Consequences of Inbreeding Depression Due to Sex-Linked Loci for the Maintenance of Males and Outcrossing in Branchiopod Crustaceans

Genet. Res., Camb. (2008), 90, pp. 73–84. f 2008 Cambridge University Press 73 doi:10.1017/S0016672307008981 Printed in the United Kingdom Consequences of inbreeding depression due to sex-linked loci for the maintenance of males and outcrossing in branchiopod crustaceans

JOHN R. PANNELL* Department of Plant Sciences, South Parks Road, University of Oxford, Oxford OX1 3RB, UK (Received 10 August 2007 and in revised form 27 October 2007)

Summary Androdioecy, where males co-occur with hermaphrodites, is a rare sexual system in plants and animals. It has a scattered phylogenetic distribution, but it is common and has persisted for long periods of evolutionary time in branchiopod crustaceans. An earlier model of the maintenance of males with hermaphrodites in this group, by Otto et al. (1993), considered the importance of male–hermaphrodite encounter rates, sperm limitation, male versus hermaphrodite viability and inbreeding depression suffered by selfed progeny. Here I advance this model in two ways: (1) by exploring the conditions that would allow the invasion of hermaphrodites into a dioecious population and that of females into an androdioecious population; and (2) by incorporating a term that accounts for the potential effects of genetic load linked to a dominant hermaphrodite- determining allele in androdioecious populations. The new model makes plausible sense of observations made in populations of the species Eulimnadia texana, one of a number of related species whose common ancestor evolved hermaphroditism (and androdioecy) from dioecy. In particular, it offers an explanation for the long evolutionary persistence of androdioecy in branchiopods and suggests reasons for why dioecy has not re-evolved in the clade. Finally, it provides a rather unusual illustration of the implications of the degeneration of loci linked to a sex-determining locus.

1. Introduction et al., 1999; Sakai, 2001; reviewed in Pannell, 2002; Weeks et al., 2006a). Although androdioecy must still Androdioecy, the occurrence of males and hermaphro- count as exceedingly rare, its discovery has led to dites in a population, is a rare sexual system in both new insights regarding selective factors that maintain plants and animals. The term was coined by Darwin combined versus separate sexes. In particular, while (1877), who considered it as a possible path from androdioecy may be diﬃcult to evolve from her- hermaphroditism to dioecy. However, he knew no maphroditism via the spread of female-sterility example of it and did not consider it further. Over a mutations, phylogenetic evidence (e.g. Rieseberg century later, Charlesworth (1984) reviewed the et al., 1992; Swensen et al., 1998; Wolf et al., putative cases of androdioecy in plants and found 2001; Krahenbuhl et al., 2002; Obbard et al., 2006) none that was convincing. On the basis of her litera- and modelling (Pannell, 1997a, 2001; Wolf & ture review and evolutionary models for the evolution Takebayashi, 2004) both point to dioecy as a more and maintenance of males with hermaphrodites, likely ancestral state, with self-fertile hermaphrodites she concluded that ‘androdioecy is probably not an spreading in a population and replacing females, important phenomenon’. Since Charlesworth’s (1984) because self-fertility confers an advantage of repro- review, a number of androdioecious species have now ductive assurance in the absence of mates (Baker, been discovered amongst both plants and animals 1955; Wolf & Takebayashi, 2004). (Liston et al., 1990; Sassaman, 1991; Turner et al., It seems clear that androdioecy has evolved from 1992; Connor, 1996; Pannell, 1997b; e.g. Akimoto dioecy on several occasions, but how long can it be * e-mail: [email protected] maintained? On the one hand, we might expect

