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Fisheries, as indispensable natural resources for human, need to be managed with both short‐term economical benefits and long‐term sustainability in consideration. This has remained a challenge, because the population and catch dynamics of the fisheries are complex and noisy, while the data available is often scarce and only provides partial information on the dynamics. To address these challenges, we formulate the population and catch dynamics as a Partially Observable Markov Decision Process (POMDP), and propose a model‐based offline reinforcement learning approach to learn an optimal management policy. Our approach allows learning fishery management policies from possibly incomplete fishery data generated by a stochastic fishery system. This involves first learning a POMDP fishery model using a novel least squares approach, and then computing the optimal policy for the learned POMDP. The learned fishery dynamics model is useful for explaining the resulting policy's performance. We perform systematic and comprehensive simulation study to quantify the effects of stochasticity in fishery dynamics, proliferation rates, missing values in fishery data, dynamics model misspecification, and variability of effort (e.g., the number of boat days). When the effort is sufficiently variable and the noise is moderate, our method can produce a competitive policy that achieves 85% of the optimal value, even for the hardest case of noisy incomplete data and a misspecified model. Interestingly, the learned policies seem to be robust in the presence of model learning errors. However, non‐identifiability kicks in if there is insufficient variability in the effort level and the fishery system is stochastic. This often results in poor policies, highlighting the need for sufficiently informative data. We also provide a theoretical analysis on model misspecification and discuss the tendency of a Schaefer model to overfit compared with a Beverton–Holt model. [ABSTRACT FROM AUTHOR]

Abstract Most models of ecological and eco‐evolutionary processes involve creating trajectories of something, be it population densities, average trait values, or environmental states, over time. This requires decision‐making regarding how to represent the flow of time in models. Most ecologists are exposed to continuous‐time models (typically in the form of ordinary differential equations) as part of their training, especially since the famous Lotka‐Volterra predator–prey dynamics are formulated this way. However, few appear sufficiently well trained to produce their own work with continuous‐time models and may lack exposure to the true versatility of available methods. Specifically, knowledge that discrete individuals can be modelled in continuous time using the Gillespie algorithm is not as widespread as it should be. I will illustrate the flexibility of continous‐time modelling methods such that researchers can make informed choices, and not resort to discretizing time as a ‘default’ without a clear biological motivation to do so. I provide three example‐based tutorials: (1) a comparison of deterministic and stochastic dynamics of the Lotka‐Volterra predator–prey model, (2) an evaluation of matelessness in a hypothetical insect population (and of selection to mate more often by either searching more efficiently or by shortening the ‘time out’ after each mating) and (3) within‐season density dependence followed by a birth pulse leading to Beverton‐Holt or Ricker dynamics depending on whether the deaths of conspecifics help reduce the mortality of others or not (compensatory mortality). I highlight properties of the exponential distribution that, while counter‐intuitive, are good to know when deriving expected lifetime reproductive success or other similar quantities. I also give guidance on how to proceed if the so‐called memorylessness assumption does not hold in a given situation, and show how continuous and discrete times can be freely mixed if the biological situation dictates this to be the preferred option. Continuous‐time models can also be empirically fitted to data, and I review briefly the insight this gives into the so‐called ‘do hares eat lynx?’ paradox that has been plaguing the interpretation of the Hudson Bay hare and lynx dataset.

