The ratio versus difference optimization and its implications for optimality theory

Among the classical models of optimization, some models maximize the ratio of returns per investment, others maximize the difference between returns and investment. However, the question under what conditions use of the ratio model is appropriate and under what conditions a difference model should be used remained unaddressed until recently. 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 for the set of conditions for appropriate use of ratio versus difference optimum. When the investable amount is perceived as limiting but not the investment opportunities a ratio optimum is appropriate and when the investment opportunities are perceived to be limiting but not the investable amount, difference optimum is appropriate. Taking examples of Concorde fallacy, parental investment, r and K selection, nectar production, pollinator behavior, protein synthesis and stability, viral burst size and human economic behavior we show that the ratio-difference distinction in optimization models resolves many long standing debates and conundrums in evolution, behavior and economics.