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hermaphrodites to completely displace both females summarize the essential features that motivate the and males if selection for reproductive assurance is suf- model. These can be listed as follows: ficiently strong (Pannell, 1997a; Wolf & Takebayashi, 2004). On the other hand, androdioecy might easily 1. As noted above, although ancient in origin, revert to dioecy if selection for reproductive assurance androdioecy in Eulimnadia is derived from dioecy is relaxed, for example in response to selection for (Sassaman, 1995; Weeks et al., 2006b). Not only inbreeding avoidance or gender specialization (re- is the sister genus Metalimnadia dioecious, but viewed in Charlesworth, 1999). Certainly, both the hermaphrodites are anatomically derived from rarity of androdioecy and its generally scattered females (Zucker et al., 1997). Thus androdioecy phylogenetic distribution amongst plants and animals appears to have evolved through the displace- (Pannell, 2002; Weeks et al., 2006a) would suggest ment of females by derived hermaphrodites that that males do not tend to be maintained with her- possess an ovotestis and an ability to self-fertilize. maphrodites for long periods of evolutionary time. Hermaphrodites are also modified females in the There is, however, at least one striking exception to plants Datisca glomerata (Wolf et al., 2001) and this pattern: on the basis of a phylogenetic recon- Mercurialis annua (Pannell, 1997b). struction of the largely androdioecious crustacean 2. Eulimnadia hermaphrodites either self-fertilize their genus Eulimnadia, Weeks et al. (2006b) recently sug- progeny, or, if they are available, they outcross gested that androdioecy has been maintained for at with a male. Importantly, and unlike the situation least 24 million years and possibly for much longer. in known androdioecious plants, hermaphrodites The authors thus rejected the hypothesis that andro- cannot cross with one another (Sassaman & Weeks, dioecy ‘can only be a short-lived, transitory phase 1993). Hermaphrodites in populations that lack between hermaphroditism and dioecy (or vice versa)’ males are thus entirely self-fertilizing (Knoll & and called for a model that might ‘explain the long- Zucker, 1995; Weeks et al., 2001b), whereas her- lived coexistence of males with hermaphrodites in the maphrodites in androdioecious populations are Eulimnadia crustacean’. able to outcross by mating with males. Indeed, In this paper, I propose a model that might explain hermaphrodites show a preference for outcrossing the puzzlingly long marriage of males with hermaphro- by swimming more slowly, spending more time in dites in Eulimnadia and related androdioecious the vicinity of males and postponing self-fertiliza- species (see Longhurst, 1955; Sassaman, 1991, 1995). tion when males are absent (Medland et al., 2000; The model is in some respects similar to that of Otto Zucker et al., 2002); they thus effectively engage in et al. (1993), which predicted the frequency of males delayed self-fertilization, following opportunities in terms of male–hermaphrodite encounter and thus to outcross with males. As a result, the inbreeding outcrossing rates, inbreeding depression, effective coefficient in populations of E. texana varies sperm limitation and gender-specific viabilities for the widely, correlating negatively with the proportion species Eulimnadia texana. My model differs from of males present (Sassaman, 1989; Weeks & that of Otto et al. (1993) by incorporating details Zucker, 1999). of the natural history and genetics of androdioecy 3. Despite the high rates of selfing in some popu- in E. texana that have emerged through more recent lations, levels of inbreeding depression in E. texana research on the species. Before presenting the model, are high, with selfed progeny between 50% and I begin by briefly reviewing the empirical basis for 70% less fit than their outcrossed counterparts the new model, including details of the species’ life (Weeks et al., 1999, 2000). history and habitat, its sex-determination system, 4. Gender in Eulimnadia is determined by alleles seg- the mating behaviour of males and hermaphrodites, regating at a single locus. Males are homozygous and peculiarities concerning the expression of in- recessive, and hermaphrodites are either hetero- breeding depression. I finally discuss the implications zygous at the sex-determining locus (‘amphigenic’ of the model for the coexistence of males with hermaphrodites) or homozygous (‘monogenic’ hermaphrodites in Eulimnadia, as well as for the hermaphrodites) (Sassaman & Weeks, 1993). evolution of its sex-determining locus and the main- 5. Monogenic and amphigenic hermaphrodites are tenance of sex. morphologically and behaviourally equivalent, but the former have been found under experimental conditions to be 13% less fit than the latter 2. Androdioecy in Eulimnadia (Weeks et al., 1999, 2001a); this fitness differential The natural history, phylogenetic affinities, genetics is likely to be an underestimate (see Section 4). of sex determination, mating behaviour, and variation Although sex chromosomes have not been dis- in the mating system and sex ratios of species in the cerned in Eulimnadia, it appears likely that the sex- genus Eulimnadia, especially E. texana, were recently determining locus is linked to viability loci, such reviewed by Weeks et al. (2006a). Here I briefly that the dominant hermaphrodite-determining

