Metapopulation theory for fragmented landscapes

We review recent developments in spatially realistic metapopulation theory, which leads to quantitative models of the dynamics of species inhabiting highly fragmented landscapes. Our emphasis is in stochastic patch occupancy models, which describe the presence or absence of the focal species in habitat patches. We discuss a number of ecologically important quantities that can be derived from the full stochastic models and their deterministic approximations, with a particular aim of characterizing the respective roles of the structure of the landscape and the properties of the species. These quantities include the threshold condition for persistence, the contributions that individual habitat patches make to metapopulation dynamics and persistence, the time to metapopulation extinction, and the effective size of a metapopulation living in a heterogeneous patch network.     

The stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms

The global asymptotic stability of impulsive stochastic Cohen–Grossberg neural networks with mixed delays and reaction–diffusion terms is investigated. Under some suitable assumptions and using Lyapunov–Krasovskii functional method, we apply the linear matrix inequality technique to propose some new sufficient conditions for the global asymptotic stability of the addressed model in the stochastic sense. The mixed time delays comprise both the time-varying and continuously distributed delays. The effectiveness of the theoretical result is illustrated by a numerical example.     

Invasiveness of plants is predicted by size and fecundity in the native range

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On the lack of specificity of proteins and its consequences for a theory of biological organization

It is now widely recognized that gene expression and cellular processes include a probabilistic component. However, this does not essentially modify the theory of genetic programming. This stochastic aspect, which is called noise, is usually conceived as a margin of fluctuation in the way the genetic program functions and the latter remains understood as a specific mechanism guided by genetic information. In contrast, recent data show that proteins do not possess a high level of specificity. They can interact with numerous molecular partners. As a consequence molecular interactions are not simply “noisy”. Because they are subject to large combinatorial interaction possibilities, they are also intrinsically stochastic and must be sorted out by the cell structure. This contradicts the genetic programming theory which is based on the idea that protein interactions are directed by their stereospecificity and genetic information. Taking into account the lack of protein specificity leads to a new theory. Natural selection acts not only in evolution but also in ontogenesis by sorting stochastic molecular interactions. In this frame, the making up of an organism, instead of being a simple bottom-top process in which information flows from genes to phenotypes, is both a bottom-top and top-bottom process. Genes provide proteins, but their stochastic interactions are sorted by selective constraints arising from the cell and multi-cellular structures, which are themselves subject to the action of natural selection.     

Cougar Kill Rate and Prey Composition in a Multiprey System

Abstract: Assessing the impact of large carnivores on ungulate prey has been challenging in part because even basic components of predation are difficult to measure. For cougars (Puma concolor), limited field data are available concerning fundamental aspects of predation, such as kill rate, or the influence of season, cougar demography, or prey vulnerability on predation, leading to uncertainty over how best to predict or interpret cougar-ungulate dynamics. Global Positioning System (GPS) telemetry used to locate predation events in the field is an efficient way to monitor large numbers of cougars over long periods in all seasons. We applied GPS telemetry techniques combined with occasional snow-tracking to locate 1,509 predation events for 53 marked and an unknown number of unmarked cougars and amassed 9,543 days of continuous predation monitoring for a subset of 42 GPS-collared cougars in west-central Alberta, Canada. Cougars killed ungulates at rates near the upper end of the previously recorded range, and demography substantially influenced annual kill rate in terms of both number of ungulates (subad F [SAF] = 24, subad M [SAM] = 31, ad M = 35, ad F = 42, ad F with kittens <6 months = 47, ad F with kittens <6 months = 67) and kg of prey (SAF = 1,441, SAM = 2,051, ad M = 4,708, ad F = 2,423, ad F with kittens <6 months = 2,794, ad F with kittens >6 months = 4,280). Demography also influenced prey composition; adult females subsisted primarily on deer (Odocoileus spp.), whereas adult males killed more large ungulates (e.g., moose [Alces alces]), and subadults incorporated the highest proportion of nonungulate prey. Predation patterns varied by season and cougars killed ungulates 1.5 times more frequently in summer when juveniles dominated the diet. Higher kill rate in summer appeared to be driven primarily by greater vulnerability of juvenile prey and secondarily by reduced handling time for smaller prey. Moreover, in accordance with predictions of the reproductive vulnerability hypothesis, female ungulates made up a higher proportion of cougar diet in spring just prior to and during the birthing period, whereas the proportion of males increased dramatically in autumn during the rut, supporting the notion that prey vulnerability influences cougar predation. Our results have implications for the impact cougars have on ungulate populations and have application for using cougar harvest to manage ungulates.     

Influence of Density and Climate on Population Dynamics of a Large Herbivore Under Harsh Environmental Conditions

ABSTRACT Dynamics of herbivore populations can be influenced both by density-dependent processes and climate. We used age-at-harvest data for adult female white-tailed deer (Odocoileus virginianus) collected over 23 years to estimate survival and reproduction by age class and to identify effects of environmental factors. The study population was located on Anticosti Island (QC, Canada), at the northern limit of the species' range; the population was at high density, and the landscape had scarce forage and abundant snow during winter. Despite severe environmental conditions, population growth apparently increased during the study; adult survival was similar to other populations, although reproduction appeared lower. Winter severity was not related to survival, but density affected adult female survival. Density at estrus was the main factor influencing reproduction of 2- and 3–4-year-olds and also affected reproduction of prime-aged females (5–9-yr-olds), but not of older females. Reproductive rate of younger females was influenced by environmental conditions in autumn, such as high density or snow conditions that limited forage availability. Reproductive success of 5–9- and ≥10-year-old females appeared dependent on spring conditions favoring high-quality forage, probably through effects on neonatal survival. Relative to other studies on northern ungulates, demographic processes in our study appeared to be more affected by autumn and spring climate, in addition to population density, than by winter climate. We thus propose that population density, as well as autumn and spring climate, should be considered in management strategies. Harvest data offered a unique opportunity to study forest ungulates, for which individual monitoring is rarely possible.     

Stochastic epidemic models: A survey

This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic (relying on a large community) properties are presented. The purpose of modelling is illustrated by studying effects of vaccination and also in terms of inference procedures for important parameters, such as the basic reproduction number and the critical vaccination coverage. Several generalizations towards realism, e.g. multitype and household epidemic models, are also presented, as is a model for endemic diseases.     

Sensitivity summation theorems for stochastic biochemical reaction systems

We investigate how stochastic reaction processes are affected by external perturbations. We describe an extension of the deterministic metabolic control analysis (MCA) to the stochastic regime. We introduce stochastic sensitivities for mean and covariance values of reactant concentrations and reaction fluxes and show that there exist MCA-like summation theorems among these sensitivities. The summation theorems for flux variances is shown to depend on the size of the measurement time window (?) within which reaction events are counted for measuring a single flux. It is found that the degree of the ?-dependency can become significant for processes involving multi-time-scale dynamics and is estimated by introducing a new measure of time-scale separation. This ?-dependency is shown to be closely related to the power-law scaling observed in flux fluctuations in various complex networks.     

Mean-square stability of a stochastic model for bacteriophage infection with time delays

We consider the stability properties of the positive equilibrium of a stochastic model for bacteriophage infection with discrete time delay. Conditions for mean-square stability of the trivial solution of the linearized system around the equilibrium are given by the construction of suitable Lyapunov functionals. The numerical simulations of the strong solutions of the arising stochastic delay differential system suggest that, even for the original non-linear model, the longer the incubation time the more the phage and bacteria populations can coexist on a stable equilibrium in a noisy environment for very long time.