Gamete Motion, Search, and the Evolution of Anisogamy, Oogamy, and Chemotaxis

We propose a new model for the evolution of anisogamy from isogamy based on considerations of gamete motion and zygote fitness, without regard to pre-existing mating types. We begin by examining the conditions under which a large population of gametangia producing equal-sized gametes can be invaded successfully by a single gametangium producing gametes of a different size. Assuming an inverse relationship between size and velocity for gametes of a single species within a population, an expression for gametic encounter probabilities is developed. We provide analytical solutions for this problem in two and three dimensions. When coupled with considerations of zygote fitness, our analysis indicates that the invasion will be successful if the invading gametangium produces gametes of a size different from the population being invaded. This result is confirmed by numerical simulations. However, regions of local stability for isogamy at small gamete sizes are indicated by both our analytical results and our numerical simulations. We thus postulate a complex adaptive topography for the evolution of anisogamy with a fitness saddle separating the low adaptive peak of isogamy and the higher adaptive peak for anisogamy. Our model also allows us to make rough estimates of the length of fertilization window for gametes given empirical data concerning their sizes and swimming speeds. As a result, we predict the gametes of isogamous taxa to generally have a longer period of fertilization competency than gametes of anisogamous taxa. We have not addressed the issue of potential benefits or hazards of sexual differentiation; our results for the evolution of anisogamy do not require such differentiation. Using considerations of gamete motion, we predict decreasing benefit of flagella to female gametes as the female gamete size increases, thus providing impetus for the evolution of oogamy in taxa with large female gametes. Effective target size for macrogametes can be greatly increased through the release of chemotactic substances. Using data from the fungal genus Allomyces, we have analyzed a chemotactic search pattern based on only two microgametic swimming behaviors: a swimming glide and a jerk. A surprisingly sophisticated search pattern emerges from these two behaviors. We develop a numerical simulation of this search pattern and demonstrate its effectiveness.