A new way to integrate selection when both demography and selection gradients vary over time

When both selection and demography vary over time, how can the long-run expected strength of selection on quantitative traits be measured? There are two basic steps in the proposed new analysis: one relates trait values to fitness components and the other relates fitness components to total fitness. We used one population projection matrix for each state of the environment together with a model of environmental dynamics, defining total fitness as the stochastic growth rate. We multiplied environment-specific, stage-specific mean-standardized selection gradients by environment-specific, stage-specific elasticities of the stochastic growth rate, summing over all relevant life history and environmental paths. Our two example traits were floral tube length in a rainforest herb and the timing of birth in Red Deer. For each species, we constructed two models of environmental dynamics, including one based on historical climate records. We found that total integrated selection, as well as the relative contributions of life-history pathways and environments, varied with environmental dynamics. Temporal patterning in the environment has selective consequences. Linking models of environmental change to relevant short term data on demography and selection may permit estimation of the force of selection over the long-term in variable environments.