Individual growth rate of animals is increasingly used as an indicator of ecological stressors. Environmental contaminants often affect physiological processes within individuals, which in turn affect the animal’s growth rate. Consequently, there is an increasing need to estimate parameters in physiologically based individual growth models. Here, we present a method for estimating parameters in an energetic-based individual growth model (a dynamic energy budget model). This model is a system of stochastic differential equations in which one of the state variables (the energy reserve) is unobservable. There is no analytical solution to the probability density of size at given age, so we use a numerical nonlinear state–space method to calculate the likelihood. An algorithm to calculate the likelihood is outlined in this paper. This method is general enough to apply to other stochastic differential equation models. We assessed the estimability of parameters in the individual growth model, and analyzed size trajectory data from delta smelt (Hypomesus transpacificus). We expect this method to become an important tool in ecological studies as computers become faster, as the models that we deal with become more complex, and as the data that we collect become more detailed.

Demographic heterogeneity—variation among individuals in survival and reproduction—is ubiquitous in natural populations. Structured population models address heterogeneity due to age, size, or major developmental stages. However, other important sources of demographic heterogeneity, such as genetic variation, spatial heterogeneity in the environment, maternal effects, and differential exposure to stressors, are often not easily measured and hence are modeled as stochasticity. Recent research has elucidated the role of demographic heterogeneity in changing the magnitude of demographic stochasticity in small populations. Here we demonstrate a previously unrecognized effect: heterogeneous survival in long-lived species can increase the long-term growth rate in populations of any size. We illustrate this result using simple models in which each individual's annual survival rate is independent of age but survival may differ among individuals within a cohort. Similar models, but with nonoverlapping generations, have been extensively studied by demographers, who showed that, because the more “frail” individuals are more likely to die at a young age, the average survival rate of the cohort increases with age. Within ecology and evolution, this phenomenon of “cohort selection” is increasingly appreciated as a confounding factor in studies of senescence. We show that, when placed in a population model with overlapping generations, this heterogeneity also causes the asymptotic population growth rate λ to increase, relative to a homogeneous population with the same mean survival rate at birth. The increase occurs because, even integrating over all the cohorts in the population, the population becomes increasingly dominated by the more robust individuals. The growth rate increases monotonically with the variance in survival rates, and the effect can be substantial, easily doubling the growth rate of slow-growing populations. Correlations between parent and offspring phenotype change the magnitude of the increase in λ, but the increase occurs even for negative parent–offspring correlations. The effect of heterogeneity in reproductive rate on λ is quite different: growth rate increases with reproductive heterogeneity for positive parent–offspring correlation but decreases for negative parent–offspring correlation. These effects of demographic heterogeneity on λ have important implications for population dynamics, population viability analysis, and evolution.

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