The Role of Density Regulation in Extinction Processes and Population Viability Analysis

We review the role of density dependence in the stochastic extinction of populations and the role density dependence has played in population viability analysis (PVA) case studies. In total, 32 approaches have been used to model density regulation in theoretical or applied extinction models, 29 of them are mathematical functions of density dependence, and one approach uses empirical relationships between density and survival, reproduction, or growth rates. In addition, quasi-extinction levels are sometimes applied as a substitute for density dependence at low population size. Density dependence further has been modelled via explicit individual spacing behaviour and/or dispersal. We briefly summarise the features of density dependence available in standard PVA software, provide summary statistics about the use of density dependence in PVA case studies, and discuss the effects of density dependence on extinction probability. The introduction of an upper limit for population size has the effect that the probability of ultimate extinction becomes 1. Mean time to extinction increases with carrying capacity if populations start at high density, but carrying capacity often does not have any effect if populations start at low numbers. In contrast, the Allee effect is usually strong when populations start at low densities but has only a limited influence on persistence when populations start at high numbers. Contrary to previous opinions, other forms of density dependence may lead to increased or decreased persistence, depending on the type and strength of density dependence, the degree of environmental variability, and the growth rate. Furthermore, effects may be reversed for different quasi-extinction levels, making the use of arbitrary quasi-extinction levels problematic. Few systematic comparisons of the effects on persistence between different models of density dependence are available. These effects can be strikingly different among models. Our understanding of the effects of density dependence on extinction of metapopulations is rudimentary, but even opposite effects of density dependence can occur when metapopulations and single populations are contrasted. We argue that spatially explicit models hold particular promise for analysing the effects of density dependence on population viability provided a good knowledge of the biology of the species under consideration exists. Since the results of PVAs may critically depend on the way density dependence is modelled, combined efforts to advance statistical methods, field sampling, and modelling are urgently needed to elucidate the relationships between density, vital rates, and extinction probability.     

The macroecology of population dynamics: taxonomic and biogeographic patterns in population cycles

Regular cycles in population abundance are fascinating phenomena, but are they common in natural populations? How are they distributed among taxa? Are there differences between different regions of the world, or along latitudinal gradients? Using the new Global Population Dynamics Database we analysed nearly 700 long (25 + years) time series of animal field populations, looking for large-scale patterns in cycles. Nearly 30% of the time series were cyclic. Cycle incidence varied among taxonomic classes, being most common in mammal and fish populations, but only in fish did cycle incidence vary among orders. Cycles were equally common in European and North American populations, but were more common in Atlantic fish than Pacific fish. The incidence of cycles increased with latitude in mammals only. There was no latitudinal gradient in cycle period, but cycle amplitude declined with latitude in some groups of fish. Even after considering the biases in the data source and expected type I error, population cycles seem common enough to warrant ecological attention.     

Density, climate and varying return points: an analysis of long-term population fluctuations in the threatened European tree frog

Experimental research has identified many putative agents of amphibian decline, yet the population-level consequences of these agents remain unknown, owing to lack of information on compensatory density dependence in natural populations. Here, we investigate the relative importance of intrinsic (density-dependent) and extrinsic (climatic) factors impacting the dynamics of a tree frog (Hyla arborea) population over 22 years. A combination of log-linear density dependence and rainfall (with a 2-year time lag corresponding to development time) explain 75% of the variance in the rate of increase. Such fluctuations around a variable return point might be responsible for the seemingly erratic demography and disequilibrium dynamics of many amphibian populations.     

On the stabilization of animal numbers. Problems of testing

Summary When testing for regulation of population numbers, rather than using Bulmer's second test in cases where population numbers are estimated instead of measured, we prefer to correct Bulmer's first test for estimation error. A correction method is expounded, discussed, and applied to two series of census data: the pine looper of Klomp and the garden chafer of Milne. In neither case the tentative conclusion from using the uncorrected test was changed after correction. Therefore, in practice Bulmer's first test without correction can be used well as a first orientation. Twelve long series (more than 10 years) of census data of both univoltine and semelparous (a necessary condition) insects were tested for significant density dependence in the fluctuations of numbers with the randomization test of Pollard et al. None of the series, all we could find to meet the necessary condition as well as being longer than 10 years, showed significant density dependence at the 0.05 level, though the pine looper of Klomp did so at the 0.1 level. Next, the same series were tested for regulation in the sense of keeping density within limits with both the first test of Bulmer and the permutation test of Reddingius and Den Boer. Onky Klomp's pine looper population at Hoge Veluwe scored significantly. In a following paper this population will be considered more closely, in order to enable understanding of this test result.Communication No. 362 of the Biological Station, Wijster     

Elasticity analysis as an important tool in evolutionary and population ecology

Elasticity analysis estimates the proportional change in the population growth rate for a proportional change in a vital rate (i.e. survival, growth or reproduction). It can be used to pinpoint those parts of an organism’s life history that should be the focus of management effort, or those that contribute most to fitness. Recent theoretical work has emphasized some limitations of the technique, has overcome other problems, and has shown that it is robust to some violations of its underlying assumptions. Thus, although care is needed, elasticity analysis is a simple first step in answering important questions in evolutionary and population ecology.     

