Shripad Tuljapurkar

Population dynamics in variable environments

1 Introduction.- 2 Beginnings: Classical Theory.- 3 Deterministic Temporal Variation.- 4 Random Rates: General Theory.- 5 Examples.- 6 Ess and Allele Invasion.- 7 Moments of the Population Vector.- 8 Random Survival or Fertility: Exact Results.- 9 Age Structure: Bounds, Growth, Convergence.- 10 Synergy, Constraints, Convexity.- 11 Sensitivity Analysis of Growth Rate.- 12 Growth Rates for Small Noise.- 13 Population Structure for Small Noise.- 14 Population Projection.- 15 Life History and Iteroparity.- 16 Life History Evolution: Delayed Flowering.

A universal pattern of mortality decline in the G7 countries

Human lifespan has increased enormously this century. But we remain uncertain about the forces that reduce mortality, and about the cost implications of ageing populations and their associated social burden. The poor understanding of the factors driving mortality decline, and the difficulty of forecasting mortality are due in part to the pronounced irregularity of annual to decadal mortality change. Here we examine mortality over five decades in the G7 countries (Canada, France, Germany, Italy, Japan, UK, US). In every country over this period, mortality at each age has declined exponentially at a roughly constant rate. This trend places a constraint on any theory of society-driven mortality decline, and provides a basis for stochastic mortality forecasting. We find that median forecasts of life expectancy are substantially larger than in existing official forecasts. In terms of the costs of ageing, we forecast values of the dependency ratio (that is, the ratio of people over 65 to working people) in 2050 that are between 6% (UK) and 40% (Japan) higher than official forecasts.

Coupled dynamics of body mass and population growth in response to environmental change

Environmental change has altered the phenology, morphological traits and population dynamics of many species. However, the links underlying these joint responses remain largely unknown owing to a paucity of long-term data and the lack of an appropriate analytical framework. Here we investigate the link between phenotypic and demographic responses to environmental change using a new methodology and a long-term (1976–2008) data set from a hibernating mammal (the yellow-bellied marmot) inhabiting a dynamic subalpine habitat. We demonstrate how earlier emergence from hibernation and earlier weaning of young has led to a longer growing season and larger body masses before hibernation. The resulting shift in both the phenotype and the relationship between phenotype and fitness components led to a decline in adult mortality, which in turn triggered an abrupt increase in population size in recent years. Direct and trait-mediated effects of environmental change made comparable contributions to the observed marked increase in population growth. Our results help explain how a shift in phenology can cause simultaneous phenotypic and demographic changes, and highlight the need for a theory integrating ecological and evolutionary dynamics in stochastic environments.

LONGEVITY CAN BUFFER PLANT AND ANIMAL POPULATIONS AGAINST CHANGING CLIMATIC VARIABILITY

Both means and year-to-year variances of climate variables such as temperature and precipitation are predicted to change. However, the potential impact of changing climatic variability on the fate of populations has been largely unexamined. We analyzed multiyear demographic data for 36 plant and animal species with a broad range of life histories and types of environment to ask how sensitive their long-term stochastic population growth rates are likely to be to changes in the means and standard deviations of vital rates (survival, reproduction, growth) in response to changing climate. We quantified responsiveness using elasticities of the long-term population growth rate predicted by stochastic projection matrix models. Short-lived species (insects and annual plants and algae) are predicted to be more strongly (and negatively) affected by increasing vital rate variability relative to longer-lived species (perennial plants, birds, ungulates). Taxonomic affiliation has little power to explain sensitivity to increasing variability once longevity has been taken into account. Our results highlight the potential vulnerability of short-lived species to an increasingly variable climate, but also suggest that problems associated with short-lived undesirable species (agricultural pests, disease vectors, invasive weedy plants) may be exacerbated in regions where climate variability decreases.

Population dynamics in variable environments I. Long-run growth rates and extinction

Abstract A model of population growth is studied in which the Leslie matrix for each time interval is chosen according to a Markov process. It is shown analytically that the distribution of total population number is lognormal at long times. Measures of population growth are compared and it is shown that a mean logarithmic growth rate and a logarithmic variance effectively describe growth and extinction at long times. Numerical simulations are used to explore the convergence to lognormality and the effects of environmental variance and autocorrelation. The results given apply to other geometric growth models which involve nonnegative growth matrices.

Senescence rates are determined by ranking on the fast-slow life-history continuum

Comparative analyses of survival senescence by using life tables have identified generalizations including the observation that mammals senesce faster than similar-sized birds. These generalizations have been challenged because of limitations of life-table approaches and the growing appreciation that senescence is more than an increasing probability of death. Without using life tables, we examine senescence rates in annual individual fitness using 20 individual-based data sets of terrestrial vertebrates with contrasting life histories and body size. We find that senescence is widespread in the wild and equally likely to occur in survival and reproduction. Additionally, mammals senesce faster than birds because they have a faster life history for a given body size. By allowing us to disentangle the effects of two major fitness components our methods allow an assessment of the robustness of the prevalent life-table approach. Focusing on one aspect of life history - survival or recruitment - can provide reliable information on overall senescence.

The Dynamics of Phenotypic Change and the Shrinking Sheep of St. Kilda

Little Lambs In changing environments, ecological and evolutionary dynamics are intimately intertwined. However, understanding the dynamics of phenotypic traits under natural conditions is still rudimentary. Ozgul et al. (p. 464; published online 2 July) dissected the dynamics of a phenotypic trait in the context of the contributing ecological and evolutionary processes. In a wild population of Soay sheep where mean body size has fluctuated substantially over the past 25 years and has, on average, gotten smaller, an ecological response to environmental variation is the major driver of the dynamics; evolutionary change has contributed relatively little: The sheep have become smaller because climate change has modified the way that density-dependence influences lamb growth rates. Environmental change has led to decreasing body size in a sheep population over 20 years, despite selection for increased size. Environmental change, including climate change, can cause rapid phenotypic change via both ecological and evolutionary processes. Because ecological and evolutionary dynamics are intimately linked, a major challenge is to identify their relative roles. We exactly decomposed the change in mean body weight in a free-living population of Soay sheep into all the processes that contribute to change. Ecological processes contribute most, with selection—the underpinning of adaptive evolution—explaining little of the observed phenotypic trend. Our results enable us to explain why selection has so little effect even though weight is heritable, and why environmental change has caused a decline in the body size of Soay sheep.

The many growth rates and elasticities of populations in random environments.

Despite considerable interest in the dynamics of populations subject to temporally varying environments, alternate population growth rates and their sensitivities remain incompletely understood. For a Markovian environment, we compare and contrast the meanings of the stochastic growth rate ( \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape

The Evolutionary Demography of Ecological Change: Linking Trait Variation and Population Growth

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