Species vary in their functional traits, vital rates, and dispersal ability and this can affect their ability to keep up with climate change. We examined how assumptions of the underlying distribution in vital rates and dispersal parameters, their variation, and covariation among populations influence the distribution of spread rates for structured and unstructured populations. To do this, we used integro-difference equations to predict spread rates of populations in the form of wave speeds. These models include information on growth, survival, and dispersal of a population in a homogeneous environment. We used an exponentially-bounded dispersal kernel, such as the Gaussian distribution, to describe dispersal. We conducted a computer experiment with simulations that assume a multivariate normal distribution for parameters and examined the following cases: 1) randomly chosen parameter values for dispersal parameters and growth rate for unstructured populations, 2) covarying dispersal and growth parameters for unstructured populations, 2) dispersal parameters varying independently from covarying vital rates for structured populations, and 3) dispersal parameters and vital rates covarying for structured populations.
We find that the distribution of wave speeds is related to the distributional assumptions of the vital rates and dispersal parameters. Previous results suggest functional traits are log-normally distributed, and analyses of variation in dispersal parameters and population growth suggest a log-normal distribution. Assuming a Gaussian dispersal kernel, we determine the distribution of wave speeds based on the known analytical solution of the integrodifference equation, assuming a marginal Gaussian distribution for log-transformed dispersal and population growth parameters. In this case, increasing covariance among population growth and dispersal parameters, increases the variance of the spread rate. Results from this study suggest that information of the variance and covariance in dispersal and vital rates among populations can help predict what fraction of species may be able to keep up with climate change through the spread of their populations.