Destabilization and chaos induced by harvesting: insights from one-dimensional discrete-time models.

One-dimensional discrete-time population models are often used to investigate the potential effects of increasing harvesting on population dynamics, and it is well known that suitable harvesting rates can stabilize fluctuations of population abundance. However, destabilization is also a possible outcome of increasing harvesting even in simple models. We provide a rigorous approach to study when harvesting is stabilizing or destabilizing, considering proportional harvesting and constant quota harvesting, that are usual strategies for the management of exploited populations.

Dynamics and bifurcations of a family of piecewise smooth maps arising in population models with threshold harvesting.

We study a discrete-time model for a population subject to harvesting. A maximum annual catch H is fixed, but a minimum biomass level T must remain after harvesting. This leads to a mathematical model governed by a continuous piecewise smooth map, whose dynamics depend on two relevant parameters H and T.

Proportional threshold harvesting in discrete-time population models.

Threshold-based harvesting strategies tend to give high yields while protecting the exploited population. A significant drawback, however, is the possibility of harvesting moratoria with their socio-economic consequences, if the population size falls below the threshold and harvesting is not allowed anymore. Proportional threshold harvesting (PTH) is a strategy, where only a fraction of the population surplus above the threshold is harvested.

A Global Picture of the Gamma-Ricker Map: A Flexible Discrete-Time Model with Factors of Positive and Negative Density Dependence.

The gamma-Ricker model is one of the more flexible and general discrete-time population models. It is defined on the basis of the Ricker model, introducing an additional parameter [Formula: see text]. For some values of this parameter ([Formula: see text], population is overcompensatory, and the introduction of an additional parameter gives more flexibility to fit the stock-recruitment curve to field data.

Potential Impact of Carry-Over Effects in the Dynamics and Management of Seasonal Populations.

For many species living in changing environments, processes during one season influence vital rates in a subsequent season in the same annual cycle. The interplay between these carry-over effects between seasons and other density-dependent events can have a strong influence on population size and variability. We carry out a theoretical study of a discrete semelparous population model with an annual cycle divided into a breeding and a non-breeding season; the model assumes carry-over effects coming from the non-breeding period and affecting breeding performance through a density-dependent adjustment of the growth rate parameter.

Delayed population models with Allee effects and exploitation.

Allee effects make populations more vulnerable to extinction, especially under severe harvesting or predation. Using a delay-differential equation modeling the evolution of a single-species population subject to constant effort harvesting, we show that the interplay between harvest strength and Allee effects leads not only to collapses due to overexploitation; large delays can interact with Allee effects to produce extinction at population densities that would survive for smaller time delays. In case of bistability, our estimations on the basins of attraction of the two coexisting attractors improve some recent results in this direction.

Harvest timing and its population dynamic consequences in a discrete single-species model.

The timing of harvesting is a key instrument in managing and exploiting biological populations and renewable resources. Yet, there is little theory on harvest timing, and even less is known about the impact of different harvest times on the stability of population dynamics, even though this may drive population variability and risk of extinction. Here, we employ the framework proposed by Seno to study how harvesting at specific moments in the reproductive season affects not only population size but also stability.

Global dynamics in a stage-structured discrete-time population model with harvesting.

The purpose of this paper is to analyze the effect of constant effort harvesting upon global dynamics of a discrete-time population model with juvenile and adult stages. We consider different scenarios, including adult-only mortality, juvenile-only mortality, and equal mortality of juveniles and adults. In addition to analytical study of equilibria of the system, we analyze global dynamics by means of an automated set-oriented rigorous numerical method.

The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting.

We analyze the effects of a strategy of constant effort harvesting in the global dynamics of a one-dimensional discrete population model that includes density-independent survivorship of adults and overcompensating density dependence. We discuss the phenomenon of bubbling (which indicates that harvesting can magnify fluctuations in population abundance) and the hydra effect, which means that the stock size gets larger as harvesting rate increases. Moreover, we show that the system displays chaotic behaviour under the combination of high per capita recruitment and small survivorship rates.

Global stabilization of fixed points using predictive control.

We analyze the global stability properties of some methods of predictive control. We particularly focus on the optimal control function introduced by de Sousa Vieira and Lichtenberg [Phys. Rev.

Globally attracting fixed points in higher order discrete population models.

We address the global stability properties of the positive equilibrium in a general delayed discrete population model. Our results are used to investigate in detail a well-known model for baleen whale populations.

Global stability in discrete population models with delayed-density dependence.

We address the global stability issue for some discrete population models with delayed-density dependence. Applying a new approach based on the concept of the generalized Yorke conditions, we establish several criteria for the convergence of all solutions to the unique positive steady state. Our results support the conjecture stated by Levin and May in 1976 affirming that the local asymptotic stability of the equilibrium of some delay difference equations (including Ricker's and Pielou's equations) implies its global stability.