Most models of ecological and eco‐evolutionary processes involve creating trajectories of something, be it population densities, average trait values, or environmental states, over time. This requires decision‐making regarding how to represent the flow of time in models. Most ecologists are exposed to continuous‐time models (typically in the form of ordinary differential equations) as part of their training, especially since the famous Lotka‐Volterra predator–prey dynamics are formulated this way. However, few appear sufficiently well trained to produce their own work with continuous‐time models and may lack exposure to the true versatility of available methods. Specifically, knowledge that discrete individuals can be modelled in continuous time using the Gillespie algorithm is not as widespread as it should be.I will illustrate the flexibility of continous‐time modelling methods such that researchers can make informed choices, and not resort to discretizing time as a 'default' without a clear biological motivation to do so. I provide three example‐based tutorials: (1) a comparison of deterministic and stochastic dynamics of the Lotka‐Volterra predator–prey model, (2) an evaluation of matelessness in a hypothetical insect population (and of selection to mate more often by either searching more efficiently or by shortening the 'time out' after each mating) and (3) within‐season density dependence followed by a birth pulse leading to Beverton‐Holt or Ricker dynamics depending on whether the deaths of conspecifics help reduce the mortality of others or not (compensatory mortality).I highlight properties of the exponential distribution that, while counter‐intuitive, are good to know when deriving expected lifetime reproductive success or other similar quantities. I also give guidance on how to proceed if the so‐called memorylessness assumption does not hold in a given situation, and show how continuous and discrete times can be freely mixed if the biological situation dictates this to be the preferred option.Continuous‐time models can also be empirically fitted to data, and I review briefly the insight this gives into the so‐called 'do hares eat lynx?' paradox that has been plaguing the interpretation of the Hudson Bay hare and lynx dataset. [ABSTRACT FROM AUTHOR]

In this paper we study the scalar delay differential equation x ′ (t) = α (t) x (t - g 1 (t)) f (a (t) , x (t - g 2 (t))) - β (t) x (t) where f is decreasing in both arguments and the coefficients are positive and bounded. Sufficient conditions for the permanence and global attractivity for a fixed positive solution are derived. We apply our results to nonautonomous variants of Nicholson's blowfly equation and the Beverton–Holt model. [ABSTRACT FROM AUTHOR]

The logistic growth model is one of the most frequently used formalizations of density dependence affecting population growth, persistence and evolution. Ecological and evolutionary theory, and applications to understand population change over time often include this model. However, the assumptions and limitations of this popular model are often not well appreciated. Here, we briefly review past use of the logistic growth model and highlight limitations by deriving population growth models from underlying consumer–resource dynamics. We show that the logistic equation likely is not applicable to many biological systems. Rather, density‐regulation functions are usually non‐linear and may exhibit convex or concave curvatures depending on the biology of resources and consumers. In simple cases, the dynamics can be fully described by the Schoener model. More complex consumer dynamics show similarities to a Maynard Smith–Slatkin model. We show how population‐level parameters, such as intrinsic rates of increase and equilibrium population densities are not independent, as often assumed. Rather, they are functions of the same underlying parameters. The commonly assumed positive relationship between equilibrium population density and competitive ability is typically invalid. We propose simple relationships between intrinsic rates of increase and equilibrium population densities that capture the essence of different consumer–resource systems. Relating population level models to underlying mechanisms allows us to discuss applications to evolutionary outcomes and how these models depend on environmental conditions, like temperature via metabolic scaling. Finally, we use time‐series from microbial food chains to fit population growth models as a test case for our theoretical predictions. Our results show that density‐regulation functions need to be chosen carefully as their shapes will depend on the study system's biology. Importantly, we provide a mechanistic understanding of relationships between model parameters, which has implications for theory and for formulating biologically sound and empirically testable predictions. [ABSTRACT FROM AUTHOR]

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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 M breeding cycles. Under realistic model assumptions, we prove the existence of a critical delay threshold, τ˜ c . For given delay kernel length τ M , if each individual takes at least τ˜ c time units to reach maturity, then the population is predicted to go extinct. We show that the positive equilibrium is decreasing in both τ and τ M . In the case of a constant reproductive rate, we provide an equation to determine τ˜ c for fixed τ M , and similarly, provide a lower bound on the kernel length, τ˜ M for fixed τ such that the population goes extinct if τ M ≥τ˜ M . We compare these critical thresholds for different maturation distributions and show that if all else is the same, to avoid extinction it is best if all individuals in the population have the shortest delay possible. We apply the model derivation to a Beverton-Holt model and discuss its global dynamics. For this model with kernels that share the same mean delay, we show that populations with the largest variance in the time required to reach maturity have higher population levels and lower chances of extinction., Competing Interests: Declaration of competing interest The authors, declare that they have no conflicts of interest., (Copyright © 2024 Elsevier Inc. All rights reserved.)