Effects of density dependent sex allocation on the dynamics of a simultaneous hermaphroditic population: Modelling and analysis

In this work we present a mathematical model describing the dynamics of a population where sex allocation remains flexible throughout adult life and so can be adjusted to current environmental conditions. We consider that the fractions of immature individuals acquiring male and female sexual roles are density dependent through nonlinear functions of a weighted total population size. The main goal of this work is to understand the role of life-history parameters on the stabilization or destabilization of the population dynamics.The model turns out to be a nonlinear discrete model which is analysed by studying the existence of fixed points as well as their stability conditions in terms of model parameters. The existence of more complex asymptotic behaviours of system solutions is shown by means of numerical simulations.Females have larger fertility rate than males. On the other hand, increasing population density favours immature individuals adopting the male role. A positive equilibrium of the system exists whenever fertility and survival rates of one of the sexual roles, if shared by all adults, allow population growing while the opposite happens with the other sexual role. In terms of the female inherent net reproductive number, η_F, it is shown that the positive equilibria are stable when η_F is larger and closed to 1 while for larger values of η_F a certain asymptotic assumption on the investment rate in the female function implies that the population density is permanent. Depending on the other parameters values, the asymptotic behaviour of solutions becomes more complex, even chaotic. In this setting the stabilization/destabilization effects of the abruptness rate in density dependence, of the survival rates and of the competition coefficients are analysed.     

Models for testing

Summary This is a comment on a note by Solow (1990). It is shown that Solow's simulation results indicate that Bulmer's test for density dependence is non-robust to a particular kind of second-order Markovity that might well be overlooked by an ecologist. It is suggested that Solow's claim that Bulmer's test is insensitive is not wholly justified. Some scepticism concerning the applicability of statistical testing theory to animal population data is expressed.Communication no. 410 of the Biological Station, Wijster     

亚热带中山地区草芦无性系种群的密度制约

亚热带中山立地条件下草芦无性种群密度制约的定量分析结果表明,不同时期草芦无性系种的平均蘖重,平均蘖叶重和平均蘖茎重均随着密度的增加呈函数下降。     

种群生存力分析（PVA）的方法与应用

随着人们对资源的加速利用,生境丧失和破碎化导致物种濒危问题日益严重.以岛屿生物地理学为理论起源的种群生存力分析（PVA）,通过分析和模拟种群动态过程并建立灭绝概率与种群数量之间的关系,为濒危物种保护提供了重要的理论依据和研究途径.在过去的几十年中,种群生存力分析已成为保护生物学中一项重要的研究内容.目前种群生存力分析发展稳定,但对其实际预测能力和准确性尚存质疑,应用方面也有待进一步发展.种群生存力分析的进一步完善还需要在理论和方法上的创新,特别是籍于景观生态学和可持续性科学的理念,将空间分析手段、经济社会因素纳入到物种和种群的预测和管理上,从而使其具有更完整的理论基础和更高的实用价值.为此,本文对种群生存力分析的历史、基本概念、研究方法、模型应用和准确性进行了综述,并提出了有关的研究展望.     

植物种群生存力分析研究进展

对十多年来国外植物PVA的研究进行了综合评述;具体分析了影响植物种群生存力的各种随机性因子及确定性因子;总结了植物PVA研究的方法步骤及采用的模拟模型;探讨了植物PVA的难点,PVA对管理措施的评价效果;并提出对今后植物PVA的研究展望,认为PVA是研究濒危植物种群灭绝及评价管理或保护措施的有力工具;发展描述复杂种间关系的多种种的PVA模型以及包含多个影响因素的PVA应用模型是未来植物PVA的研究方向。     

The effect of spatial scale on interactions between two weevils and their parasitoid

1. The effect of spatial scale on the interactions between three hymenopteran parasitoids and their weevil hosts was investigated. The parasitoid Mesopolobus incultus (Walker) parasitised Gymnetron pascuorum Gyll.; the parasitoids Entodon sparetus (Walker) and Bracon sp. parasitised Mecinus pyraster Herbst. Both of these weevils develop inside the seedhead of Plantago lanceolata L. but occupy different niches. Seedheads were sampled annually from 162 plants at each of two experimental sites consisting of a series of habitat patches of two distinct sizes. Data were analysed from three site‐years. 2. Parasitoid densities at each site‐year were closely related to the abundance of their respective weevil hosts. The overall proportion of hosts parasitised was more variable for M. incultus than for E. sparetus and Bracon sp. 3. Changes in spatial scale affected the variability of parasitoid densities. For M. incultus, there was generally a greater degree of additional heterogeneity for all increases of scale; for E. sparetus, this was true only at the largest scales; for Bracon sp., all components of variance were negative. 4. The rate of parasitism was related to host density in different ways at different spatial scales. Mesopolobus incultus exhibited inverse density dependence at the finest (seedhead) scale, direct density dependence at the intermediate (plant) scale, and density independence at the large (habitat area 729 m²) scale. Entodon sparetus showed no response to variation in host density at any spatial scale. Bracon sp. showed direct density dependence only at the intermediate and largest scales. 5. Parasitoids E. sparetus and Bracon sp. seemed able to detect more than one M. pyraster individual in seedheads with multiple host occupancy; a greater incidence of conspecific parasitoids than expected emerged from such seedheads.