Biomedical subjects

Sebastian J Schreiber

Publications and source records attributed to Sebastian J Schreiber.

6 recordsLinked to original sources

PubMed2006

Persistence despite perturbations for interacting populations.

Two definitions of persistence despite perturbations in deterministic models are presented. The first definition, persistence despite frequent small perturbations, is shown to be equivalent to the existence of a positive attractor i.e. an attractor bounded away from extinction. The second definition, persistence despite rare large perturbations, is shown to be equivalent to permanence i.e. a positive attractor whose basin of attraction includes all positive states. Both definitions set up a natural dichotomy for classifying models of interacting populations. Namely, a model is either persistent despite perturbations or not. When it is not persistent, it follows that all initial conditions are prone to extinction due to perturbations of the appropriate type. For frequent small perturbations, this method of classification is shown to be generically robust: there is a dense set of models for which persistent (respectively, extinction prone) models lies within an open set of persistent (resp. extinction prone) models. For rare large perturbations, this method of classification is shown not to be generically robust. Namely, work of Josef Hofbauer and the author have shown there are open sets of ecological models containing a dense sets of permanent models and a dense set of extinction prone models. The merits and drawbacks of these different definitions are discussed.

Animals↗

PubMed2006

Host-parasitoid dynamics of a generalized Thompson model.

A discrete-time host-parasitoid model including host-density dependence and a generalized Thompson escape function is analyzed. This model assumes that parasitoids are egg-limited but not search-limited, and is proven to exhibit five types of dynamics: host failure in which the host goes extinct in the parasitoid's presence or absence, unconditional parasitoid failure in which the parasitoid always goes extinct while the host persists, conditional parasitoid failure in the host and the parasitoid go extinct or coexist depending on the initial host-parasitoid ratio, parasitoid driven extinction in which the parasitoid invariably drives the host to extinction, and coexistence in which the host and parasitoid coexist about a global attractor. The latter two dynamics only occur when the parasitoid's maximal rate of growth exceeds the host's maximal rate of growth. Moreover, coexistence requires parasitism events to be sufficiently aggregated. Small additive noise is proven to alter the dynamical outcomes in two ways. The addition of noise to parasitoid driven extinction results in random outbreaks of the host and parasitoid with varying intensity. Additive noise converts conditional parasitoid failure to unconditional parasitoid failure. Implications for classical biological control are discussed.

Animals↗

PubMed2006

Handling time promotes the coevolution of aggregation in predator-prey systems.

Predators often have type II functional responses and live in environments where their life history traits as well as those of their prey vary from patch to patch. To understand how spatial heterogeneity and predator handling times influence the coevolution of patch preferences and ecological stability, we perform an ecological and evolutionary analysis of a Nicholson-Bailey type model. We prove that coevolutionarily stable prey and searching predators prefer patches that in isolation support higher prey and searching predator densities, respectively. Using this fact, we determine how environmental variation and predator handling times influence the spatial patterns of patch preferences, population abundances and per-capita predation rates. In particular, long predator handling times are shown to result in the coevolution of predator and prey aggregation. An analytic expression characterizing ecological stability of the coevolved populations is derived. This expression implies that contrary to traditional theoretical expectations, predator handling time can stabilize predator-prey interactions through its coevolutionary influence on patch preferences. These results are shown to have important implications for classical biological control.

Animals↗

PubMed2003

The evolution of resource use.

The evolution of a consumer exploiting two resources is investigated. The strategy x under selection represents the fraction of time or energy an individual invests into extracting the first resource. In the model, a dimensionless parameter alpha quantifies how simultaneous consumption of both resources influences consumer growth; alpha<0 corresponds to hemi-essential resources, 0 1 corresponds to antagonistic resources. An analysis of the ecological and evolutionary dynamics leads to five conclusions. First, when alpha< or =1, there is a unique singular strategy x* for the adaptive dynamics and it is evolutionarily stable and globally convergent stable. Second, when alpha=1, the singular strategy x* corresponds to the populations exhibiting an ideal free distribution and a population playing this strategy can invade and displace populations playing any other strategy. Third, when alpha>1, the strategies x=0 and x=1 are evolutionarily stable and convergent stable. Hence, if the populations initially specialize on one resource, evolution amplifies this specialization. Fourth, when alpha is slightly larger than one (i.e. the resources are slightly antagonistic), there is a convergent stable singular strategy whose basin of attraction is almost the entire strategy space (0,1). This singular strategy is evolutionarily unstable and serves as an evolutionary branching point. Following evolutionary branching, our analysis and numerical simulations suggest that evolutionary dynamics are driven toward an end state consisting of two populations specializing on different resources. Fifth, when alpha>>1, there is only one singular strategy and it is convergent unstable and evolutionarily unstable. Hence, if resources are overly antagonistic, evolutionary branching does not occur and ultimately only one resource is exploited.

Animals↗

PubMed2003

Allee effects, extinctions, and chaotic transients in simple population models.

Discrete time single species models with overcompensating density dependence and an Allee effect due to predator satiation and mating limitation are investigated. The models exhibit four behaviors: persistence for all initial population densities, bistability in which a population persists for intermediate initial densities and otherwise goes extinct, extinction for all initial densities, and essential extinction in which "almost every" initial density leads to extinction. For fast-growing populations, these models show populations can persist at high levels of predation even though lower levels of predation lead to essential extinction. Alternatively, increasing the predator's handling time, the population's carrying capacity, or the likelihood of mating success may lead to essential extinction. In each of these cases, the mechanism behind these disappearances are chaotic dynamics driving populations below a critical threshold determined by the Allee effect. These disappearances are proceeded by chaotic transients that are proven to be approximately exponentially distributed in length and highly sensitive to initial population densities.

Alleles↗

PubMed2000

Coevolution of Contrary Choices in Host-Parasitoid Systems.

We investigate patch selection strategies of hosts and parasitoids in heterogeneous environments. Previous theoretical work showed that when host traits vary among patches, coevolved populations of hosts and parasitoids make congruent choices (i.e., hosts and parasitoids preferentially select the same patches) and exhibit direct density dependence in the distribution of percent parasitism. However, host-parasitoid systems in the field show a range of patterns in percent parasitism, while behavioral studies indicate that hosts and parasitoids can exhibit contrary choices (i.e., hosts avoid patches favored by the parasitoid). We extend previous theory by permitting life-history traits of the parasitoid as well as the host to vary among patches. Our analysis implies that in coevolutionarily stable populations, hosts preferentially select patches that intrinsically support higher host equilibrium numbers (i.e., the equilibrium number achieved by hosts when both populations are confined to a single patch) and that parasitoids preferentially select patches that intrinsically support higher parasitoid equilibrium numbers (i.e., the equilibrium number achieved by the parasitoids when both populations are confined to a patch). Using this result, we show how variation in life-history traits among patches leads to contrary or congruent choices or leads to direct density dependence, inverse density dependence, or density independence in the distribution of percent parasitism. In addition, we determine when populations playing the coevolutionarily stable strategies are ecologically stable. Our analysis shows that heterogeneous environments containing patches where the intrinsic rate of growth of the host and the survivorship rate of the parasitoid are low result in the coevolved populations exhibiting contrary choices and, as a result, promote ecological stability.

coevolution↗