The ratio versus difference optimization and its implications for optimality theory

Abstract

Among the classical models of optimization, some models maximize the ratio of returns to investment and others maximize the difference between returns and investment. However, an understanding of under what conditions the ratio or the difference approaches are appropriate is still fragmentary. Under specific contexts, it has been stated that when the investable amount, but not the opportunity for investment, is perceived to be limiting, a ratio optimum is appropriate, whereas a difference optimum is appropriate when the opportunity for investment, but not the investable amount, is perceived to be limiting. The question is important because the strategies indicated by ratio optimum can be substantially different than the ones suggested by difference optimum. We make a general case here to examine and expand this principle and apply it to many evolutionary ecological problems including parental investment, offspring quality-quantity trade-off, nectar production, pollinator behavior viral burst size, and intracellular protein handling. We show that the ratio-difference distinction in optimization models resolves many long-standing debates and conundrums in evolution and behavior.

Keywords: Difference optimum; offspring quality-quantity trade-off; optimality theory; parental investment; pollination; ratio optimum.