allele is linked to fitness-reducing loci on the same a mutant female possessing an ovotestis and an ability chromosome (see Weeks, 2004). to self-fertilize some of her progeny when mates are scarce (i.e. a hermaphrodite). This hermaphrodite has genotype ZW*. Let her probability of finding a mate be az, and let c=p/a. Following Otto et al. (1993), we 3. Hypothesis and model assume that hermaphrodites that find a mate outcross In dioecious or gonochoristic species with single-locus all their eggs, whereas those that fail to find a mate or chromosomal sex determination, recombination in self-fertilize a proportion b of their eggs. Further, the region surrounding the sex-determining locus assume that females produce v times as many eggs should be suppressed (Nei, 1969; Charlesworth & as mutant hermaphrodites. Note that the product Charlesworth, 1978; Bull, 1983; Charlesworth et al., vc denotes the relative effective fecundity of females 2005). Indeed, there is good evidence from species over hermaphrodites. ZW* hermaphrodites that are with young sex chromosomes that the size of the non- fertilized by a male produce ZW* hermaphrodites and recombining region has increased over evolutionary ZZ males at a ratio of 1 : 1; ZW* hermaphrodites that time as the sex chromosome evolves (e.g. Nicolas self-fertilize their progeny produce W*W* hermaphro- et al., 2005; Bergero et al., 2007). An important im- dites, ZW* hermaphrodites and ZZ males at a ratio plication of reduced recombination between homo- of 1 : 2 : 1. Let the viability of ZW* hermaphrodites logous regions around a sex-determining locus is and ZZ males produced by selfing be 1 – d times the that alleles linked in coupling with the dominant sex- viability of their outcrossed counterparts, and let the determining allele (e.g. the male-determining allele viability of W*W* hermaphrodites be (1 – d)(1 – l) or chromosomal region in XY systems with male that of outcrossed hermaphrodites; d thus denotes the heterogamety such as in mammals, fruit flies and inbreeding depression suffered by selfed progeny due some plants, or the female-determining region in ZW to non-W*linked viability loci, and l denotes the systems with female heterogamety in birds and many further reduction in fitness of selfed progeny due to invertebrates) will ultimately fail to recombine at all. homozygosity at viability loci linked to the W* allele. These alleles are thus susceptible to the accumulation l thus accounts for the effects of W-chromosome de- of deleterious mutations, through processes such as generation. Finally, let the viability of males be (1 – s) background selection, Muller’s Ratchet, and selective times that of females. Note that this model is identical interference caused by the Hill–Robertson effect to that of Otto et al. (1993), except for (1) the in- (Charlesworth & Charlesworth, 2000). Because Y and clusion of ancestral females, the distinction between W chromosomes occur only in the heterogametic sex, females and hermaphrodites in their egg production they are particularly susceptible to the accumulation (term v) and their ability to find a mate (a versus p); of deleterious recessive, or partly recessive, mutations and (2) the inclusion of the term l that accounts for that are not expressed (Nei, 1970). the genetic load of the W chromosome. Now consider a semelparous dioecious species, such Let w, x, y and z be the frequencies of genotypes as a putative ancestor of Eulimnadia, in which females ZW, W*W*, ZW* and ZZ, respectively (i.e. females, are the heterogametic sex (Sassaman & Weeks, 1993). monogenic hermaphrodites, amphigenic hermaphro- Although sex chromosomes have not been discerned dites and males). The recurrence equations for these in Eulimnadia, it is convenient to regard males and genotypes will therefore be females as having genotypes ZZ and ZW, respectively. We expect the W chromosome to have undergone w wkT= vcaz (1a) a degree of degeneration during the dioecious history 2 of the lineage that eventually led to Eulimnadia. Indeed, as noted above, the fact that WW hermaphro- xkT=xb(1xaz)(1xd)(1xl) y dites are less fit than ZW hermaphrodites of + b(1xaz)(1xd)(1xl) (1b) E. texana would seem to provide good evidence 4 for W degeneration. Note that we should expect W y y ykT=xaz+ az+ b(1xaz)(1xd) (1c) degeneration to continue in these animals as a result 2 2 of the fact that different W chromosomes never meet hi w y y (because hermaphrodites cannot mate with one zkT=ðÞ1xs vcaz+ az+ b(1xaz)(1xd) (1d) another). 2 2 4 Let pz be the frequency-dependent probability that a female finds a mate while she is receptive; z is where the prime denotes frequencies in the next the frequency of males, which we expect to be 0.5in generation and T is the sum of the right-hand side dioecious populations (Duesing, 1884; Fisher, 1930), of (1a) to (1d). Otto et al. (1993) found equilibrium and p is a constant. Females will therefore die without solutions for the frequencies of males and the two reproducing with probability 1 – pz. Now consider hermaphrodite genotypes. However, inclusion of the