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. If the time delay exceeds this threshold, the model predicts that the population will go extinct for all non-negative initial conditions. If the delay is below this threshold, the population survives and its size converges to a positive globally asymptotically stable equilibrium that is decreasing in size as the delay increases. We show global asymptotic stability of the positive equilibrium using two different techniques. For one set of parameter values, a contraction mapping result is applied, while the proof for the remaining set of parameter values, relies on showing that the map is eventually componentwise monotone. [ABSTRACT FROM AUTHOR]

We use juvenile-adult discrete-time infectious disease models with intrinsically generated demographic population cycles to study the effects of age structure on the persistence or extinction of disease and the basic reproduction number, $\mathcal {R}_{0} $. Our juvenile-adult Susceptible-Infectious-Recovered (SIR) and Infectious-Salmon Anemia-Virus (ISA $v) $ models share a common disease-free system that exhibits equilibrium dynamics for the Beverton-Holt recruitment function. However, when the recruitment function is the Ricker model, a juvenile-adult disease-free system exhibits a range of dynamic behaviours from stable equilibria to deterministic period k population cycles to Neimark-Sacker bifurcations and deterministic chaos. For these two models, we use an extension of the next generation matrix approach for calculating $\mathcal {R}_{0} $ to account for populations with locally asymptotically stable period k cycles in the juvenile-adult disease-free system. When $\mathcal {R}_{0} \lt 1 $ and the juvenile-adult demographic system (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove that the juvenile-adult disease goes extinct whenever $\mathcal {R}_{0} \lt 1 $. Under the same period k juvenile-adult demographic assumption but with $\mathcal {R}_{0} \gt 1 $, we prove that the juvenile-adult disease-free period k population cycle is unstable and the disease persists. When $\mathcal {R}_{0} \gt 1 $, our simulations show that the juvenile-adult disease-free period k cycle dynamics drives the juvenile-adult SIR disease dynamics, but not the juvenile-adult ISAv disease dynamics.

Overpopulation and environmental degradation due to inadequate resource-use are outcomes of human's ecosystem engineering that has profoundly modified the world's landscape. Despite the age-old concern that unchecked population and economic growth may be unsustainable, the prospect of societal collapse remains contentious today. Contrasting with the usual approach to modeling human-nature interactions, which are based on the Lotka-Volterra predator-prey model with humans as the predators and nature as the prey, here we address this issue using a discrete-time population dynamics model of ecosystem engineers. The growth of the population of engineers is modeled by the Beverton-Holt equation with a density-dependent carrying capacity that is proportional to the number of usable habitats. These habitats (e.g., farms) are the products of the work of the individuals on the virgin habitats (e.g., native forests), hence the denomination engineers of ecosystems to those agents. The human-made habitats decay into degraded habitats, which eventually regenerate into virgin habitats. For slow regeneration resources, we find that the dynamics is dominated by rounds of prosperity and collapse, in which the population reaches vanishing small densities. However, increase of the efficiency of the engineers to explore the resources eliminates the dangerous oscillatory patterns of feast and famine and leads to a stable equilibrium that balances population growth and resource availability. This finding supports the viewpoint of growth optimists that technological progress may avoid collapse.

The study of the role of environmental variation in community dynamics has traditionally assumed that the environment is a stationary stochastic process or a periodic deterministic process. However, the physical environment in nature is nonstationary. Moreover, anthropogenically driven climate change provides a new challenge emphasizing a persistent but frequently ignored problem: how to make predictions about the dynamics of communities when the nonstationarity of the physical environment is recognized. Recent work is providing a path to conclusions with none of the traditional assumptions of environmental stationarity or periodicity. Traditional assumptions about convergence of long-term averages of functions of environmental states can be replaced by assumptions about temporal sums, allowing convergence and persistence of population processes to be demonstrated in general nonstationary environments. These tools are further developed and illustrated here with some simple models of nonstationary community dynamics, including the Beverton-Holt model, the threshold exponential and the lottery model.

