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• W2009043020 abstract "The adoption of a functional perspective of gender constituted an important milestone in the study of plant sexual systems (Lloyd, 1976, 1977, 1980). This perspective formally recognised that a plant's gender depends both on its own sex allocation (i.e. its investment in male vs female functions) and on the sex allocation of other individuals in the population (Lloyd, 1980). It also paved the way for the analysis of plant sexual systems, and the testing of relevant evolutionary hypotheses, with reference to the phenotypic distribution of sex allocations within populations. This phenotypic, or functional, perspective of plant gender has greatly advanced our understanding of plant sexual strategies, and was the main conceptual framework for the recent review of Delph & Wolf (2005) of gender plasticity in populations with dimorphic sexual systems. In their section on gynodioecy, where females and hermaphrodites co-occur, Delph & Wolf (2005) re-emphasise the idea that gender of the hermaphroditic class may often be plastic in their gender, and that individuals in this class may, in the extreme, fail to produce any seeds (Darwin, 1877; Burrows, 1960; Webb, 1979). The frequency of females at equilibrium will depend on the average gender of individuals in the hermaphroditic class, irrespective of the plastic nature of gender expression. Thus, if conditions cause individuals in the hermaphroditic class to allocate reproductive resources almost entirely to their male function, then the frequency of females will approach 0.5; in contrast, if (e.g. under more benign conditions) the hermaphrodites disperse more pollen, then the female frequency will fall. Importantly, the equilibrium frequency of females will correspond to the phenotypic gender of the hermaphrodite class, irrespective of how gender is determined developmentally. Although much of their argument followed the functional perspective, Delph & Wolf (2005) also championed a ‘population-genetic perspective’ in their section on androdioecy, where males co-occur with hermaphrodites. This view seems to differ from the functional perspective. For instance, Delph & Wolf (2005, p. 126) question whether ‘a species can be considered androdioecious’ if there is a plastic component to the determination of gender in males. They state that, ‘from a population-genetic perspective, it is the fitness and functional gender of the morphs across both gender phases that will determine the persistence of each gender morph, and is the relevant factor to define the breeding system’, and they conclude that a population composed of hermaphrodites and a morph that spends most of its time in the male phase might be regarded as ‘essentially androdioecious’ (Delph & Wolf, 2005, p. 126). The view that androdioecy needs to be defined in qualified terms when there is a plastic component to gender has also been expressed elsewhere (e.g. Wolf et al., 1997; Webb, 1999). In the extreme, such qualifications give precedent to a classing of the gender of individuals according to their genotype, rather than simply to their function. In general, however, the grounds for a genetic vs functional assessment of gender are left ambiguous. The functional view provides a robust way of making predictions about equilibrium gender frequencies in sexually dimorphic populations, but models that form the foundation of these predictions tend to have been coined in genetic terms. It is thus pertinent to ask how important the genetic view in these models actually is. Delph & Wolf (2005, p. 126) state their case clearly: ‘A better understanding of the breeding system [where genotypes may be either phenotypically plastic or canalised for gender] would result from a comparison of the proportion of fitness that the two [genetic] morphs (plastic and canalized) gain through male function in the field.’ This perspective gives precedent to a classing of individuals in the population according to their genotype. The functional perspective, in contrast, views individuals first and foremost in terms of their phenotypes. The functional perspective does not deny the importance of the genetic architecture of populations for understanding or predicting evolutionary trajectories (see the Discussion section below), but it begins by classing individuals in terms of their relative contributions through male vs female functions. In this Letter, I ask whether established evolutionary theory on plant sexual-system evolution applies better to the phenotypic categories of male, female and hermaphrodite, or to the genotypic morphs of a population-genetics perspective. For the sake of illustration and brevity, I focus here on the example of androdioecy, but the basic argument should apply to a population with any mix of genders. I reframe an established model for the evolution and maintenance of androdioecy by explicitly including a plastic component to the determination of maleness. I thus recognise the genotypic morphs referred to by Delph & Wolf (2005), and I consider whether a potentially plastic behaviour in one of these morphs alters the predictions of the more general model. Assume that a large population comprises individuals that express one of two genetically determined gender strategies, which we shall call genotypes. Individuals of genotype 1 are always hermaphrodites, whereas individuals of genotype 2 are