term l makes it diﬃcult to derive useful analytic (a) δ у 0, λ = 0 equilibrium solutions for the more general model 100 δ = 0·00 here. Nevertheless, criteria for the invasion of δ = 0·1 δ = 0·3 hermaphrodites into a dioecious population and δ = 0·5 equilibrium solutions for genotype frequencies for δ = 0·7 δ = 0·9 the more general model here are easily found using δ = 0·99 deterministic iterations of the equations (1). 10 vc

(i) Invasion of hermaphrodites into a dioecious population Setting x=y=0 for a population without hermaphrodites, recursions (1a) and (1d) can be solved to find the 1 equilibrium (secondary) sex ratio in a dioecious 0·0 0·5 1·0 1·5 2·0 population: (b) δ = 0, λ у 0 100 1xs λ = 0·00 z= (2a) λ = 0·1 2xs λ = 0·3 λ = 0·5 1 λ = 0·7 w= : (2b) λ = 0·9 2xs λ = 0·99 10 It is difficult to derive useful analytic formulae for the vc conditions under which hermaphrodites can invade such a population when l>0. This is because hermaphrodite fitness depends on the frequency of both monogenics and amphigenics (only the former of which suffer inbreeding depression at sex-linked loci 1 if l>0). However, for the special case where l=0, 0·0 0·5 1·0 1·5 2·0 α the fitness of females and mutant hermaphrodites are given, respectively, by Fig. 1. The boundary conditions for the invasion of hermaphrodites into a dioecious population under the Wf=vcaz, (3a) assumptions of the model; hermaphrodites can invade for parameter combinations encompassed by the area under Wh=az+2b(1xaz)(1xd): (3b) each curve. Curves are shown (a) for a range of values of inbreeding depression caused by autosomal loci, d, and Note that because the fitnesses of the two her- (b) for a range of values of inbreeding depression caused by W-linked loci, l (see inset for details). Other parameter maphrodite genotypes are identical when l=0, we values for these curves are: s=0; b=1. need only consider the phenotypes involved to deter- mine hermaphrodite invasion criteria. Stability analysis (Otto & Day, 2007, chapter 7) then reveals hermaphrodite invasion decreases with d, i.e. with that hermaphrodites will invade a dioecious popu- the expression of genetic load at non-sex-linked loci lation if (Fig. 1a). The criteria for the invasion of hermaphrodites into a dioecious population when l>0 can be 2b(1xd)(2xs)+a(1x2b+2bd)(1xs) found numerically. In contrast to the effect of in- vc< : (4a) a(1xs) breeding depression at autosomal loci, hermaphrodite invasion is influenced relatively little by the homo- When s=0 (so that z=1/2), this reduces to zygous expression of genetic load at sex-linked loci (compare Fig. 1a and b). a+4bx2abx2bd(2xa) vc< : (4b) Simulations suggest that conditions for the a invasion of hermaphrodites into a dioecious popu- With decreasing a, self-fertile hermaphrodites are lation also correspond to those sufficient for their at an increasing reproductive advantage over females, complete displacement of females, i.e. a male–female– which fail to reproduce if they cannot outcross, hermaphrodite trimorphism does not appear to be i.e. females must have increasing values of vc to resist stable. In other words, if hermaphrodites can invade a being displaced by hermaphrodites. Because inbreed- dioecious population under selection for reproductive ing depression compromises the fitness gained by assurance (low a), the population will evolve to andro- hermaphrodites through self-fertilization, the thres- dioecy or hermaphroditism. Thus, for all iterations hold value of vc that females must attain to prevent explored in Fig. 1, hermaphrodites introduced at a low

