Optimal allocation in annual plants with density dependent fitness

TL;DR

This paper develops a model for optimal resource allocation in annual plants considering density-dependent effects, variable environments, and different production functions, predicting how plants optimize growth and reproduction timing.

Contribution

It extends previous models by incorporating a wider range of production functions and analyzing the effects of lifetime correlation on optimal plant strategies.

Findings

Optimal maturity timing shifts earlier with increased lifetime correlation.

Mixed growth and reproduction schedules are optimal in intermediate cases.

Less concave production functions favor longer vegetative growth periods.

Abstract

We study optimal two-sector (vegetative and reproductive) allocation models of annual plants in temporally variable environments, that incorporate effects of density dependent lifetime variability and juvenile mortality in a fitness function whose expected value is maximized. Only special cases of arithmetic and geometric mean maximizers have previously been considered in the literature, and we also allow a wider range of production functions with diminishing returns. The model predicts that the time of maturity is pushed to an earlier date as the correlation between individual lifetimes increases, and while optimal schedules are bang-bang at the extremes, the transition is mediated by schedules where vegetative growth is mixed with reproduction for a wide intermediate range. The mixed growth lasts longer when the production function is less concave allowing for better leveraging of plant size when generating seeds. Analytic estimates are obtained for the power means that interpolate between arithmetic and geometric mean and correspond to partially correlated lifetime distributions.