Metapopulation-Level Adaptation of Insect Host plant Preference and Extinction-Colonization Dynamics in Heterogenous Landscapes

Species living in highly fragmented landscapes typically occur as metapopulations with frequent turnover of local populations. The turnover rate depends on population sizes and connectivities, but it may also depend on the phenotypic and genotypic composition of populations. The Glanville fritillary butterfly ("Melitaea cinxia") in Finland uses two host plant species, which show variation in their relative abundances at two spatial scales: locally among individual habitat patches and regionally among networks of patches. Female butterflies in turn exhibit spatial variation in genetically-determined host plant preference within and among patch networks. Emigration, immigration and establishment of new populations have all been shown to be strongly influenced by the match between the host plant composition of otherwise suitable habitat patches and the host plant preference of migrating butterflies. The evolutionary consequences of such biased migration and colonization with respect to butterfly phenotypes might differ depending on spatial configuration and plant species composition of the patches in heterogenous patch networks. Using a spatially realistic individual-based model we show that the model-predicted evolution of host plant preference due to biased migration explains a significant amount of the observed variation in host plant use among metapopulations living in dissimilar networks. This example illustrates how the ecological extinction-colonization dynamics may be linked with the evolutionary dynamics of life history traits in metapopulations

Reduction of a metapopulation genetic model to an effective one island model

We explore a model of metapopulation genetics which is based on a more ecologically motivated approach than is frequently used in population genetics. The size of the population is regulated by competition between individuals, rather than by artificially imposing a fixed population size. The increased complexity of the model is managed by employing techniques often used in the physical sciences, namely exploiting time-scale separation to eliminate fast variables and then constructing an effective model from the slow modes. Remarkably, an initial model with 2$\mathcal{D}$ variables, where $\mathcal{D}$ is the number of islands in the metapopulation, can be reduced to a model with a single variable. We analyze this effective model and show that the predictions for the probability of fixation of the alleles and the mean time to fixation agree well with those found from numerical simulations of the original model.Comment: 16 pages, 4 figures. Supplementary material: 22 pages, 3 figure

Self-organized patterns of coexistence out of a predator-prey cellular automaton

We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one individual of each species or can be empty. The system evolves in time according to a probabilistic cellular automaton composed by a set of local rules which describe interactions between species individuals and mimic the process of birth, death and predation. By performing computational simulations, we found that, depending on the values of the parameters of the model, the following states can be reached: a prey absorbing state and active states of two types. In one of them both species coexist in a stationary regime with population densities constant in time. The other kind of active state is characterized by local coupled time oscillations of prey and predator populations. We focus on the self-organized structures arising from spatio-temporal dynamics of the coexistence. We identify distinct spatial patterns of prey and predators and verify that they are intimally connected to the time coexistence behavior of the species. The occurrence of a prey percolating cluster on the spatial patterns of the active states is also examined.Comment: 19 pages, 11 figure

The mode of host-parasite interaction shapes coevolutionary dynamics and the fate of host cooperation

Antagonistic coevolution between hosts and parasites can have a major impact on host population structures, and hence on the evolution of social traits. Using stochastic modelling techniques in the context of bacteria-virus interactions, we investigate the impact of coevolution across a continuum of host-parasite genetic specificity (specifically, where genotypes have the same infectivity/resistance ranges (matching alleles, MA) to highly variable ranges (gene-for-gene, GFG)) on population genetic structure, and on the social behaviour of the host. We find that host cooperation is more likely to be maintained towards the MA end of the continuum, as the more frequent bottlenecks associated with an MA-like interaction can prevent defector invasion, and can even allow migrant cooperators to invade populations of defectors.Comment: 8 pages, 4 figures, 1 Supplementary Material file attached (to view it, please download the source file listed under "Other formats"

A Computational Approach for Designing Tiger Corridors in India

Wildlife corridors are components of landscapes, which facilitate the movement of organisms and processes between intact habitat areas, and thus provide connectivity between the habitats within the landscapes. Corridors are thus regions within a given landscape that connect fragmented habitat patches within the landscape. The major concern of designing corridors as a conservation strategy is primarily to counter, and to the extent possible, mitigate the effects of habitat fragmentation and loss on the biodiversity of the landscape, as well as support continuance of land use for essential local and global economic activities in the region of reference. In this paper, we use game theory, graph theory, membership functions and chain code algorithm to model and design a set of wildlife corridors with tiger (Panthera tigris tigris) as the focal species. We identify the parameters which would affect the tiger population in a landscape complex and using the presence of these identified parameters construct a graph using the habitat patches supporting tiger presence in the landscape complex as vertices and the possible paths between them as edges. The passage of tigers through the possible paths have been modelled as an Assurance game, with tigers as an individual player. The game is played recursively as the tiger passes through each grid considered for the model. The iteration causes the tiger to choose the most suitable path signifying the emergence of adaptability. As a formal explanation of the game, we model this interaction of tiger with the parameters as deterministic finite automata, whose transition function is obtained by the game payoff.Comment: 12 pages, 5 figures, 6 tables, NGCT conference 201