x10 frequency of 10 into a dioecious population always (a) δ у 0, λ = 0 went on to displace all females. The apparent insta- bility of ‘trioecy’ is not surprising: the invasion of 100 hermaphrodites into a population dilutes the frequency of males, z, so that the probability of finding a mate, az, is reduced for any value of a. This should affect females more than hermaphrodites, because the latter can self-fertilize their progeny. 10 vc As indicated by (4a), male viability also affects the invasion of hermaphrodites into a dioecious population: hermaphrodites more easily invade a population as the proportion of pre-adult male mortality, s, increases. This is simply because, when males die 1 before they are available for mating, they become 0·0 0·5 1·0 1·5 2·0 more difficult to find, so that az is smaller and hermaphrodites may enjoy the relative benefits of re- (b) δ = 0, λ у 0 productive assurance. Thus, the conditions for her- 100 maphrodite invasion are eased with reductions in either female or male fitness components; under both circumstances, the hermaphrodites exclude females, but they may still persist with males if d>0. In other words, reduced male survivorship can cause females 10 to be displaced from the population by hermaphro- vc dites even though males may persist; this applies particularly to the case where inbreeding depression is caused by sex-linked loci (see below).

(ii) Invasion of females into a population 1 0·0 0·5 1·0 1·5 2·0 with hermaphrodites α Just as hermaphrodites completely displace females Fig. 2. The boundary conditions for the invasion of if they are able to invade a dioecious population, so females into an androdioecious (or hermaphroditic) females completely displace hermaphrodites if they population under the assumptions of the model; females can invade for parameter combinations encompassed by can invade. However, whereas the area under the the area above each curve. Curves are shown (a) for a curves in Fig. 1a represents parameter space that range of values inbreeding depression caused by autosomal allows the invasion of hermaphrodites into a di- loci, d, and (b) for a range of values of inbreeding oecious population, these curves do not demarcate the depression caused by W-linked loci, l (see inset in Fig. 1 threshold for female invasion into a population with for details). Other parameter values for these curves are: hermaphrodites. Rather, the parameter space allow- s=0; b=1. ing female invasion is more restricted. For the special case where l=0, an androdioecious population is dioecious population if vc<1. However, the right- stable to the invasion of females unless hand sides of (4b) and (5b) diverge as a falls below (1xs)(a+2bx2bdx2ab+2abd) 2, with (4b) greater than (3b) and their diﬀerence vc> : (5a) given by axasx2b(1xd) 4(2xa)b2(1xd)2 When males and hermaphrodites are equally viable, : (6) i.e. when s=0, then (5a) reduces to a(ax2b+2bd) a(2xa) This can be seen in Fig. 2, where the area under the vc>ax1+ : (5b) ax2b(1xd) lower curve represents parameter combinations that allow hermaphrodites to invade a dioecious popu- When a=2, the right-hand sides of (4b) and (5b) are lation, whereas females can only invade populations equal; this is as we should expect, given that a=2 with hermaphrodites for parameter combinations causes z to approach 0.5 in an androdioecious popu- above the upper curve. Thus both females and her- lation and hermaphrodites are thus equivalent to maphrodites are relatively resistant to displacement females; females then invade an androdioecious by the other phenotype; essentially, a phenotype must population if vc>1, and hermaphrodites invade a cross the empty area between the two curves in Fig. 2

before it can invade a population containing its (a) δ у 0, λ = 0 counterpart. It is intuitive why females should ﬁnd it diﬃcult to 0·5 re-invade a population once they have been displaced 0·4

by hermaphrodites. In situations where males are ) sufficiently difficult to find (a low), self-fertile her- z maphrodites will displace both females and males 0·3 (see below). But once males have been lost from a population, females can never re-invade, and the 0·2 population is locked into a strategy of perpetual Male frequency ( self-fertilization. More generally, the separation in 0·1 parameter space of the curves for female and hermaphrodite invasion can be explained by noting 0·0 that the frequency of males in a population with her- 0·0 0·5 1·0 1·5 2·0 maphrodites must be <0.5 (Lloyd, 1975, and see be- (b) δ = λ у low; Charlesworth, 1984), whereas it equals 0.5ina 0, 0 dioecious population, so that az in a population with 0·5 hermaphrodites must be less than az in a dioecious population for the same value of a. If we replace all 0·4 ) terms in az in equations (1) with a/2 (i.e. if we remove z the male frequency-dependence from the recursions), 0·3 the curves for the invasion of hermaphrodites into a dioecious population (Fig. 1) divides parameter space 0·2 into two parts: hermaphrodites invade below the