hermaphrodite with probability q and male with probability (1 − q). Let f1 and f2 be the frequencies of genotypes 1 and 2, respectively, with f1 + f2 = 1. We assume that all hermaphroditic phenotypes allocate proportions a and (1 –a) of their reproductive resources to their male and female functions, respectively. If we assume a linear increase in male fitness with allocation to the male function and that all pollen grains dispersed by individuals in the population compete on an equal basis to fertilise ovules, then males produce and disperse r = 1/a times more pollen than do hermaphrodites. Hermaphrodites self-fertilise a proportion s of their ovules, and the viability of selfed offspring is 1 –δ times that of outcrossed offspring (i.e. δ denotes the inbreeding depression suffered by selfed progeny). If all ovules are fertilised, then we can write the fitness of genotypes 1 and 2 as where g and p are the numbers of ovules and pollen grains produced per unit of investment to female and male functions, respectively, and G = g(1 − a)(1 − s)(f1 + qf2) and P = p[a(f1 + qf2) + (1 − q)f2] are the average numbers of ovules available for outcrossing and the average number of pollen grains produced per individual, respectively. At equilibrium, the genotype fitnesses will be equal. Thus, setting w1 = w2 and solving for f2, we find that the equilibrium frequency of the plastic phenotype is It follows from Equation 2 that f2 > 0 only if r > 2(1 − sδ)/(1 − s) = A, independent of q. This condition is identical to that predicted by models for androdioecy that do not take explicit account of a plastic component to gender expression. Thus, a genotype that expresses a fully male phenotype with any probability can be maintained in a population with hermaphrodites only if it successfully disperses more than twice as much pollen when it is a male as that dispersed by hermaphrodites. As established by earlier models, this twofold fertility threshold for the maintenance of androdioecy increases with the population selfing rate. It is also evident from Equation 2 that the plastic genotype will completely replace the fixed hermaphroditic phenotype in the population if r > 2q(δs − 1)/[1 − 2q + s(1 − 2δ + 2δq)] = B, which also requires that q > 0.5. Thus A < r < B defines the parameter space in which a genetic polymorphism can be maintained; this space is illustrated in Fig. 1. The minimum value of r required for fixation of the plastic genotype 1 (i.e. the genotype with partial male expression), as a function of q, the probability that the plastic genotype has a hermaphroditic phenotype. (Note that the domain of q ranges from 0.5 to 1.0.) Populations occupying parameter space above each curve will be monomorphic for the plastic genotype (and dimorphic for gender, with male and hermaphrodite frequencies given by Equation 3). Populations occupying the space below each curve and above the corresponding horizontal lines will be segregating for the fixed and plastic gender genotypes (and dimorphic for gender, with male and hermaphrodite frequencies given by Equation 3). Populations occupying the space below the straight lines will be monomorphic for the fixed hermaphroditic genotype (and monomorphic for gender). Curves are shown for three scenarios with different selfing rates and levels of inbreeding depression (indicated). Note that m = f2(1 − q) is the frequency of individuals in the population with a male phenotype – in other words, the frequency of the plastic genotype multiplied by the probability that it expresses a male phenotype. Substituting f2 =m/(1 − q) into Equation 2 and solving for m gives This is the frequency of males in an androdioecious population at equilibrium, as first derived by Lloyd (1975). It is evident that the frequency of males is independent of the extent to which gender expression is genetically fixed or plastic, so that the equilibrium condition is fully described in terms of gender by models that ignore the possibility of plastic sex expression. In particular, the same male frequency can be maintained in populations that differ widely in their value of q, because of frequency-dependent covariation in the underlying genotype frequencies (Fig. 2). Note that when q > 0 and A < r < B, there will be both a genetic and a plastic component to the variation in sex expression, with the genetic component maintained by negative frequency-dependent selection (Fig. 1). When r > B, the plastic genotype will be fixed and genetic variation for sex determination will thus be lost from the population (Fig. 1). However, the population will still be dimorphic in gender, and Equation 3 will still formally apply at evolutionary equilibrium. The frequency of the plastic genotype, f2, in a population in which the plastic genotype expresses a hermaphroditic phenotype with probability q. Each curve corresponds to a population at sex-allocation equilibrium with the indicated frequency of males. How will selection act in a population in which gender variation is entirely plastic? Assume, as before, that individuals develop as hermaphrodites with probability q and as males with probability (1 − q). Let the gender of a single mutant be hermaphroditic and male with probabilities q′ and (1 −q′), respectively. We use the standard technique to find the evolutionarily stable probability of hermaphrodite expression, q*, by solving and setting f2 = 1. We find that (1 − q*) is equal to the solution