Russell Lande
University of Chicago
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The American Naturalist | 1993
Russell Lande
Stochastic factors affecting the demography of a single population are analyzed to determine the relative risks of extinction from demographic stochasticity, environmental stochasticity, and random catastrophes. Relative risks are assessed by comparing asymptotic scaling relationships describing how the average time to extinction, T, increases with the carrying capacity of a population, K, under each stochastic factor alone. Stochastic factors are added to a simple model of exponential growth up to K. A critical parameter affecting the extinction dynamics is
Evolution | 1985
Russell Lande; Douglas W. Schemske
Evolution | 1976
Russell Lande
tilde r,
Evolution | 1985
Douglas W. Schemske; Russell Lande
The American Naturalist | 1987
Russell Lande
the long-run growth rate of a population below K, including stochastic factors. If r̃ is positive, with demographic stochasticity T increases asymptotically as a nearly exponential function of K, and with either environmental stochasticity or random catastrophes T increases asymptotically as a power of K. If r̃ is negative, under any stochastic demographic factor, T increases asymptotically with the logarithm of K. Thus, for sufficiently large populations, the risk of extinction from demographic stochasticity is less important than that from either environmental stochasticity or random catastrophes. The relative risks of extinction from environmental stochasticity and random catastrophes depend on the mean and environmental variance of population growth rate, and the magnitude and frequency of catastrophes. Contrary to previous assertions in the literature, a population of modest size subject to environmental stochasticity or random catastrophes can persist for a long time, if r̃ is substantially positive.
Oecologia | 1988
Russell Lande
The amounts of inbreeding depression upon selfing and of heterosis upon outcrossing determine the strength of selection on the selfing rate in a population when this evolves polygenically by small steps. Genetic models are constructed which allow inbreeding depression to change with the mean selfing rate in a population by incorporating both mutation to recessive and partially dominant lethal and sublethal alleles at many loci and mutation in quantitative characters under stabilizing selection. The models help to explain observations of high inbreeding depression (> 50%) upon selfing in primarily outcrossing populations, as well as considerable heterosis upon outcrossing in primarily selfing populations. Predominant selfing and predominant outcrossing are found to be alternative stable states of the mating system in most plant populations. Which of these stable states a species approaches depends on the history of its population structure and the magnitude of effect of genes influencing the selfing rate.
Ecology | 1989
Craig M. Pease; Russell Lande; James J. Bull
In discussions of the major features of evolution, Simpson (1953) applied population genetic models to the interpretation of the fossil record. Most population genetics theory concentrates on details of the genetic system, such as gene frequencies and recombination rates, which cannot be directly observed or inferred from measurements on polygenic characters. Analysis of phenotypic data, particularly fossil material, requires models which are framed as much as possible in phenotypic terms. Starting from a simple formula of quantitative genetics, the methods of population genetics are used here to make a theory of the evolution of the average phenotype in a population by natural selection and random genetic drift. By analogy with Wrights (1931) adaptive topography for genotypes, Simpson (1953) proposed the concept of adaptive zones for phenotypes. This is an intuitive method of visualizing the dynamics of phenotypic evolution in terms of the degree of adaptation of the various phenotypes in a population, it usually being thought that natural selection increases adaptation. Such qualitative ideas are used by most evolutionary biologists and the notion of adaptive zones is popular among paleontologists. In the present paper, the concept of adaptive zones is clarified by the construction of an adaptive topography for the average phenotype in a population. This shows that with constant fitnesses the average phenotype evolves toward the nearest adaptive zone in the phenotype space. But if fitnesses are frequency-dependent the average phenotype may evolve away from an adaptive zone. A method is developed for estimating the minimum selective mortality necessary to produce an observed rate of evolution. In examples of the evolution of tooth characters in Tertiary mammals, these minimum selective mortalities are found to be exceedingly small. In his paper on the measurement of rates of evolution, Haldane (1949) stated that The slowness of the rate of change makes it clear that agencies other than natural selection cannot be neglected because they are extremely slow by laboratory standards or even undetectable during a human lifetime. He briefly discussed mutation pressure. Random genetic drift due to finite population size is another such agency. The relative importance of natural selection and random genetic drift has been debated since Wright (1931, 1932) proposed that evolution is a stochastic process. Fisher (1958), for example, believed that random genetic drift is insignificant in relation to natural selection. The debate continues today at a more biochemical level (Lewontin, 1974). In order to objectively evaluate the role of random genetic drift in macro-evolutionary events, it is necessary to use mathematical models to determine the rate of evolution which can occur by repeated samplings of genetic material in a finite population. This paper presents a statistical test for the hypothesis of evolution by random genetic drift, contingent on the effective population size. In examples from the fossil record, it is found that rates of evolution equal to or greater than those observed have a significant probability of occurring by random genetic drift
Science | 1988
Russell Lande
A bimodal distribution of outcrossing rates was observed for natural plant populations, with more primarily selfing and primarily outcrossing species, and fewer species with intermediate outcrossing rate than expected by chance. We suggest that this distribution results from selection for the maintenance of outcrossing in historically large, outcrossing populations with substantial inbreeding depression, and from selection for selfing when increased inbreeding, due to pollinator failure or population bottlenecks, reduces the level of inbreeding depression. Few species or populations are fixed at complete selfing or complete outcrossing. A low level of selfing in primarily outcrossing species is unlikely to be selectively advantageous, but will not reduce inbreeding depression to the level where selfing is selectively favored, particularly if accompanied by reproductive compensation. Similarly, occasional outcrossing in primarily selfing species is unlikely to regularly provide sufficient heterosis to maintain selection for outcrossing through individual selection. Genetic, morphological and ecological constraints may limit the potential for outcrossing rates in selfers to be reduced below some minimum level.
Conservation Biology | 1991
Georgina M. Mace; Russell Lande
A basic demographic model is constructed for territorial species in a region where patches of habitat suitable for survival and reproduction are randomly (or evenly) interspersed with patches of unsuitable habitat. The model predicts the equilibrium occupancy of suitable habitat as a function of the proportion of the region composed of suitable habitat, h, and of the demographic potential of the population, k, which is determined by parameters of the life history and dispersal behavior of individuals. If 0 < k < 1, the demographic potential gives the equilibrium occupancy in a completely suitable region, and the population will become extinct in the region if h
Conservation Biology | 1995
Russell Lande
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