curves, and females invade above the curves. For the Male frequency ( 0·1 special case of l=0, this curve is again given by equations (4) above. 0·0 0·0 0·5 1·0 1·5 2·0 (iii) Maintenance of males with hermaphrodites α Fig. 3. The frequency of males maintained at equilibrium If hermaphrodites invade a dioecious population, with hermaphrodites as a function of a. Frequencies are they displace females and are taken to a frequency shown (a) for a range of values of inbreeding depression >0.5 by negative frequency-dependent selection. caused by autosomal loci, d, and (b) for a range Thus, not only do they displace females, they also of inbreeding depression caused by W-linked loci, at least partially displace males, because any self- l (see inset in Fig. 1 for details). Other parameter values fertilization by hermaphrodites reduces the mating for these curves are: s=0; b=1. opportunities for males. It is thus clear that the frequency of males will decrease with decreasing a autosomal loci: the equilibrium frequency of males is (Fig. 3). If self-fertilization comes at a cost, for ex- elevated for a given value of a (Fig. 3b). However, ample not all eggs can be fertilized (i.e. b<1 in the the male frequency for a given l is in general higher model; results not shown), or if selfed progeny suffer than that for an equivalent d, all else being equal. inbreeding depression due, for example, to the ex- Particularly notable is the qualitative difference be- pression of recessive deleterious alleles at autosomal tween the effects of l and d: while males are eventu- loci (d>0), then the equilibrium frequency of males ally lost from a population for sufficiently low a, even is correspondingly increased for any given value of as d approaches 1, males are maintained at a fre- a (Fig. 3a). Thus, in situations where a is small quency z>0 for l>0.5, even as a approaches zero. (e.g. when population densities are low and her- Indeed, the equilibrium frequency of males in the limit maphrodites rarely enjoy the benefits of outcrossing of a=0 is given by with a male), males can be maintained at relatively ðÞ1x2l ðÞ1xs high frequencies if d is sufficiently large (Fig. 3a). z*= , (7a) 2 5l s 2ls Importantly, however, males are always lost from x x + populations as a approaches zero if inbreeding de- which simplifies to pression is due only to the expression of deleterious 1x2l genes on the autosomes. These results were also ob- z*= (7b) tained by Otto et al. (1993). 2x5l The effect of inbreeding depression at sex-linked for the case where males and hermaphrodites are loci (l>0) is in some respects similar to that at equally viable, i.e. s=0 (Fig. 3b). Thus, in the limit

(a) δ у 0, λ = 0 thus favour W*- over Z-linked genes. This reduces the frequency, or causes the elimination, of males, just as it 0·7 reduces the frequency of amphigenic hermaphrodites.

) 0·6 When selfed progeny suﬀer inbreeding depression y due to the expression of deleterious alleles at auto- 0·5 somal loci, the erosion of heterozygosity is diminished, 0·4 and we thus expect more amphigenic hermaphrodites (Fig. 4a). As illustrated in Fig. 3, we expect inbreeding 0·3 depression at autosomal loci to increase the frequency 0·2 of males, too. This is not so much because of a direct advantage of Z-linked genes, but rather because such Amphigenic frequency ( 0·1 inbreeding depression eﬀectively favours the out- 0·0 crossed progeny of hermaphrodites, and these are 0·0 0·5 1·0 1·5 2·0 always sired by males. By contrast, when inbreeding depression is the result of the expression of deleterious (b) δ = 0, λ у 0 recessive W*-linked loci, Z-linked genes are favoured 0·7 directly. At the extreme of l=1.0, all W*W* monogenic hermaphrodites are eliminated from the popu-

