Sexual reproduction is not always synonymous with the existence of two morphologically different sexes; isogamous species produce sex cells of equal size, typically falling into multiple distinct self-incompatible classes, termed mating types. A long-standing open question in evolutionary biology is: what governs the number of these mating types across species? Simple theoretical arguments imply an advantage to rare types, suggesting the number of types should grow consistently, however, empirical observations are very different. While some isogamous species exhibit thousands of mating types, such species are exceedingly rare, and most have fewer than ten. In this paper, we present a mathematical analysis to quantify the role of fitness variation -characterised by different mortality rates -in determining the number mating types emerging in simple evolutionary models. We predict that the number of mating types decreases as the variance of mortality increases. the sexes. However unlike true sexes, the number of mating types is not restricted to two; D. discoideum has three mating types [5].A natural question that then arises is what drives the evolution of the number or mating types? Within anisogamous species, a series of trade-offs (it is difficult to produce gametes that are both small and well-provisioned or large and numerous) restrict the number of morphological types to two [6]. In contrast, isogamous species, in which such trade-offs are absent, do not face such a restriction. In fact, simple evolutionary reasoning suggests that a population with two mating types should be a very unstable configuration.To explain this idea, let us discuss the following scenario: An isogamous population with two distinct self-incompatible mating types A and B of equal frequencies. Assuming massaction encounter rates, individuals of each type have a 50% chance of locating an individual of the opposite complementary type within the population. Now a mutation occurs, leading to a novel self-incompatible mating type C. An individual of this rare type C is now able to mate with all individuals of type A and B (a large proportion of the population) and thus is selected for, until the population reaches a new equilibrium in which all three types have equal frequencies. This "rare sex advantage" to novel isogamous mating types leads to the prediction that their number should consistently grow [7]. In a very extreme case, we might imagine as many distinct mating types as there are individuals in the population.By the above theoretical argument, one might predict that D. discoideum, with its three mating types, should be an evolutionary outlier, restricting its opportunities for sexual reproduction to a mere two thirds of the population. In fact, the empirical data paints rather the opposite picture. The majority of isogamous species (including the yeast Saccharomyces cerevisiae [8], the ciliate Blepharisma japonicum [9] and the green algae Chlamydomonas reinhardtii [10]) have two mating types [11]. A smaller variety of species have ...

Understanding the relationship between complexity and stability in large dynamical systems—such as ecosystems—remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty years. The vast majority of this theory addresses asymptotic linear stability around equilibrium points, but the idea of ‘stability’ in fact has other uses in the empirical ecological literature. The important notion of ‘temporal stability’ describes the character of fluctuations in population dynamics, driven by intrinsic or extrinsic noise. Here we apply tools from random matrix theory to the problem of temporal stability, deriving analytical predictions for the fluctuation spectra of complex ecological networks. We show that different network structures leave distinct signatures in the spectrum of fluctuations, and demonstrate the application of our theory to the analysis of ecological time-series data of plankton abundances.

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