We use juvenile-adult discrete-time infectious disease models with intrinsically generated demographic population cycles to study the effects of age structure on the persistence or extinction of disease and the basic reproduction number, R 0 . Our juvenile-adult Susceptible-Infectious-Recovered (SIR) and Infectious-Salmon Anemia-Virus (ISA v) models share a common disease-free system that exhibits equilibrium dynamics for the Beverton-Holt recruitment function. However, when the recruitment function is the Ricker model, a juvenile-adult disease-free system exhibits a range of dynamic behaviours from stable equilibria to deterministic period k population cycles to Neimark-Sacker bifurcations and deterministic chaos. For these two models, we use an extension of the next generation matrix approach for calculating R 0 to account for populations with locally asymptotically stable period k cycles in the juvenile-adult disease-free system. When R 0 < 1 and the juvenile-adult demographic system (in the absence of the disease) has a locally asymptotically stable period k population cycle, we prove that the juvenile-adult disease goes extinct whenever R 0 < 1. Under the same period k juvenile-adult demographic assumption but with R 0 > 1 , we prove that the juvenile-adult disease-free period k population cycle is unstable and the disease persists. When R 0 > 1 , our simulations show that the juvenile-adult disease-free period k cycle dynamics drives the juvenile-adult SIR disease dynamics, but not the juvenile-adult ISAv disease dynamics. [ABSTRACT FROM AUTHOR]

Numerous studies have documented the importance of individual variation (IV) in determining the outcome of competition between species. However, little is known about how the interplay between IV and habitat heterogeneity (i.e. variation and spatial autocorrelation in habitat quality) affects species coexistence at the landscape scale. Here, we incorporate habitat heterogeneity into a competition model with IV, in order to explore the mechanism of spatial species coexistence. We find that individual-level variation and habitat heterogeneity interact to promote species coexistence, more obviously at lower dispersal rates. This is in stark contrast to early non-spatial models, which predicted that IV reinforces competitive hierarchies and therefore speeds up species exclusion. In essence, increasing variation in patch quality and/or spatial habitat autocorrelation moderates differences in the competitive ability of species, thereby allowing species to coexist both locally and globally. Overall, our theoretical study offers a mechanistic explanation for emerging empirical evidence that both habitat heterogeneity and IV promote species coexistence and therefore biodiversity maintenance. [ABSTRACT FROM AUTHOR]

The study of the role of environmental variation in community dynamics has traditionally assumed that the environment is a stationary stochastic process or a periodic deterministic process. However, the physical environment in nature is nonstationary. Moreover, anthropogenically driven climate change provides a new challenge emphasizing a persistent but frequently ignored problem: how to make predictions about the dynamics of communities when the nonstationarity of the physical environment is recognized. Recent work is providing a path to conclusions with none of the traditional assumptions of environmental stationarity or periodicity. Traditional assumptions about convergence of long-term averages of functions of environmental states can be replaced by assumptions about temporal sums, allowing convergence and persistence of population processes to be demonstrated in general nonstationary environments. These tools are further developed and illustrated here with some simple models of nonstationary community dynamics, including the Beverton-Holt model, the threshold exponential and the lottery model. [ABSTRACT FROM AUTHOR]

Abstract: Although individual‐level variation (IV) is ubiquitous in nature, it is not clear how it influences species coexistence. Theory predicts that IV will hinder coexistence but empirical studies have shown that it can facilitate, inhibit, or have a neutral effect. We use a theoretical model to explore the consequences of IV on local and regional species coexistence in the context of spatial environmental structure. Our results show that individual variation can have a positive effect on species coexistence and that this effect will critically depend on the spatial structure of such variation. IV facilitates coexistence when a negative, concave‐up relationship between individuals’ competitive response and population growth rates propagates to a disproportionate advantage for the inferior competitor, provided that each species specialises in a habitat. While greater variation in the preferred habitat generally fosters coexistence, the opposite is true for non‐preferred habitats. Our results reconcile theory with empirical findings. [ABSTRACT FROM AUTHOR]

