Models of density-dependent population growth usually focus on changes in a population’s mean density. On the other hand, empirical studies show that local densities often vary greatly from the population mean and can influence individual performance. Accounting for variance in density can affect estimates of population growth rates and carrying capacity, suggesting that linking the individual-level and population-level effects of density will be critical for predicting larger-scale and longer-term processes. However, the role of spatial scale – which can both mediate density-dependent interactions and define how patterns of local density are measured – has been largely ignored. In this study, we used life stage and density environment as structuring elements in a set of population models for the leaf beetle, Leptinotarsa juncta. We estimated parameters using vital rate data from density manipulation field experiments and observations of how individuals are distributed among density groups in natural populations. Then, we investigated (1) how initial density distributions affect transient population dynamics, (2) the sensitivity of population growth to demographic and density (i.e., group size) transitions, (3) how closely density distributions in natural populations match predicted optimal distributions, and (4) how these results depend on the spatial scale at which local density is defined.
Results/Conclusions
We analyzed population models using L. juncta density at the plant-level and patch-level, as experimental data indicated that the effects of density at these spatial scales were strongest. Analyses suggest rapid growth after emergence from overwintering when initiated at reasonable adult densities. Population growth is most sensitive to density during the egg life stage: this is likely because movement among plants or patches is relatively rare, even for more mobile late-instar larvae, so that even the effects of density experienced by larvae are largely determined by their density as eggs. For the plant-level model, stable density distributions closely matched observed distributions of eggs and early-instar larvae, but overestimated the mean density of late-instar larvae. However, lacking a positive effect of density on growth rates (and therefore later fecundity), the patch-level model had a stable density distribution that was a better match with observational data. Together these results demonstrate the importance of spatial scale in mediating the effects of local density on population-level outcomes. By considering density in a demographic framework, we can pinpoint life stages at which density most affects fitness, and thus generate predictions about which density-related traits might be under strong selection.