Mathematical modeling of optimal seasonal reproductive strategies of plant populations and a comparison of long-term viabilities of annuals and perennials

In 1954, Lamont Cole posed a question which has motivated much ecological work in the past 50 years: When is the life history strategy of semelparity (organisms reproduce once, then die) favored, via evolution, over iteroparity (organisms may reproduce multiple times in their lifetime)? Although common sense should dictate that iteroparity would always be favored, we can observe that this is not always the case, since annual plants are not only prevalent, but can dominate an area. Also, certain plant species may be perennial in one region, but annual in another. Thus, in these areas, certain characteristics must be present which favor annuals. It has been shown, in prior work, that high environmental volatility, a short growing season, and a low survivorship of adult plants for perennials should favor annuals. In this work, we seek to answer Cole\u27s question by constructing a single-season, continuous-time model which takes random environmental effects into account. Using this model, we derive an optimal reproduction strategy to maximize the expected yield for the following season for both annuals and perennials. Then, assuming that evolutionary forces dictate this strategy be adopted, we repeat the single-season model for multiple seasons to determine, over a long period of time, which of annuals or perennials is more likely to experience growth under various conditions. The goal is to confirm the prior results as well as construct new results with a more general model