The dynamics of a single population with non-overlapping generations can be described deterministically by a scalar difference equation in this study. A discrete-time Beverton-Holt stock recruitment model with Allee effect, harvesting and hydra effect is proposed and studied. Model with strong Allee effect results from incorporating mate limitation in the Beverton-Holt model. We show that these simple models exhibit some interesting (and sometimes unexpected) phenomena such as the hydra effect, sudden collapses and essential extinction. Along with this, harvesting is a socio-economic issue to continue any system generation after generation. Different dynamical behaviors for these situations have been illustrated numerically also. The biological implications of our analytical and numerical findings are discussed critically. [ABSTRACT FROM AUTHOR]

Trichiurus japonicus is an economically valuable species in the East China Sea, whose allowable capture size varies with fishing effort in different years. To clarify the optimum capture size for T. japonicus in the East China Sea, we collected samples and data from T. japonicus targeting fishing gears such as trawls, canvas spreader stow nets and longlines from 2016 to 2020. We estimated growth and mortality parameters using the FiSAT II software, and calculated the size limit standards for capture. The results showed that the inflection point of anal length, the critical anal length and the anal length of one-year-old T. japonicus was 382.84, 397.12, and 216.05 mm, respectively. The anal length of maturity was 230.38 mm, and the minimum capture size (anal length) was 219.23 mm. Based on the yield per recruitment analysis using Beverton-Holt model, the current fishery reference points were under overfishing condition ( t c =0.38 a, F =2.11), and the suggested optimum capture size was 364.64 mm. There would be a sharp decline of T. japonicus catches in the East China Sea if the suggested minimum capture size was substantially higher, which might be non-practical for local fishermen. Therefore, we suggested 220 mm as the capture size limit, which was close to the anal length of one-year-old fish and the anal length of maturity.

Our aim is to investigate the global asymptotic behaviour, oscillation, periodicity and bifurcation in discontinuous Beverton–Holt type difference equationwherex0>0, functionskandrare discontinuous piecewise constant functionssatisfyingandhis Heaviside function. [ABSTRACT FROM AUTHOR]

Coilia nasustaihuensis is the most abundant species in Dianshan Lake and plays an important role in the lake ecosystem. From July 2010 to August 2011, a total of 3107 samples of C. nasustaihuensis were collected from Dianshan Lake. Based on length data of these samples, ELEFAN I technique was employed to estimate growth and mortality parameters, and the Beverton-Holt dynamic model was used to evaluate the population dynamics trend for C. nasustaihuensis. Growth of this species was described using a von Bertalanffy model, and the estimated parameters were L∞=35. 70 cm, k =0. 54, and t0 =-0. 48 a. The turning point for body mass growth curve of the stock was situated at t =1. 37 a. Natural mortality coefficient M was then estimated using Pauly's empirical equation and found to be 0. 872. Length-converted catch curves were used to estimate the total mortality coefficient Z, which was found to be 2. 121. Accordingly, the fishing mortality coefficient (F) was equal to 1. 249, and the current exploitation rate was 0. 589, suggesting the stock was over-exploited. According to the Beverton-Holt dynamic model, the minimum capture size for C. nasustaihuensis should be 21. 42 cm (age 1. 22 years). [ABSTRACT FROM AUTHOR]

