Survival in continuous structured populations models

The extended McKendrick-von Foerster structured population model is employed to derive a nonautonomous ordinary differential equation model of a population. The derivation assumes that the individual life history can be delineated into several physiological stages. We study the persistence of the population when the model is autonomous and base the nonautonomous survival analysis on the autonomous case and a comparison principle. A brief excursion into alternate life history strategies is presented.This work was supported in part by the U.S. Environmental Protection Agency under cooperative agreement CR 813353010     

Global asymptotic stability of density dependent integral population projection models

Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium.     

Density dependence and risk of extinction in a small population of sea otters

Sea otters (Enhydra lutris (L.)) were hunted to extinction off the coast of Washington State early in the 20th century. A new population was established by translocations from Alaska in 1969 and 1970. The population, currently numbering at least 550 animals, A major threat to the population is the ongoing risk of majour oil spills in sea otter habitat. We apply population models to census and demographic data in order to evaluate the status of the population. We fit several density dependent models to test for density dependence and determine plausible values for the carrying capacity (K) by comparing model goodness of fit to an exponential model. Model fits were compared using Akaike Information Criterion (AIC). A significant negative relationship was found between the population growth rate and population size (r ²=0.27, F=5.57, df=16, p<0.05), suggesting density dependence in Washington state sea otters. Information criterion statistics suggest that the model is the most parsimonious, followed closely by the logistic Beverton–Holt model. Values of K ranged from 612 to 759 with best-fit parameter estimates for the Beverton–Holt model including 0.26 for r and 612 for K. The latest (2001) population index count (555) puts the population at 87–92% of the estimated carrying capacity, above the suggested range for optimum sustainable population (OSP). Elasticity analysis was conducted to examine the effects of proportional changes in vital rates on the population growth rate (). The elasticity values indicate the population is most sensitive to changes in survival rates (particularly adult survival).     

Overcompensatory recruitment and generation delay in discrete age-structured population models

 The effect of overcompensatory recruitment and the combined effect of overcompensatory recruitment and generation delay in discrete nonlinear age-structured population models is studied. Considering overcompensatory recruitment alone, we present formal proofs of the supercritical nature of bifurcations (both flip and Hopf) as well as an extensive analysis of dynamics in unstable parameter regions. One important finding here is that in case of small and moderate year to year survival probabilities there are large regions in parameter space where the qualitative behaviour found in a general n+1 dimensional model is retained already in a one-dimensional model. Another result is that the dynamics at or near the boundary of parameter space may be very complicated. Generally, generation delay is found to act as a destabilizing effect but its effect on dynamics is by no means unique. The most profound effect occurs in the n-generation delay cases. In these cases there is no stable equilibrium X ^* at all, but whenever X ^* small, a stable cycle of period n+1 where the periodic points in the cycle are on a very special form. In other cases generation delay does not alter the dynamics in any substantial way. Received 25 April 1995; received in revised form 21 November 1995     

Effects of delay,truncations and density dependence in reproduction schedules on stability of nonlinear Leslie matrix models

Understanding effects of hypotheses about reproductive influences, reproductive schedules and the model mechanisms that lead to a loss of stability in a structured model population might provide information about the dynamics of natural population. To demonstrate characteristics of a discrete time, nonlinear, age structured population model, the transition from stability to instability is investigated. Questions about the stability, oscillations and delay processes within the model framework are posed. The relevant processes include delay of reproduction and truncation of lifetime, reproductive classes, and density dependent effects. We find that the effects of delaying reproduction is not stabilizing, but that the reproductive delay is a mechanism that acts to simplify the system dynamics. Density dependence in the reproduction schedule tends to lead to oscillations of large period and towards more unstable dynamics. The methods allow us to establish a conjecture of Levin and Goodyear about the form of the stability in discrete Leslie matrix models.This research was supported in part by the US Environmental Protection Agency under cooperation agreement CR-816081     

On the action of population density in the population fluctuation of the flour moth,Ephestia cautella

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Contributions from the Entomological Laboratory, Kyoto University, No. 228.     

