Towards some general ecological principles

Discrete deterministic age-structured, stage-structured and difference delay equation population models are analysed and compared with respect to stability and nonstationary behaviour. All three models show that species with iteroparous life histories tend to be more stable than species with semelparous life histories which allow us to conclude that this must be a fairly general ecological principle. Considering iteroparity, the precocious case appears to be more stable than the delayed case. The nonstationary dynamics shows a great deal of resemblance too, but when the number of age classes are even there is a mismatch between the dynamical outcomes of the age- and stage-structured case whenever the survival probabilities are large or moderate. Regarding semelparous species the analysis of the age-structured and the difference delay equation model clearly suggest that precocious semelparous species are more stable than delayed semelparous species and, moreover, that the transfer from stability to instability goes through a Hopf bifurcation. This is in great contrast to the outcome of the stage-structured model. In this case we find that the delayed case is more stable than the precocious and in unstable parameter regions there are orbits of period 2k , k > 1, which we do not find when the life history is precocious

An Analysis of a Semelparous Population Model with Density-Dependent Fecundity and Density - Dependent Survival Probabilities.

Source at https://doi.org/10.1155/2017/8934295 .A discrete age-structured semelparous Leslie matrix model where density dependence is included both in the fecundity and in the survival probabilities is analysed. Depending on strength of density dependence, we show in the precocious semelparous case that the nonstationary dynamics may indeed be rich, ranging from SYC (a dynamical state where the whole population is in one age class only) dynamics to cycles of low period where all age classes are populated. Quasiperiodic and chaotic dynamics have also been identified. Moreover, outside parameter regions where SYC dynamics dominates, we prove that the transfer from stability to instability goes through a supercritical Neimark − Sacker bifurcation, and it is further shown that when the population switches from possessing a precocious to a delayed semelparous life history both stability properties and the possibility of periodic dynamics become weaker

Compensatory and overcompensatory dynamics in prey–predator systems exposed to harvest

Density dependent prey–predator systems under the impact of harvest are considered. The recruitment functions for both the prey and predator belong to the Deriso–Schnute family which allow us to study how the dynamical behaviour of both populations changes when compensatory density dependence turns overcompensatory. Depending on the degree of overcompensation, we show in the case of no harvest that an increase of the fecundity of the prey always acts in a destabilizing fashion. If the degree of overcompensation becomes sufficiently large, such an increase can lead to large amplitude chaotic oscillations of the prey, which actually may drive the predator population to extinction. The impact of harvest also depends on the degree of overcompensatory density dependence. If only the prey is the target population, increased harvest in general seems to stabilize the dynamics. On the other hand, harvesting only the predator may in some cases tend to stabilize dynamics, but there are also parameter regions where this turns out to be a strong destabilizing effect

Stage-Dependent Predation on Prey Species Who Possess Different Life Histories

Two stage-structuredone-population (prey) models together with four prey-predator models are analyzed. Regarding the prey models, where one of them has fecundity elements which depend on the total population while the fecundities of the other depend on the mature part of the population only, we prove that both of them are permanent and moreover that their fixed points undergo supercritical bifurcations, flip, and Neimark-Sacker, respectively, at the various instability thresholds. By use of the models, we also provide a discussion of stability and dynamical properties of species who possess different life histories and extent results obtained elsewhere. Turning to predation, in contrast to what one finds in most papers, we scrutinize cases where both the immature subpopulation of the prey and the mature part are targets for the predator. Among our findings, here is that increased predation may act in both a stabilizing and destabilizing fashion depending on the size of fecundity of prey. Moreover, we present new results about the transition from stability to instability, and we show that whenever predation acts destabilizing, the effect is most profound in cases where the prey possesses a precocious semelparous life history. We also provide several examples where increased predation may turn a stable system chaotic

Discrete Dynamical Systems: with an Introduction to Discrete Optimization Problems - eBooks and textbooks from bookboon.com

254 PagesThis book covers important topics like stability, hyperbolicity, bifurcation theory and chaos, topics which are essential in order to understand the fascinating behavior of nonlinear discrete dynamical systems. The theory is illuminated by several examples and exercises, many of them taken from population dynamical studies. Solution methods of linear systems as well as solution methods of discrete optimization (control) problems are also included. In an Appendix it is explained how to estimate parameters in nonlinear discrete models

On the Interplay between Cannibalism and Harvest in Stage-Structured Population Models

By use of a nonlinear stage-structured population model the role of cannibalism and the combined role of cannibalism and harvest have been explored. Regarding the model, we prove that in most parts of parameter space it is permanent. We also show that the transfer from stability to nonstationary dynamics always occurs when the unique stable equilibrium undergoes a supercritical Neimark-Sacker (Hopf) bifurcation. Moreover, the dynamic consequences of catch depend not only on which part of the population (immature or mature) is exposed to increased harvest pressure but also on which part of the immature population (newborns, older immature individuals) suffers from cannibalism. Indeed, if only newborns are exposed to cannibalism an enlargement of harvest pressure on the mature part of the population may act in a stabilizing fashion. On the other hand, whenever the whole immature population is exposed to cannibalism there are parts in parameter space where increased harvest on the mature population acts in a destabilizing fashion

An analysis of Discrete stage-structured prey and prey-predator population models.

Discrete stage-structured prey and prey-predator models are considered. Regarding the former, we prove that the models at hand are permanent (i.e., the population will neither go extinct nor exhibit explosive oscillations) and, moreover, that the transfer from stability to nonstationary behaviour always goes through a supercritical Neimark−Sacker bifurcation.The prey model covers species that possess a wide range of different life histories. Predation pressure may both stabilize and destabilize the prey dynamics but the strength of impact is closely related to life history. Indeed, if the prey possesses a precocious semelparous life history and exhibits chaotic oscillations, it is shown that increased predation may stabilize the dynamics and also, in case of large predation pressure, transfer the population to another chaotic regime