Cadigan, N. G. 2013. Fitting a non-parametric stock–recruitment model in R that is useful for deriving MSY reference points and accounting for model uncertainty. – ICES Journal of Marine Science, 70:56–67.Modelling the relationship between parental stock size and subsequent recruitment of fish to a fishery is often required when deriving reference points, which are a fundamental component of fishery management. A non-parametric approach to estimate stock–recruitment relationships is illustrated using a simulated example and nine case studies. The approach preserves compensatory density dependence in which the recruitment rate monotonically decreases as stock size increases, which is a basic assumption of commonly used parametric stock–recruitment models. The implications of the non-parametric estimates on maximum sustainable yield (MSY) reference points are illustrated. The approach is used to provide non-parametric bootstrapped confidence intervals for reference points. The efficacy of the approach is investigated using simulations. The results demonstrate that the non-parametric approach can provide a more realistic estimation of the stock–recruitment relationship when informative data are available compared with common parametric models. Also, bootstrap confidence intervals for MSY reference points based on different parametric stock–recruitment models often do not overlap. The confidence intervals based on the non-parametric approach tend to be much wider, and reflect better uncertainty due to stock–recruit model choice. [ABSTRACT FROM PUBLISHER]

1. For social species, the link between individual behaviour and population dynamics is mediated by group-level demography. 2. Populations of obligate cooperative breeders are structured into social groups, which may be subject to inverse density dependence (Allee effects) that result from a dependence on conspecific helpers, but evidence for population-wide Allee effects is rare. 3. We use field data from a long-term study of cooperative meerkats ( Suricata suricatta; Schreber, 1776) - a species for which local Allee effects are not reflected in population-level dynamics - to empirically model interannual group dynamics. 4. Using phenomenological population models, modified to incorporate environmental conditions and potential Allee effects, we first investigate overall patterns of group dynamics and find support only for conventional density dependence that increases after years of low rainfall. 5. To explain the observed patterns, we examine specific demographic rates and assess their contributions to overall group dynamics. Although per-capita meerkat mortality is subject to a component Allee effect, it contributes relatively little to observed variation in group dynamics, and other (conventionally density dependent) demographic rates - especially emigration - govern group dynamics. 6. Our findings highlight the need to consider demographic processes and density dependence in subpopulations before drawing conclusions about how behaviour affects population processes in socially complex systems. [ABSTRACT FROM AUTHOR]

In this theoretical study, we investigate the effect of different harvesting strategies on the discrete Beverton-Holt model in a deterministic environment. In particular, we make a comparison between the constant, periodic and conditional harvesting strategies. We find that for large initial populations, constant harvest is more beneficial to both the population and the maximum sustainable yield. However, periodic harvest has a short-term advantage when the initial population is low, and conditional harvest has the advantage of lowering the risk of depletion or extinction. Also, we investigate the periodic character under each strategy and show that periodic harvesting drives population cycles to be multiples (period-wise) of the harvesting period. [ABSTRACT FROM AUTHOR]

Abstract: Local influence diagnostics are used to develop a theoretical understanding of the sensitivity of some management parameters derived from the Beverton–Holt and Ricker stock–recruit models using a common estimation method. The diagnostics provide an understanding of how characteristics of the data and model affect estimates. Sensitivity is assessed for the slope at the origin, the maximum recruitment, and the stock size corresponding to 50% of the maximum recruitment. Two types of sensitivity are considered. The first is with respect to the weighting that stock–recruit observation pairs (i.e. cases) are given in estimation. Case-weight local influence equations are developed to provide insights about why estimates change when cases are deleted. The second type of sensitivity is with respect to the stock size measurements. These are commonly assumed to be measured without error when fitting a stock–recruit model, when in fact stock size measurements often have substantial error. Local influence diagnostics are developed to assess the impact of errors in stock size, with a particular focus on measurement errors. The diagnostics are applied to 15 case-studies. [Copyright &y& Elsevier]

In this paper, we analyze r-periodic orbits of k-periodic difference equations, i.e.[image omitted] and their stability. These special orbits were introduced in S. Elaydi and R.J. Sacker (Global stability of periodic orbits of non-autonomous difference equations and population biology, J. Differ. Equ. 208(1) (2005), pp. 258-273). We discuss that, depending on the values of r and k, such orbits generically only occur in finite dimensional systems that depend on sufficiently many parameters, i.e. they have a large codimension in the sense of bifurcation theory. As an example, we consider the periodically forced Beverton-Holt model, for which explicit formulas for the globally attracting periodic orbit, having the minimal period k = r, can be derived. When r factors k the Beverton-Holt model with two time-variant parameters is an example that can be studied explicitly and that exhibits globally attracting r-periodic orbits. For arbitrarily chosen periods r and k, we develop an algorithm for the numerical approximation of an r-periodic orbit and of the associated parameter set, for which this orbit exists. We apply the algorithm to the generalized Beverton-Holt, the 2D stiletto model, and another example that exhibits periodic orbits with r and k relatively prime. [ABSTRACT FROM AUTHOR]

