Stability switching and hydra effect in a predator-prey metapopulation model.

A metapopulation model is investigated to explore how the spatial heterogeneity affects predator-prey interactions. A Rosenzweig-MacArthur (RM) predator-prey model with dispersal of both the prey and predator is formulated. We propose such a system as a well mixed spatial model. Here, partially mixed spatial models are defined in which the dispersal of only one of the communities (prey or predator) is considered. In our study, the spatial heterogeneity is induced by dissimilar (unbalanced) dispersal rates between the patches. A large difference between the predator dispersal rates may stabilize the unstable positive equilibrium of the model. The existence of two ecological phenomena are found under independent harvesting strategy: stability switching and hydra effect. When prey or predator is harvested in a heterogenious environment, a positive stable steady state becomes unstable with increasing the harvesting effort, and a further increase in the effort leads to a stable equilibrium. Thus, a stability switching happens. Furthermore, the predator biomass (at stable state) in both the patches (and hence total predator stock) increases when the patch with a higher predator density is harvested; resulting a hydra effect. These two phenomena do not occur in the non-spatial RM model. Hence, spatial heterogeneity induces stability switching and hydra effect.

Influence of the components of propagule pressure, Allee effects, and stochasticity on the time to establish introduced populations.

Forecasting whether individuals of an introduced population will succeed to establish is a challenge in invasion and conservation biology. The present work aims to decouple the impact of the components of propagule pressure on the time for population establishment in the presence of Allee effects and stochasticity in propagule sizes. The mean first passage time (MFPT) for a population to reach a viable size is used as a measure of the establishment success for the introduction processes involving periodic introductions. By fixing the introduction rate (mean number of introduced individuals per unit time) and varying the period of introduction from small ranges (small and frequent introductions) to large ones (infrequent and large releases), we study the influence of introduction distribution over time. These patterns of introduction are compared in a semi-stochastic model by observing which factors minimize the MFPT from an initially absent population, and hence, ensure the fastest population establishment. We investigate the influence on these minima of the introduction rate, variability in the introduction sizes, and occurrence of catastrophes that temporarily wipe out the population. Whereas most investigated cases show that infrequent and large introductions favor population establishment as expected, small and frequent introductions are preferred when the introduction rate is large and/or the variability in the introduction size is strong. Moreover, we observed counterintuitively that catastrophes strongly increase MFPT at small periods of introduction. In addition, we showed that stochasticity in introduction tends to increase the MFPT except when the introduction rate is small and introductions are evenly spread out in time.

Number of Source Patches Required for Population Persistence in a Source-Sink Metapopulation with Explicit Movement.

We consider a simple metapopulation model with explicit movement of individuals between patches, in which each patch is either a source or a sink. We prove that similarly to the case of patch occupancy metapopulations with implicit movement, there exists a threshold number of source patches such that the population potentially becomes extinct below the threshold and established above the threshold. In the case where the matrix describing the movement of populations between spatial locations is irreducible, the result is global; further, assuming a complete mobility graph with equal movement rates, we use the principle of equitable partitions to obtain an explicit expression for the threshold. Brief numerical considerations follow.

Augmentative biocontrol when natural enemies are subject to Allee effects.

Intraspecific interactions such as Allee effects are key properties that can guide population management. This contribution considers component Allee effects that are elementary mechanisms leading to declines of fitness at the population scale, i.e. demographic Allee effects. It especially focuses on the consequences of such properties in predator populations, and investigates their repercussions in a biological control context. A modelling framework able to account for reproductive and/or foraging component Allee effects is proposed. From this, four models of augmentative biological control, corresponding to the periodic introduction of natural enemies, have been investigated. This is done using semi-discrete models: ordinary differential equations are used to depict predator-prey dynamics and a discrete equation describes the abrupt augmentation of predators at periodic intervals. In that context, stability of a prey-free solution corresponding to pest eradication has been analyzed. It has been found that rare but large introductions should be preferred over frequent and small ones, when Allee effects influence predator populations. In particular, the occurrence of foraging, rather than reproducing, Allee effects significantly hinders pest eradication. Cases where the pest-free solution is locally, but not globally, stable were also observed and were shown to be favored by the occurrence of reproductive Allee effects among predators.