Search

In (st)age-structured populations, the long-run population growth rate is negatively affected by temporal variation in vital rates. In most cases, natural selection should minimize temporal variation in the vital rates to which the long-run population growth is most sensitive, resulting in demographic buffering. By reviewing empirical studies on demographic buffering in wild populations, we found overall support for this hypothesis. However, we also identified issues when testing for demographic buffering. In particular, solving scaling problems for decomposing, measuring, and comparing stochastic variation in vital rates and accounting for density dependence are required in future tests of demographic buffering. In the current context of climate change, demographic buffering may mitigate the negative impact of environmental variation and help populations to persist in an increasingly variable environment. This article is available under the Creative Commons CC-BY-NC-ND license and permits non-commercial use of the work as published, without adaptation or alteration provided the work is fully attributed.

Harvesting in space affects, in general, the spatial scale of the synchrony in the population fluctuations, which determines the size of the areas subjected to simultaneous quasi-extinction risk. Here we show that harvesting reduces the population synchrony scale if it depends more strongly on population fluctuations than the density dependence of the growth rate in the absence of harvesting. We show that constant and proportional harvesting always increases the spatial scale, using a theta-logistic model for density regulation. We also provide exact scaling results under harvesting for the Beverton–Holt and the Ricker stock-recruitment models that are commonly applied, e.g. in fisheries. Our results indicate that harvest in areas with large abundances should be encouraged to avoid increase of the spatial scale of synchrony in the population fluctuations that can lead to unexpected quasi-extinction of populations over large areas. Our results quantify this harvesting impact giving the resulting scales of spatial synchrony of population fluctuations. This emphasizes the importance of estimating the form of density dependence as well as the dependency of harvest upon population density of exploited populations, in order to get reliable predictions of the size of areas that can undergo simultaneous quasi-extinction.

We analyze a spatial age-structured model with density regulation, age specific dispersal, stochasticity in vital rates and proportional harvesting. We include two age classes, juveniles and adults, where juveniles are subject to logistic density dependence. There are environmental stochastic effects with arbitrary spatial scales on all birth and death rates, and individuals of both age classes are subject to density independent dispersal with given rates and specified distributions of dispersal distances. We show how to simulate the joint density fields of the age classes and derive results for the spatial scales of all spatial autocovariance functions for densities. A general result is that the squared scale has an additive term equal to the squared scale of the environmental noise, corresponding to the Moran effect, as well as additive terms proportional to the dispersal rate and variance of dispersal distance for the age classes and approximately inversely proportional to the strength of density regulation. We show that the optimal harvesting strategy in the deterministic case is to harvest only juveniles when their relative value (e.g. financial) is large, and otherwise only adults. With increasing environmental stochasticity there is an interval of increasing length of values of juveniles relative to adults where both age classes should be harvested. Harvesting generally tends to increase all spatial scales of the autocovariances of densities.

Here we analyze how dispersal, genetic drift, and adaptation to the local environment affect the geographical differentiation of a quantitative character through natural selection using a spatial dynamic model for the evolution of the distribution of mean breeding values in space and time. The variation in optimal phenotype is described by local Ornstein-Uhlenbeck processes with a given spatial autocorrelation. Selection and drift are assumed to be governed by phenotypic variation within areas with a given mean breeding value and constant additive genetic variance. Between such neighboring areas there will be white noise variation in mean breeding values, while the variation at larger distances has a spatial structure and a spatial scale that we investigate. The model is analyzed by solving balance equations for the stationary distribution of mean breeding values. We also present scaling results for the spatial autocovariance function for mean breeding values as well as that for the covariance between mean breeding value and the optimal phenotype expressing local adaption. Our results show in particular how these spatial scales depend on population density. For large densities the spatial scale of fluctuations in mean breeding values have similarities with corresponding results in population dynamics, where the effect of migration on spatial scales may be large if the local strength of density regulation is small. In our evolutionary model strength of density regulation corresponds to strength of local selection so that weak local selection may produce large spatial scales of autocovariances. Genetic drift and stochastic migration are shown to act through the population size within a characteristic area with much smaller variation in optimal phenotypes than in the whole population.