The evolution of dispersal in a Levins’ type metapopulation model

We study the evolution of the dispersal rate in a metapopulation model with extinction and colonisation dynamics, akin to the model as originally described by Levins. To do so we extend the metapopulation model with a description of the within patch dynamics. By means of a separation of time scales we analytically derive a fitness expression from first principles for this model. The fitness function can be written as an inclusive fitness equation (Hamilton’s rule). By recasting this equation in a form that emphasizes the effects of competition we show the effect of the local competition and on the local population size on the evolution of dispersal. We find that the evolution of dispersal cannot be easily interpreted in terms of avoidance of kin competition, but rather that increased dispersal reduces the competitive ability. Our model also yields a testable prediction in term of relatedness and life history parameters

Host--parasite models on graphs

The behavior of two interacting populations, ``hosts''and ``parasites'', is investigated on Cayley trees and scale-free networks. In the former case analytical and numerical arguments elucidate a phase diagram, whose most interesting feature is the absence of a tri-critical point as a function of the two independent spreading parameters. For scale-free graphs, the parasite population can be described effectively by Susceptible-Infected-Susceptible-type dynamics in a host background. This is shown both by considering the appropriate dynamical equations and by numerical simulations on Barab\'asi-Albert networks with the major implication that in the termodynamic limit the critical parasite spreading parameter vanishes.Comment: 10 pages, 6 figures, submitted to PRE; analytics redone, new calculations added, references added, appendix remove

The milliarcsecond-scale jet of PKS 0735+178 during quiescence

We present polarimetric 5 GHz to 43 GHz VLBI observations of the BL Lacertae object PKS 0735+178, spanning March 1996 to May 2000. Comparison with previous and later observations suggests that the overall kinematic and structural properties of the jet are greatly influenced by its activity. Time intervals of enhanced activity, as reported before 1993 and after 2000 by other studies, are followed by highly superluminal motion along a rectilinear jet. In contrast the less active state in which we performed our observations, shows subluminal or slow superluminal jet features propagating through a twisted jet with two sharp bends of about 90 deg. within the innermost three-milliarcsecond jet structure. Proper motion estimates from the data presented here allow us to constrain the jet viewing angle to values < 9 deg., and the bulk Lorentz factor to be between 2 and 4.Comment: 11 pages, 12 figures. Accepted for publication in A&

Contagion dynamics in time-varying metapopulation networks

The metapopulation framework is adopted in a wide array of disciplines to describe systems of well separated yet connected subpopulations. The subgroups or patches are often represented as nodes in a network whose links represent the migration routes among them. The connections have been so far mostly considered as static, but in general evolve in time. Here we address this case by investigating simple contagion processes on time-varying metapopulation networks. We focus on the SIR process and determine analytically the mobility threshold for the onset of an epidemic spreading in the framework of activity-driven network models. We find profound differences from the case of static networks. The threshold is entirely described by the dynamical parameters defining the average number of instantaneously migrating individuals and does not depend on the properties of the static network representation. Remarkably, the diffusion and contagion processes are slower in time-varying graphs than in their aggregated static counterparts, the mobility threshold being even two orders of magnitude larger in the first case. The presented results confirm the importance of considering the time-varying nature of complex networks

Migration paths saturations in meta-epidemic systems

In this paper we consider a simple two-patch model in which a population affected by a disease can freely move. We assume that the capacity of the interconnected paths is limited, and thereby influencing the migration rates. Possible habitat disruptions due to human activities or natural events are accounted for. The demographic assumptions prevent the ecosystem to be wiped out, and the disease remains endemic in both populated patches at a stable equilibrium, but possibly also with an oscillatory behavior in the case of unidirectional migrations. Interestingly, if infected cannot migrate, it is possible that one patch becomes disease-free. This fact could be exploited to keep disease-free at least part of the population