Stability of a certain class of a host-parasitoid models with a spatial refuge effect

A certain class of a host-parasitoid models, where some host are completely free from parasitism within a spatial refuge is studied. In this paper, we assume that a constant portion of host population may find a refuge and be safe from attack by parasitoids. We investigate the effect of the presence of refuge on the local stability and bifurcation of models. We give the reduction to the normal form and computation of the coefficients of the Neimark-Sacker bifurcation and the asymptotic approximation of the invariant curve. Then we apply theory to the three well-known host-parasitoid models, but now with refuge effect. In one of these models Chenciner bifurcation occurs. By using package Mathematica, we plot bifurcation diagrams, trajectories and the regions of stability and instability for each of these models.

Loss of consumers constrains phenotypic evolution in the resulting food web

The loss of biodiversity is altering the structure of ecological networks; however, we are currently in a poor position to predict how these altered communities will affect the evolution of remaining populations. Theory on fitness landscapes provides a framework for predicting how selection alters the evolutionary trajectory and adaptive potential of populations, but often treats the network of interacting populations as a “black box.” Here, we integrate ecological networks and fitness landscapes to examine how changes in food‐web structure shape phenotypic evolution. We conducted a field experiment that removed a guild of larval parasitoids that imposed direct and indirect selection pressures on an insect herbivore. We then measured herbivore survival as a function of three key phenotypic traits to estimate directional, quadratic, and correlational selection gradients in each treatment. We used these selection gradients to characterize the slope and curvature of the fitness landscape to understand the direct and indirect effects of consumer loss on phenotypic evolution. We found that the number of traits under directional selection increased with the removal of larval parasitoids, indicating evolution was more constrained toward a specific combination of traits. Similarly, we found that the removal of larval parasitoids altered the curvature of the fitness landscape in such a way that tended to decrease the evolvability of the traits we measured in the next generation. Our results suggest that the loss of trophic interactions can impose greater constraints on phenotypic evolution. This indicates that the simplification of ecological communities may constrain the adaptive potential of remaining populations to future environmental change.

Top-down network analysis characterizes hidden termite-termite interactions

The analysis of ecological networks is generally bottom-up, where networks are established by observing interactions between individuals. Emergent network properties have been indicated to reflect the dominant mode of interactions in communities that might be mutualistic (e.g., pollination) or antagonistic (e.g., host-parasitoid communities). Many ecological communities, however, comprise species interactions that are difficult to observe directly. Here, we propose that a comparison of the emergent properties from detail-rich reference communities with known modes of interaction can inform our understanding of detail-sparse focal communities. With this top-down approach, we consider patterns of coexistence between termite species that live as guests in mounds built by other host termite species as a case in point. Termite societies are extremely sensitive to perturbations, which precludes determining the nature of their interactions through direct observations. We perform a literature review to construct two networks representing termite mound cohabitation in a Brazilian savanna and in the tropical forest of Cameroon. We contrast the properties of these cohabitation networks with a total of 197 geographically diverse mutualistic plant-pollinator and antagonistic host-parasitoid networks. We analyze network properties for the networks, perform a principal components analysis (PCA), and compute the Mahalanobis distance of the termite networks to the cloud of mutualistic and antagonistic networks to assess the extent to which the termite networks overlap with the properties of the reference networks. Both termite networks overlap more closely with the mutualistic plant-pollinator communities than the antagonistic host-parasitoid communities, although the Brazilian community overlap with mutualistic communities is stronger. The analysis raises the hypothesis that termite-termite cohabitation networks may be overall mutualistic. More broadly, this work provides support for the argument that cryptic communities may be analyzed via comparison to well-characterized communities.

Impulsive spatial control of invading pests by generalist predators

We model the conditions for pest eradication in a reaction-diffusion system made of a prey and a generalist predator through spatial impulsive control within a bounded domain. The motivating example is the control of the invasive horse chestnut leafminer moth through the yearly destruction of leaves in autumn, in which both the pest and its parasitoids overwinter. The model is made of two integro-partial differential equations, the integral portion describing the within-year immigration from the whole domain. The problem of pest eradication is strongly related to some appropriate eigenvalue problems. Basic properties of the principal eigenvalues of these problems are derived by using of Krein-Rutman's theorem and of comparison results for parabolic equations with non-local terms. Spatial control of the pest can be achieved, if one of these principal eigenvalues is large enough, at an exponential rate. This is true without and with parasitoids, the latter case being of course more rapid. We discuss the possible implementation of these results to the leafminer invasion problem and discuss complementary methods.