Eurasian lynx in Scandinavia are subject to regular harvest and lethal control to reduce depredation on domestic livestock and semi-domestic reindeer. Here we introduce the use of total reproductive value to model the effects of current harvest on population dynamics and to propose sustainable harvest strategies for lynx. Demographic stochasticity strongly influences lynx population dynamics. Analyses of the number of lynx shot in relation to the number of family groups registered in annual censuses showed proportional harvest in large parts of Norway because the quotas were higher at larger population sizes. In other areas of Norway the number of lynx shot was independent of population size. The analyses of the model showed that a pure proportional harvest strategy may lead to rapid extinction of lynx populations. In contrast, applying a threshold or proportional threshold harvest strategy in which no harvest occurs below a given threshold can result in the maintenance of viable populations. Thus, this study shows that harvest without any lower threshold for stopping harvest will result in rapid extinction of lynx populations. Accordingly, lynx harvest is not likely to be sustainable if the illegal killing of animals is not controlled because poaching can result in a de facto proportional harvest even at very small population sizes. Under the influence of the large demographic stochasticity in lynx populations this harvest would result in short expected times to extinction. This gives an empirical demonstration that a correct choice of harvest strategy is essential for maintenance of viable populations of harvested species. Our analyses illustrate that parameters determining the viability of small populations can be estimated from individual-based demographic data from a sample of individuals without using time series of fluctuations in population size, which facilitates quantitative analyses of how harvest or removal of individuals, e.g. for captive breeding or translocations, affect the expected lifetime of populations.

Mechanisms generating inequalities among males in reproductive success are key to understanding the evolutionary significance of sexual selection. This paper develops a stochastic model to quantitatively describe and analyze mating systems on a continuous scale from strict monogamy to extreme polygyny. The variance in male mating success is shown to increase with increased differences among males, with decreased interdependence of mating events, with increased population size, and with an increased number of females per male. The latter condition decreases the opportunity for sexual selection. It is found that different combinations of mating system characteristics can lead to the same variance in male mating success, although the distribution differs. This emphasizes the importance of using a model of this type to study mating systems, rather than relying solely on the variance in reproductive success as a descriptor of different systems.

The dynamics of reproductive value are used to provide a simple derivation of Tuljapurkar's approximation for the long-run growth rate and environmental variance of lnN, in a density-independent age-structured population in a random environment. With no environmental autocorrelation, the dynamics of total population size, N, generally shows time lags and autocorrelation caused by life history, which may strongly bias estimates of environmental variance obtained by ignoring age structure. In contrast, the total reproductive value, V, is Markovian and obeys a first-order autoregressive process. This suggests a simple method for estimating the environmental variance, and avoiding potentially large bias due to age-structure fluctuations, by converting a multivariate time series of age structure to a univariate time series of lnV. We illustrate the method by estimating the long-run growth rate and the environmental variance in an exponentially growing population of Bighorn Sheep.

This paper deals with models for optimal annual harvesting of populations in a fluctuating environment. By adopting threshold harvesting and assuming known population size, the optimal threshold that maximizes the expected cumulative yield before extinction is derived. The optimal threshold is practically independent of the form of density regulation, is smaller than the carrying capacity, and decreases with the environmental variance. We also analyse the effect of uncertainty in the population estimates, defined by a parameter θ0, which is the coefficient of variation in the population estimate when the population is at the carrying capacity. By adopting threshold harvesting based on the estimated population size, the optimal threshold increases with θ0. For large uncertainty in the estimates we propose a new harvesting strategy calledproportional threshold harvestingfor which only a given fraction,q, of the difference between the population estimate and the threshold is harvested if the population estimate is larger than the threshold. Numerical calculations show that this method is preferable to pure threshold harvesting when the uncertainty in the estimate exceeds some value depending on the environmental variance. A formula for the optimal threshold for a givenqand a small θ0is derived. This formula is also independent of the form of density regulation. We also give examples of numerical calculations of the expected time to extinction, mean annual yield and the mean fraction of years the population can be harvested. Finally, we present some simulations demonstrating population fluctuations and harvesting based on uncertain population estimates.

Recently, the results from several long-term individual-based population studies of ungulates have been published. One major conclusion is that the population dynamics of ungulates in predator-free environments is strongly influenced by a combination of stochastic variation in the environment, and population density. Both density dependence and environmental stochasticity operate through changes in life history traits, correlated with variation in body weight. This generates delays in the response of the population to changes in environment. In the absence of predation, a stable equilibrium is therefore unlikely to exist between an ungulate population and its food resources. This thorough understanding of the mechanisms generating population fluctuations suggests that studies of ungulates will provide an important source for examining effects of long-term changes in the environment, for instance, resulting from a climatic change.