) 0·6 y lation each generation, so that hermaphrodites are 0·5 represented only by ZW* amphigenics. Even if these 0·4 never encounter males, or never choose to mate with males (i.e. if a=0), males will still be maintained at a 0·3 frequency of 1/3 in the population (as predicted by equation (1) above; see Fig. 4b). This extreme scen- 0·2 ario, where both ZZ males and W*W* hermaphro- Amphigenic frequency ( 0·1 dites have a fitness of zero, neatly illustrates the maintenance of males by overdominant selection at 0·0 0·0 0·5 1·0 1·5 2·0 the sex-determination locus. This also applies to the α interesting situation when s=1, i.e. when the viability Fig. 4. The frequency of amphigenic hermaphrodites of males is so low that they die before reproducing (or, maintained at equilibrium with monogenic hermaphrodites if they survive, are refused the opportunity of mating and males as a function of a. Frequencies are shown with hermaphrodites). In this special case, it is easy to (a) for a range of values of inbreeding depression caused show by solving equations (1) that the frequency of by autosomal loci, d, and (b) for a range of inbreeding amphigenics following mortality due to inbreeding depression caused by W-linked loci, l (see inset in Fig. 1 for details). Other parameter values for these curves are: depression will be (2–4l)/(1–3l), and that the primary s=0; b=1. sex ratio (frequency of males prior to their mortality) will be (2–4l)/(5–11l). where a approaches 0, when inbreeding depression is caused by autosomal loci, only a value of d=1.0 will ensure the maintenance of males. In contrast, when 4. Discussion inbreeding depression is caused by sex-linked load, (i) Transitions from dioecy to androdioecy l>0.5 ensures that z>0 (Fig. 3b). and hermaphroditism The model presented here advances that of Otto et al. (iv) The frequency of ‘amphigenics’ versus (1993) by exploring the invasion of hermaphrodites ‘monogenics’ in androdioecious populations into a dioecious population and that of females into In the absence of females and selfing (i.e., when az= an androdioecious population. The main results are 1), there are only two genotypes in the population: intuitive: partially selfing hermaphrodites can invade males (ZZ homozygotes at the sex-determining locus) a population of males and females if the advantage and ‘amphigenic’ hermaphrodites (ZW* hetero- of self-fertilization outweighs the disadvantage of in- zygotes), at a ratio of 1 : 1. Selfing reduces the fitness breeding depression suffered by their selfed offspring. of males, which cannot fertilize those eggs, and thus Hermaphrodites may invade a totally outcrossing causes a reduction in the male frequency, as noted population (e.g. where males are abundant) if they above; it thus selects against Z-linked genes. Selfing produce marginally more (fertilized) eggs than their also increases the frequency of W*W* homozygotes female counterparts. This condition differs from that (because self-fertilization by W*W* parents produces predicted for the invasion into a dioecious population only W*W* progeny). Both implications of selfing of hermaphrodites that can both self-fertilize and