Abstract: This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology. [Copyright &y& Elsevier]

Abstract: The Allee effect means reduction in individual fitness at low population densities. There are many discrete-time population models with an Allee effect in the literature, but most of them are phenomenological. Recently, Geritz and Kisdi [2004. On the mechanistic underpinning of discrete-time population models with complex dynamics. J. Theor. Biol. 228, 261–269] presented a mechanistic underpinning of various discrete-time population models without an Allee effect. Their work was based on a continuous-time resource-consumer model for the dynamics within a year, from which they derived a discrete-time model for the between-year dynamics. In this article, we obtain the Allee effect by adding different mate finding mechanisms to the within-year dynamics. Further, by adding cannibalism we obtain a higher variety of models. We thus present a generator of relatively realistic, discrete-time Allee effect models that also covers some currently used phenomenological models driven more by mathematical convenience. [Copyright &y& Elsevier]

We present a derivation of various discrete-time population models within a single unifying mechanistic context. By systematically varying the with in year patterns of reproduction and aggression between individuals we can derive various discrete-time population models. These models include classical examples such as the Ricker model, the Beverton-Holt model, the Skellam model, the Hassell model, and others. Some of these models until now lacked a good mechanistic interpretation or have been derived in a different context. By using this mechanistic approach, the model parameters can be interpreted in terms of individual behavior. [ABSTRACT FROM AUTHOR]

Abstract: Supply in fisheries is traditionally known for its backward bending nature, owing to externalities in production. Such a supply regime, however, exist only for pure open access fisheries. Since most fisheries worldwide are neither pure open access, nor optimally managed, rather between the extremes, the traditional understanding of supply regimes in fisheries needs modification. This paper identifies through a case study of the East Baltic cod fishery supply regimes in fisheries, taking alternative fisheries management schemes and mesh size limitations into account. An age-structured Beverton–Holt based bio-economic supply model with mesh sizes is developed. It is found that in the presence of realistic management schemes, the supply curves are close to vertical in the relevant range. Also, the supply curve under open access with mesh size limitations is almost vertical in the relevant range, owing to constant recruitment. The implications are that the effects on supply following from e.g. trade liberalisation and reductions of subsidies are small in several and probably most fisheries worldwide. [Copyright &y& Elsevier]

In this paper, we study the asymptotic behavior of positive solutions of nonautonomous Beverton-Holt equationwhere { K n} is a positive persistent and bounded sequence. In our main result, we proved that all positive solutions { x n} satisfy the inequalityThe obtained result represents the extension of the Cushing-Hensons's conjecture. Applications to the case when { K n} is a positive periodic sequence are given and the alternative proof of the Cushing-Henson's conjecture is also presented. [ABSTRACT FROM AUTHOR]

We present a mechanistic underpinning for various discrete-time population models that can produce limit cycles and chaotic dynamics. Specific examples include the discrete-time logistic model and the Hassell model, which for a long time eluded convincing mechanistic interpretations, and also the Ricker- and Beverton–Holt models. We first formulate a continuous-time resource consumption model for the dynamics within a year, and from that we derive a discrete-time model for the between-year dynamics. Without influx of resources from the outside into the system, the resulting between-year dynamics is always overcompensating and hence may produce complex dynamics as well as extinction in finite time. We recover a connection between various standard types of continuous-time models for the resource dynamics within a year on the one hand and various standard types of discrete-time models for the population dynamics between years on the other. The model readily generalizes to several resource and consumer species as well as to more than two trophic levels for the within-year dynamics. [Copyright &y& Elsevier]