Understanding the factors that affect most severely the extinction risk of populations is crucial for maintaining biodiversity. An important general pattern derived from stochastic population theory is that time to extinction should decrease with increasing environmental stochasticity. Drake and Lodge recently provided one of the first pieces of experimental support for this simple prediction by artificially manipulating the dynamics of populations of Daphnia. A future challenge will be to include both demographic stochasticity and environmental stochasticity in such studies.

Many of the best field studies in evolutionary ecology are located on remote islands. Therefore, when listening to talks that are accompanied by slides of sun-drenched sandy beaches, the thought that some substitute motif has been involved in the choice of study site is unavoidable. However, no one can accuse the researchers who study the Soay sheep on the St Kilda archipelago off the northwest coast of Scotland of having a study site that offers the opportunity to spend leisure time in the sun. Soay Sheep. Dynamics and Selection in an Island Population, edited by Tim Clutton-Brock and Josephine Pemberton, demonstrates clearly that this study site was chosen for purely scientific reasons, because it offers a rare opportunity to study fundamental ecological and evolutionary processes.The Soay sheep was introduced to the study island (Hirta) from the neighbouring island of Soay in 1932 and their population was subsequently allowed to develop freely. The large-scale study of the sheep was launched in 1985 by a team from the University of Cambridge. Most of the sheep in the study area were individually marked and, since then, a unique database has accumulated on individual variation in reproductive success and survival. This has enabled the study to be expanded to cover a wide range of general-interest questions with a unique cross-disciplinary focus integrating several research fields. Thus, several research groups are now involved in the project and, accordingly, Soay Sheep has 25 coauthors.The book begins with a description of the general biology of the sheep, followed by a chapter outlining their population dynamics. From these chapters, we learn that the large fluctuations in the population levels of the sheep are caused by a combination of density dependence and stochastic variation in climate, as well as being strongly influenced by temporal variation in the age and sex composition of the population. In the two subsequent chapters, the mechanisms that might cause this large variation in population growth rates over time are examined. Described for the first time is an important characteristic of the ecosystem on Hirta; that is, that the plant communities appear to be extremely resilient to grazing, but that the grazing pressure towards the end of winter is extremely high and will probably result in die-offs at high population densities. However, the effects of parasites are more subtle. I found Chapter five to be an excellent illustration of how difficult it is to assess how host–parasite interactions affect the population dynamics of large herbivores. Chapters 6–8 detail how the huge effort invested by the St Kilda research group in developing advanced genetic tools has provided a unique understanding of the social organization and genetic structure of the population. The final chapters describe the life history and population dynamics of the Soay sheep. In particular, I think that the last chapter about regulatory mechanisms will become a classic in population ecology because its non-quantative approach will attract a wide audience.Is there anything new in Soay Sheep? Yes, there is. The book has merit that is far greater than the sum of its parts. For example, the authors and editors provide a balanced treatment of the various mechanisms that influence population biological processes of the sheep. Even for researchers who are familiar with the individual papers, it is often difficult to get an overall view of how different factors affect the sheep. This is hardly surprising, given that the reference list of the book includes 50 papers published about the Soay sheep since 1985. In particular, the balanced treatment afforded in Chapter five to parasites and their impact on the population dynamical processes fills a long-awaited need. Similarly, Chapter eight, concerning genetic variation, provides a useful overview by presenting evidence that is often hidden in technically orientated genetics papers that can be difficult to access. Furthermore, to my great surprise, Soay Sheep contains previously unpublished data that enables us to better put the data resulting from the studies of the sheep in a more general context. The description of the vegetation–sheep interactions is especially welcome.Soay Sheep will undoubtedly become a classic text in population biology literature. The editors should be acknowledged for producing a book that, even with so many coauthors, follows a coherent style and contains careful cross-referencing across its chapters. The book also serves as a tribute to the British research system, which willingly provides continuous support to such important long-term studies.

Recently the methods of major axis analysis and reduced major axis analysis have frequently been used in allometric studies as a complement to linear regression analysis. This paper gives a comparison, based on some reasonable assumptions, of these three methods. It is shown how the choice of method should depend on (i) which a priori assumptions that are present and (ii) the purpose of the analysis. Neither major axis analysis nor reduced major axis analysis are appropriate for estimating regression lines, but both methods are valuable when estimating a structural relation. Major axis analysis gives consistent estimates of the coefficients when the two error variances are equal, while reduced major axis analysis gives consistent estimates when the relative sizes of the two error variances are equal. None of the methods have universal application. The three methods give rise to the same conclusions only in data-sets with very high correlation coefficients