Derivation and dynamics of discrete population models with distributed delay in reproduction.

We introduce a class of discrete single species models with distributed delay in the reproductive process and a cohort dependent survival function that accounts for survival pressure during that delay period. These delay recurrences track the mature population for species in which individuals reach maturity after at least τ and at most τ+τ breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, τ˜.

Rapid Evolution of Resistance and Tolerance Leads to Variable Host Recoveries following Disease-Induced Declines.

AbstractRecoveries of populations that have suffered severe disease-induced declines are being observed across disparate taxa. Yet we lack theoretical understanding of the drivers and dynamics of recovery in host populations and communities impacted by infectious disease. Motivated by disease-induced declines and nascent recoveries in amphibians, we developed a model to ask the following question: How does the rapid evolution of different host defense strategies affect the transient recovery trajectories of hosts following pathogen invasion and disease-induced declines? We found that while host life history is predictably a major driver of variability in population recovery trajectories (including declines and recoveries), populations that use different host defense strategies (i.

Overcoming the impossibility of age-balanced harvest.

In many countries, sustainability targets for managed fisheries are often expressed in terms of a fixed percentage of the carrying capacity. Despite the appeal of such a simple quantitative target, an unintended consequence may be a significant tilting of the proportions of biomass across different ages, from what they would have been under harvest-free conditions. Within the framework of a widely used age-structured model, we propose a novel quantitative definition of "age-balanced harvest" that considers the age-class composition relative to that of the unfished population.

Technique to derive discrete population models with delayed growth.

We provide a procedure for deriving discrete population models for the size of the adult population at the beginning of each breeding cycle and assume only adult individuals reproduce. This derivation technique includes delay to account for the number of breeding cycles that a newborn individual remains immature and does not contribute to reproduction. These models include a survival probability (during the delay period) for the immature individuals, since these individuals have to survive to reach maturity and become members of, what we consider, the adult population.

The Beverton-Hold model on isolated time scales.

In this work, we formulate the Beverton-Holt model on isolated time scales and extend existing results known in the discrete and quantum calculus cases. Applying a recently introduced definition of periodicity for arbitrary isolated time scales, we discuss the effects of periodicity onto a population modeled by a dynamic version of the Beverton-Holt equation. The first main theorem provides conditions for the existence of a unique ω -periodic solution that is globally asymptotically stable, which addresses the first Cushing-Henson conjecture on isolated time scales.

Square root identities for harvested Beverton-Holt models.

We introduce the term net-proliferation rate for a class of harvested single species models, where harvest is assumed to reduce the survival probability of individuals. Following the classical maximum sustainable yield calculations, we establish relations between the proliferation and net-proliferation that are economically and sustainably favored. The resulting square root identities are analytically derived for species following the Beverton-Holt recurrence considering three levels of complexity.

Derivation and Analysis of a Discrete Predator-Prey Model.

We derive a discrete predator-prey model from first principles, assuming that the prey population grows to carrying capacity in the absence of predators and that the predator population requires prey in order to grow. The proposed derivation method exploits a technique known from economics that describes the relationship between continuous and discrete compounding of bonds. We extend standard phase plane analysis by introducing the next iterate root-curve associated with the nontrivial prey nullcline.

An alternative delayed population growth difference equation model.

We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribution that takes into account that those individuals that die during the delay, do not contribute to growth. The model introduced differs from a delayed logistic difference equation, known as the delayed Pielou or delayed Beverton-Holt model, that was formulated as a discretization of the Hutchinson model. The analysis of our delayed difference equation model identifies a critical delay threshold.

Mistakes can stabilise the dynamics of rock-paper-scissors games.

A game of rock-paper-scissors is an interesting example of an interaction where none of the pure strategies strictly dominates all others, leading to a cyclic pattern. In this work, we consider an unstable version of rock-paper-scissors dynamics and allow individuals to make behavioural mistakes during the strategy execution. We show that such an assumption can break a cyclic relationship leading to a stable equilibrium emerging with only one strategy surviving.

A measure for intrinsic information.

We introduce an information measure that reflects the intrinsic perspective of a receiver or sender of a single symbol, who has no access to the communication channel and its source or target. The measure satisfies three desired properties-causality, specificity, intrinsicality-and is shown to be unique. Causality means that symbols must be transmitted with probability greater than chance.

Optimal harvesting policy for the Beverton--Holt model.

In this paper, we establish the exploitation of a single population modeled by the Beverton--Holt difference equation with periodic coefficients. We begin our investigation with the harvesting of a single autonomous population with logistic growth and show that the harvested logistic equation with periodic coefficients has a unique positive periodic solution which globally attracts all its solutions. Further, we approach the investigation of the optimal harvesting policy that maximizes the annual sustainable yield in a novel and powerful way; it serves as a foundation for the analysis of the exploitation of the discrete population model.