for m in Equation 3, the frequency of males in a genetically dimorphic population comprising plastic and fixed gender genotypes. In an infinite population, the second derivative of with respect to q′ is zero, indicating that q is not locally stable: a population with average gender expression q* can be invaded by plastic genotypes expressing any value of q in (0,1). In a population of finite size, the second derivative is negative at q′ = q, and q* is locally stable. We may therefore conclude that the equilibrium frequency of individuals with a male phenotype in a population of hermaphrodites is independent of the extent to which genotypes may switch their gender between male and hermaphrodite phenotypes. Phenotypic descriptions of gender are thus sufficient for predicting the frequency of gender phenotypes at evolutionary equilibrium, whether or not sex determination has a genetic component. In their review of androdioecy, Delph & Wolf (2005) claim that plasticity of the sort explicitly recognised in the model I have presented here ‘is not part of the traditional definition of androdioecy, which is defined as having individuals that are genetically determined to be pure males’ (p. 126). One may quibble about how particular terms have been defined traditionally, but the model presented here shows clearly that frequency-dependent selection will ultimately bring the phenotypic frequencies of males and hermaphrodites to rest at predictable equilibria, irrespective of their genetic or developmental basis. Delph & Wolf (2005) suggested that an analysis of sexual systems should be approached by comparing the fitness contributions of genotypes rather than of phenotypes. Equilibrium sex ratios can in fact be predicted by equating either genotype fitnesses (w1 and w2) or phenotype fitnesses (males and hermaphrodites). However, equilibrium models of androdioecy predict phenotype frequencies. Of necessity, the model presented in this paper made rather specific assumptions about the determination of gender in an androdioecious population. However, it would be easy to make similar models for other situations, including the case of gynodioecy, and these models would also predict the frequency of phenotypes, irrespective of their genetic or developmental basis. It is worth noting that this applies as much to the case of gynodioecy with cytoplasmic sex determination as it does to gynodioecy with nuclear sex determination. Under nuclear sex determination, the equilibrium phenotype frequencies are found by equating the fitness gained by each phenotype through both sexual functions, as in models for androdioecy (Lloyd, 1975; Charlesworth & Charlesworth, 1978). In the case of cytoplasmic sex determination, in contrast, phenotype fitnesses must of course be evaluated with reference only to female function, which may be pollen-limited at equilibrium (Lewis, 1941). In discussing these models, we are free to refer to the respective morphs as phenotypes or genotypes, but the phenotypic perspective will be sufficient to account for gender ratios in populations at equilibrium. This general property of phenotypic models has been widely discussed elsewhere (e.g. Lloyd, 1977; Bulmer, 1994; Frank, 1998). It is important to stress that although a genetic perspective is redundant for understanding equilibrium sex allocations, a knowledge of the genetic basis of sex determination and its potential interaction with environmental signals can be extremely valuable. For example, the genetic architecture of gender will strongly influence the shape of evolutionary trajectories in populations that have not reached equilibrium (Pannell et al., 2005). The complex dynamics that account for morph frequencies in gynodioecious species with nucleo-cytoplasmic male sterility are a good example (Frank & Barr, 2001; Bailey et al., 2003). Here, gender frequency variation is the result of nonequilibrium conditions over space and time due to mismatches between maternally inherited male sterility mutations and biparentally inherited male fertility restorer genes (Frank & Barr, 2001). Another example concerns the relative importance of dominant vs recessive sterility mutations in the evolution of gynodioecy or androdioecy (Charlesworth & Charlesworth, 1978; Pannell, 1997). Because rare recessive advantageous mutations are more likely to be lost by drift than rare dominant ones, the early spread of a sterility mutation will depend on its dominance coefficient (Charlesworth & Charlesworth, 1978). In a metapopulation, the dominance of sterility mutations can also affect the global frequency of gender morphs at equilibrium. This is because the global morph frequency is the sum over evolutionary trajectories in populations that have not reached local equilibrium (Pannell et al., 2005). Understanding these interactions involves more complex modelling and more detailed empirical knowledge than that for single populations at equilibrium (Pannell, 1997; Frank & Barr, 2001). However, the potential complexities need not influence the way we view gender a priori. I thank Spencer Barrett, Lynda Delph, Marcel Dorken, Benoit Pujol, Diana Wolf and two anonymous reviewers for helpful comments on the manuscript." @default.
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• W2009043020 title "Phenotypic plasticity and a functional vs genetic perspective of plant gender" @default.
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