Persistence in population models with demographic fluctuations

A persistence and extinction theory is developed through analytical studies of deterministic population models. Under hypotheses that require demographic parameters to fluctuate temporally, the populations may or may not oscillaate. Extinction, when it occurs, is asymptotic. An hierarchy of persistence criteria, based upon fluctuations measured by time average means, is derived. In some situations a threshold value is found to separate persistent population models from those that tend to extinction. Application of the persistence-extinction theory is to the problem of assessing effects of a toxic substance on a population when toxicant inputs to the environment and to resources are oscillatory.     

Synchronous dynamics and rates of extinction in spatially structured populations

We explore extinction rates using a spatially arranged set of subpopulations obeying Ricker dynamics. The population system is subjected to dispersal of individuals among the subpopulations as well as to local and global disturbances. We observe a tight positive correlation between global extinction rate and the level of synchrony in dynamics among thesubpopulations. Global disturbances and to a lesser extent, migration, are capable of synchronizing the temporal dynamics of the subpopulations over a rather wide span of the population growth rate r. Local noise decreases synchrony, as does increasing distance among the subpopulations. Synchrony also levels off with increasing r: in the chaotic region, subpopulations almost invariably behave asynchronously. We conclude that it is asynchrony that reduces the probability of global extinctions, not chaos as such: chaos is a special case only. The relationship between global extinction rate, synchronous dynamics and population growth rate is robust to changes in dispersal rates and ranges.     

Approximating persistence in a general class of population processes

We provide a general framework for estimating persistence in populations which may be affected by catastrophic events, and which are either unbounded or have very large ceilings. We model the population using a birth-death process modified to allow for downward jumps of arbitrary size. For such processes, it is typically necessary to truncate the process in order to make the evaluation of expected extinction times (and higher-order moments) computationally feasible. Hence, we give particular attention to the selection of a cut-off point at which to truncate the process, and we present a simple method for obtaining quantitative indicators of the suitability of a chosen cut-off.     

On parameter estimation in population models

We describe methods for estimating the parameters of Markovian population processes in continuous time, thus increasing their utility in modelling real biological systems. A general approach, applicable to any finite-state continuous-time Markovian model, is presented, and this is specialised to a computationally more efficient method applicable to a class of models called density-dependent Markov population processes. We illustrate the versatility of both approaches by estimating the parameters of the stochastic SIS logistic model from simulated data. This model is also fitted to data from a population of Bay checkerspot butterfly (Euphydryas editha bayensis), allowing us to assess the viability of this population.     

污染环境下单种群模型生存阈值

本论文研究了污染环境下毒素对单种群生存的影响。在环境容纳量较小的假设下建立了生物种群模型,在该模型中不但考虑了环境毒素浓度对生物个体生存的影响,还考虑了生物个体从食物链中吸收的毒素对其影响。通过研究得到种群一致持续生存和若平均持续生存的充分条件,同时得到种群持续生存依赖于模型参数和生物个体体内毒素净化率的某些充分条件．     

The effect of population density on the growth of an animal population

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Contribution from the Department of Fisheries, Kyoto University.

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Contribution from the Entomological Laboratory, Kyoto University, No. 201.     

Long-term population dynamics of two Carex curvula species in the Central Alps on native and alien soils

