Analysis of Sexual vs Asexual Reproduction Using Four Measurements

The prevalence of sexual reproduction has long been an outstanding problem of evolutionary biology. In accordance with the mathematical approach employed by past researchers, we propose a mathematical framework to address this problem. We define and derive four measurements, diversity measure DVM, diffusion measure DFM, optimality measure OPM, and survivability measure SVM to compare sexual reproduction with asexual reproduction. We show that DVM increases exponentially in sexual reproduction, while only linearly in asexual reproduction. Hence, sexual reproduction allows species more opportunity to adapt. We also show that DFM is bounded in sexual reproduction and OPM is inversely related to DFM. Thus, sexual reproduction leads to smaller DFM and hence a larger OPM. We further show that SVM is a monotonic increasing function of OPM. Hence, sexual reproduction is better by virtue of producing a more homogeneous population.