Population dynamics of two rodent species in agro-ecosystems of central Argentina: intra-specific competition,land-use,and climate effects

Understanding the role of feedback structure (endogenous processes) and exogenous (climatic and environmental) factors in shaping the dynamics of natural populations is a central challenge within the field of population ecology. We attempted to explain the numerical fluctuations of two sympatric rodent species in agro-ecosystems of central Argentina using Royama’s theoretical framework for analyzing the dynamics of populations influenced by exogenous climatic forces. We found that both rodent species show a first-order negative feedback structure, suggesting that these populations are regulated by intra-specific competition (limited by food, space, or enemy-free space). In Akodon azarae endogenous structure seems to be very strongly influenced by human land-use represented by annual minimum normalized difference vegetation index (NDVI), with spring and summer rainfall having little influence upon carrying capacity. Calomys venustus’ population dynamics, on the other hand, seem to be more affected by local climate, also with spring and summer rainfall influencing the carrying capacity of the environment, but combined with spring mean temperature. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Comparative population dynamics of <Emphasis Type="Italic">Peromyscus leucopus</Emphasis> in North America: influences of climate,food, and density dependence

Temporal variation in population size is regulated by both exogenous forces and density-dependent feedbacks. Furthermore, accumulating evidence indicates that temporal and spatial variation in climate and resources can modify the strength of density dependence in animal populations. We analyzed six long-term time series estimates of Peromyscus leucopus (white-footed mouse) abundance from Kansas, Ohio, Pennsylvania, Virginia, Vermont, and Maine, USA, using the Kalman filter. Model-averaged estimates of the strength of delayed density dependence increased from west to east and from south to north. The strength of direct and delayed density dependence was positively related to the annual number of days with minimum temperature below −17.8°C. Annual population growth rates of P. leucopus at the Maine site were positively related to acorn abundance and P. leucopus populations tracked the changes in red-oak acorn abundance. The populations of P. leucopus living in northern latitudes might be more dependent on northern red oak (Quercus rubra) acorns for winter food than P. leucopus in southern latitudes. Furthermore, northern red oak trees mast every 4–5 years. Thus, longer, colder winters in northerly latitudes might result in stronger delayed density dependence in mouse populations with a shortage of winter food. Mice might simply track the acorn fluctuations in a delayed autocorrelated manner; however, delayed density dependence remained in our models for the Maine mouse populations after accounting for acorns, suggesting additional sources for delayed density dependence. Our results suggest that, in seed-eating Peromyscus, cyclicity may be regulated, in part, from low to high trophic levels. Deceased: Jerry O. Wolff     

Chaotic dynamics of a three species prey-predator competition model with bionomic harvesting due to delayed environmental noise as external driving force

We consider a biological economic model based on prey-predator interactions to study the dynamical behaviour of a fishery resource system consisting of one prey and two predators surviving on the same prey. The mathematical model is a set of first order non-linear differential equations in three variables with the population densities of one prey and the two predators. All the possible equilibrium points of the model are identified, where the local and global stabilities are investigated. Biological and bionomical equilibriums of the system are also derived. We have analysed the population intensities of fluctuations i.e., variances around the positive equilibrium due to noise with incorporation of a constant delay leading to chaos, and lastly have investigated the stability and chaotic phenomena with a computer simulation.     

Timescales of population rarity and commonness in random environments

This is a mathematical study of the interactions between non-linear feedback (density dependence) and uncorrelated random noise in the dynamics of unstructured populations. The stochastic non-linear dynamics are generally complex, even when the deterministic skeleton possesses a stable equilibrium. There are three critical factors of the stochastic non-linear dynamics; whether the intrinsic population growth rate (lambda) is smaller than, equal to, or greater than 1; the pattern of density dependence at very low and very high densities; and whether the noise distribution has exponential moments or not. If lambda < 1, the population process is generally transient with escape towards extinction. When lambda > or = 1, our quantitative analysis of stochastic non-linear dynamics focuses on characterizing the time spent by the population at very low density (rarity), or at high abundance (commonness), or in extreme states (rarity or commonness). When lambda >1 and density dependence is strong at high density, the population process is recurrent: any range of density is reached (almost surely) in finite time. The law of time to escape from extremes has a heavy, polynomial tail that we compute precisely, which contrasts with the thin tail of the laws of rarity and commonness. Thus, even when lambda is close to one, the population will persistently experience wide fluctuations between states of rarity and commonness. When lambda = 1 and density dependence is weak at low density, rarity follows a universal power law with exponent -3/2. We provide some mathematical support for the numerical conjecture [Ferriere, R., Cazelles, B., 1999. Universal power laws govern intermittent rarity in communities of interacting species. Ecology 80, 1505-1521.] that the -3/2 power law generally approximates the law of rarity of 'weakly invading' species with lambda values close to one. Some preliminary results for the dynamics of multispecific systems are presented.