The demography of two closely related alpine sedges, Carex curvula subsp. curvula and Carex curvula subsp. rosae (=C. curvula and C. rosae) has been investigated on their typical sites in the Central Alps. Both species proliferate vegetatively and develop dense tussocks but they show different dominance behaviours in their respective grasslands. It was hypothesized that this may be caused by different growth abilities. The main aim of the study was to compare the vegetative growth of the species under field conditions, under competition-free conditions and under changed soil conditions. An attempt was also made to clarify whether vegetative growth is density dependent. Permanent plots were established in the respective grasslands of the two species and the ramet density was counted over 3 years. Groups of 10 and of 30 ramets of each species were grown in pots with typical and with alien substrate and their growth was observed for 5 years at the field site. The grassland populations of both species were very stable and the overall ramet growth rate (λ) was close to 1.0. Within the pots, both species reached a high ramet number. Only the group of 30 ramets of C. curvula on alien soil could not recover from the transplantation shock. Within the pots, C. rosae showed a greater ramet turnover and a higher increase in ramets than C. curvula. On their native substrate, both species had a significantly higher ramet increase than on the alien substrate. Ramet growth was found to be density dependent for both species, the increases recorded for the groups of 10 being significantly greater than for the groups of 30. Although C. curvula produced fewer ramets than C. rosae, the aboveground dry weight of the former was significantly higher. This may be decisive for its greater competitive success in closed grasslands. Received: 12 April 1997 / Accepted: 12 December 1997     

General population growth models with Allee effects in a random environment

Allee effects on population growth are quite common in nature, usually studied through deterministic models with a specific growth rate function.In order to seek the qualitative behaviour of populations induced by such effects, one should avoid model-specific behaviours. So, we use as a basis a general deterministic model, i.e. a model with a general growth rate function, to which we add the effect on the growth rate of the random fluctuations in environmental conditions. The resulting model is the general stochastic differential equation (SDE) model that we propose here.We consider two possible cases, weak Allee effects and strong Allee effects, which lead to different qualitative behaviours of the model.We will study the model properties for both cases in terms of existence and uniqueness of the solution, extinction and stationary behaviour of the population. The two cases will be compared with each other and with the general density-dependent SDE model without Allee effects.We then consider as an example the particular case of the classic logistic model and an Allee effect version of it.     

Stochastic density dependence in population size of a benthic clonal invertebrate: the regulating role of fission

The influence of environmental variation on the demography of clonal organisms has been poorly studied. I utilise a matrix model of the population dynamics of the intertidal zoanthid Palythoa caesia to examine how density dependence and temporal variation in demographic rates interact in regulating population size. The model produces realistic simulations of population size, with erratic fluctuations between soft lower and upper boundaries of approximately 55 and 90% cover. Cover never exceeds the maximum possible of 100%, and the population never goes to extinction. A sensitivity analysis indicates that the model’s behaviour is driven by density dependence in the fission of large colonies to produce intermediate sized colonies. Importantly, there is no density-dependent mortality in the model, and density dependence in recruitment, while present, is unimportant. Thus it appears that the main demographic processes which are considered to regulate population size in aclonal organisms may not be important for clonal species. Received: 18 August 1999 / Accepted: 29 October 1999     

污染环境中单种群生存分析

本文研究了污染环境中种群的动力学模型,基于已有结果,考虑了内禀增长率为非线性函数的情形.利用微分方程定性理论中的比较定理,对于种群的持续生存与绝灭给出了判别条件.     

Analysis of periodic growth-disturbance models

In this paper, I present and discuss a potentially useful modeling approach for investigating population dynamics in the presence of disturbance. Using the motivating example of wildfire, I construct and analyze a deterministic model of population dynamics with periodic disturbances independent of spatial effects. Plant population growth is coupled to fire disturbance to create a growth-disturbance model for a fluctuating population. Changes in the disturbance frequency are shown to generate a period-bubbling bifurcation structure and population dynamics that are most variable at intermediate disturbance frequencies. Similar dynamics are observed when the model is extended to include a seed bank. Some general conditions necessary for a rich bifurcation structure in growth-disturbance models are discussed.     

Persistence,extinction, and critical patch number for island populations

Sufficient conditions are derived for persistence and extinction of a population inhabiting several islands. Discrete reaction-diffusion population models are analyzed which describe growth and diffusion of a population on a group of islands or a patch environment. A critical patch number is defined as the number of islands below which the population goes extinct on that group of islands. It is shown that population persistence on one island leads to population persistence for the entire archipelago. Both single-species and multi-species models are discussed.