Dr. Johnson is currently a postdoctoral research fellow at the Center for the Study of Complex Systems at the University of Michigan. He has done fascinating work on topics ranging from the development of name brand goods in the economy, to the origin of differences in sex cells, to the emergence of multimodal distributions in coupled oscillator systems.
A Dynamical Model for the Origin of Anisogamy
The vast majority of multi-cellular organisms are anisogamous, meaning that male and female sex cells differ in size. It remains an open question how this asymmetric state evolved, presumably from the symmetric isogamous state where all gametes are roughly the same size (drawn from the same distribution). Here, we use tools from the study of nonlinear dynamical systems to develop a simple mathematical model for this phenomenon. Unlike most prior work, we do not assume the existence of mating types. We also model frequency dependent selection via “mean-field coupling,” whereby the likelihood that a gamete survives is an increasing function of its size relative to the population’s mean gamete size. Using theoretical analysis and numerical simulation, we demonstrate that this mean-referenced competition will almost inevitably result in a stable anisogamous equilibrium, and thus isogamy may naturally lead to anisogamy.”