I discuss general RPS interactions in mating systems for isopods, damselflies, fish, elephant seals, lizards, tristylous flowers, and birds. RPS systems can be classified as a true RPS (with interior NE) in which each strategy beats another, but is beaten by a third, versus an apostatic RPS (with interior ESS) in which common strategies are beaten by both rare strategies (i.e., “apostatic” advantage), but the three strategies are still intransitive. I show how mate preferences can change a true RPS into apostatic RPS and vice versa, or how it can "speciate" to reduced mating systems. Thus, I generalize RPS to higher dimensions, such as a female population with two or more alternative preferences and male RPS mating system (3 strategies), as well as higher dimensional games found in ecosystems. For example, a new co-evolutionary model describes predator/prey interactions with learning. The model is referred to as ABC-NR after conspicuous and toxic aposematic (A) models, harmless Batesian (B) mimics, and Cryptic (C) types in prey, while predators are either naïve (N) or responsive (R) to aposematic signals.
Regular RPS cycles in one sex favor invasion of a rule of thumb in the other sex in which common mating types are avoided and rare types are preferred. From such interactions, the one-population true RPS game is converted into an apostatic RPS game. The RPS also “breaks” if mates evolve preference for self-mating types, with implications for cooperation and speciation. In the ABC-NR game, I describe an example with the classic ring species of Ensatina salamanders with Batesian subspecies (B) that mimic Aposematic (A) toxic newts (Taricha), and Ensatina subspecies that are cryptic (C). From a bird's "eye" view of prey, Batesian mimics beat aposematic models by evolving more precise mimicry of model signals (used in deterring responsive predators), thus imposing more attack errors where naïve predators and aposematic models suffer. Batesian mimics increase to high frequency and the now more common responsive (R) predators distinguish mimic from model, compared to naïve (N) predators that feed indiscriminately on all 3 types. Responsive predators, drive down Batesian mimics, allowing cryptic to invade, which is then in turn driven down in frequency by responsive and naïve predators, allowing aposematic models to recover high frequency. Thus, alternative predator learning types drive RPS cycles of Aposematic-Batesian-Cryptic prey. The model shows that Fisher’s conjecture of an advantage from prey clustering is required for an interior ESS.