of host-parasitoid systems with forced generational synchronisation, for example seasonally induced diapause. The model itself may be described as an individual-based stochastic model with the individual movement rules derived from an underlying continuum PDE model. This approach permits direct comparison between the discrete model and the continuum model. The model includes both within-generation and between-generation mechanisms for population regulation and focuses on the interactions between immobile juvenile hosts, adult hosts and adult parasitoids in a two-dimensional domain. These interactions are mediated, as they are in many such host-parasitoid systems, by the presence of a volatile semio-chemical (kairomone) emitted by the hosts or the hosts' food plant. The model investigates the effects on population dynamics for different host versus parasitoid movement strategies as well as the transient dynamics leading to steady states. Despite some agreement between the individual and continuum models for certain motility parameter ranges, the model dynamics diverge when host and parasitoid motilities are unequal. The individual-based model maintains spatially heterogeneous oscillatory dynamics when the continuum model predicts a homogeneous steady state. We discuss the implications of these results for mechanistic models of phenotype evolution.

Metapopulation dynamics with quasi-local competition

Stepping-stone models for the ecological dynamics of metapopulations are often used to address general questions about the effects of spatial structure on the nature and complexity of population fluctuations. Such models describe an ensemble of local and spatially isolated habitat patches that are connected through dispersal. Reproduction and hence the dynamics in a given local population depend on the density of that local population, and a fraction of every local population disperses to neighboring patches. In such models, interesting dynamic phenomena, e.g. the persistence of locally unstable predator-prey interactions, are only observed if the local dynamics in an isolated patch exhibit non-equilibrium behavior. Therefore, the scope of these models is limited. Here we extend these models by making the biologically plausible assumption that reproductive success in a given local habitat not only depends on the density of the local population living in that habitat, but also on the densities of neighboring local populations. This would occur if competition for resources occurs between neighboring populations, e.g. due to foraging in neighboring habitats. With this assumption of quasi-local competition the dynamics of the model change completely. The main difference is that even if the dynamics of the local populations have a stable equilibrium in isolation, the spatially uniform equilibrium in which all local populations are at their carrying capacity becomes unstable if the strength of quasi-local competition reaches a critical level, which can be calculated analytically. In this case the metapopulation reaches a new stable state, which is, however, not spatially uniform anymore and instead results in an irregular spatial pattern of local population abundance. For large metapopulations, a huge number of different, spatially non-uniform equilibrium states coexist as attractors of the metapopulation dynamics, so that the final state of the system depends critically on the initial conditions. The existence of a large number of attractors has important consequences when environmental noise is introduced into the model. Then the metapopulation performs a random walk in the space of all attractors. This leads to large and complicated population fluctuations whose power spectrum obeys a red-shifted power law. Our theory reiterates the potential importance of spatial structure for ecological processes and proposes new mechanisms for the emergence of non-uniform spatial patterns of abundance and for the persistence of complicated temporal population fluctuations.

Clone mixtures and a pacemaker: new facets of Red-Queen theory and ecology

Host-parasite antagonistic interaction has been proposed as a potential agent to promote genetic polymorphism and to favour sex against asex, despite its twofold cost in reproduction. However, the host-parasite gene-for-gene dynamics often produce unstable cycles that tend to destroy genetic diversity. Here, we examine such diversity destroying coevolutionary dynamics of host and parasite, which is coupled through local or global migration, or both, between demes in a metapopulation structure. We show that, with global migration in the island model, peculiar out-of-phase islands spontaneously arise in the cluster of islands converging to a global synchrony. Such asynchrony induced by the 'pacemaker islands' serves to restore genetic variation. With increasing fraction of local migration, spots of asynchrony are converted into loci or foci of spiral and target patterns, whose rotating arms then cover the majority of demes. A multi-locus analogue of the model reproduces the same tendency toward asynchrony, and the condition arises for an advantage of asexual clones over their sexual counterpart when enough genetic diversity is maintained through metapopulation storage-migration serves as a cheap alternative to sex.

Mathematical modelling of host-parasitoid systems: effects of chemically mediated parasitoid foraging strategies on within- and between-generation spatio-temporal dynamics

In this paper we develop a novel discrete, individual-based mathematical model to investigate the effect of parasitoid foraging strategies on the spatial and temporal dynamics of host-parasitoid systems. The model is used to compare naïve or random search strategies with search strategies that depend on experience and sensitivity to semiochemicals in the environment. It focuses on simple mechanistic interactions between individual hosts, parasitoids, and an underlying field of a volatile semiochemical (emitted by the hosts during feeding) which acts as a chemoattractant for the parasitoids. The model addresses movement at different spatial scales, where scale of movement also depends on the internal state of an individual. Individual interactions between hosts and parasitoids are modelled at a discrete (micro-scale) level using probabilistic rules. The resulting within-generation dynamics produced by these interactions are then used to generate the population levels for successive generations. The model simulations examine the effect of various key parameters of the model on (i) the spatio-temporal patterns of hosts and parasitoids within generations; (ii) the population levels of the hosts and parasitoids between generations. Key results of the model simulations show that the following model parameters have an important effect on either the development of patchiness within generations or the stability/instability of the population levels between generations: (i) the rate of diffusion of the kairomones; (ii) the specific search strategy adopted by the parasitoids; (iii) the rate of host increase between successive generations. Finally, evolutionary aspects concerning competition between several parasitoid subpopulations adopting different search strategies are also examined.

'Small worlds' and the evolution of virulence: infection occurs locally and at a distance

Why are some discases more virulent than others? Vector-borne diseases such as malaria and water-borne diseases such as cholera are generally more virulent than diseases spread by direct contagion. One factor that characterizes both vector- and water-borne diseases is their ability to spread over long distances, thus causing infection of susceptible individuals distant from the infected individual. Here we show that this ability of the pathogen to infect distant individuals in a spatially structured host population leads to the evolution of a more virulent pathogen. We use a lattice model in which reproduction is local but infection can vary between completely local to completely global. With completely global infection the evolutionarily stable strategy (ESS) is the same as in mean-field models while a lower virulence is predicted as infection becomes more local. There is characteristically a period of relatively moderate increase in virulence followed by a more rapid rise with increasing proportions of global infection as we move beyond a 'critical connectivity'. In the light of recent work emphasizing the existence of 'small world' networks in human populations, our results suggests that if the world is getting 'smaller'--as populations become more connected--diseases may evolve higher virulence.

The ecology and biosafety of baculoviruses

Advances in the use of molecular techniques-particularly for virus identification, the investigation of latency and the infection process, plus the development of a theoretical framework containing a higher degree of biological realism-have pushed baculovirus ecology forward in the past few years. This has created a scenario in which many hitherto intractable questions about the behaviour of natural and genetically modified baculoviruses can now be addressed.