outcross as males, such as in many plants (Maurice & from dioecy to hermaphroditism. The extent to which Fleming, 1995; Wolf & Takebayashi, 2004); in that low population densities and mate limitation have case, we expect outcrossing hermaphrodites to be able played a role in the evolution of the sexual systems in to invade if the sum of their male and female compo- the Branchiopoda is not known. However, species nents of fitness exceeds that of the females. within the group typically inhabit ephemeral ponds If all females find a mate (pz=caz=1), and if her- where density fluctuations may be dramatic between maphrodites produce as many eggs as females (v=1) years (reviewed in Weeks et al., 2006b, and S. Weeks, and self-fertilize all those that are not fertilized by pers. comm.), so that hermaphrodites might expect males (b=1), then any selfing by hermaphrodites will periods in which males are difficult to find. Such allow them to invade a dioecious population if d<0.5, mate limitation is likely to be extreme during bouts of whereas they will be prevented from doing so if colonization of new habitat following long-distance d>0.5; note that, under these conditions, the female dispersal. In this context, it is interesting to recall that and hermaphrodite fitnesses in equations (3) become Baker (1955), in proposing the selective advantage Wf=1 and Wh=(1 – S)+2S(1 – d), where S=az is conferred upon self-fertile hermaphrodites in species the hermaphrodites’ selfing rate. This is just the with a colonizing habit, was drawn to the idea by the corollary of Fisher’s (1941) automatic transmission proposed evolution of hermaphroditism from dioecy advantage of self-fertilization: it pays to increase the in precisely this group of animals. Pannell (1997a) selfing rate because selfed progeny carry two copies and Pannell & Barrett (1998) explored the advantages of the mother’s genome, but only if those progeny are of reproductive assurance further in a metapopu- at least half as fit as their outcrossed counterparts. lation context. Given the fragmented nature of the Of course, even with an abundance of males, there natural populations of the branchiopod species in would presumably still be costs of selecting and mat- question here, exploring the maintenance of a genetic ing with them (expressed in the model, for example, polymorphism under assumptions of recurrent col- as v<1); in this case, the advantages of selfing would onization and extinction would seem to be worthwhile. then outweigh the disadvantages of inbreeding depression for values of d>0.5, and hermaphrodites can (ii) Transitions from androdioecy to dioecy invade more easily. An important prediction of the model is that the It is clear that if hermaphrodites displace both females invasion of hermaphrodites into a dioecious popu- and males from a population of shrimps, females can lation is sufficient to displace the females altogether; a not re-invade unless males do so first. Thus, once sexual polymorphism that includes both females and males have been lost from a species, the re-evolution hermaphrodites is thus ruled out in this model. This of dioecy would seem to be ruled out, so that the prediction follows directly from the frequency de- species is locked into a future without effective sexual pendence assumed in the mating interactions (i.e. that reproduction and recombination. However, females the probability that a hermaphrodite or female finds a potentially can re-invade an androdioecious popu- male is directly proportional to the male frequency): lation if the outcrossing rate (the male density), the because the frequency of hermaphrodites will always females’ fecundity relative to that of the hermaphro- be >0.5, males will be more ‘dilute’ in androdi- dites, and the level of inbreeding depression suffered oecious populations, which females will thus find more by selfed progeny are sufficiently high. It is therefore difficult to invade. As noted by Otto et al. (1993), it interesting that in the long period over which andro- seems unlikely that the outcrossing rate of hermaphro- dioecy appears to have been maintained in the dites will depend linearly on male frequency; for Limnadiidae (potentially greater than 180 million instance, it is plausible that hermaphrodites will ac- years: Weeks et al., 2006a, b), dioecy does not appear tively seek out males when they are rare, as indeed to have re-evolved. they appear to do (Hollenbeck et al., 2002). The fre- The stability of androdioecy to the invasion of quency dependence in the model is thus a simplifi- females makes sense when we consider that an in- cation. Nevertheless, we expect that hermaphrodites vading female must be a modified hermaphrodite are more likely to outcross when males are common rendered incapable of self-fertilization. Such an indi- than rare, and the model captures this expectation. vidual might enjoy the benefit of avoiding the costs of Certainly, in the limit when males are absent out- inbreeding depression. Indeed, inbreeding depression crossing is precluded; this situation is common in measured in experimental populations of Eulimnadia many species of clam shrimps, where individual texana is typically greater than 0.5 (Weeks et al., 1999, populations of otherwise androdioecious species fre- 2000, 2001b), so dioecy could evolve in response to quently lack males altogether (e.g. Sassaman, 1989; the avoidance of inbreeding depression on its own. Eder et al., 2000; Weeks et al., 2006b). However, if males are scarce from time to time (i.e. The model here invokes selection for reproductive if a is low), females will suffer from their lack of assurance as the key agent in favouring transitions reproductive assurance; we should thus expect

demographic stochasticity, which is likely to be be selectively maintained in an androdioecious species characteristic of the branchiopod crustaceans (see even when the reproductive prospects of males are above), to exclude females. More importantly, her- reduced to zero, for example if they die after being maphrodites would appear to have the best of both counted but before reproduction (s=1) or if her- worlds in the face of possible female invasion: if males maphrodites fail to encounter males (a=0). In a are scarce, they can self-fertilize, but when males be- metapopulation, if l>0.5 the male-determining allele come common (i.e. when conditions arise that might is thus effectively immune to its selective disadvantage favour females), the hermaphrodites can return to due to the inability of males to colonize populations outcrossing. Females should thus not find it easy to on their own (cf. Pannell, 1997a). re-invade androdioecious populations unless they are Given the dioecious ancestry of the androdioecious substantially better at finding mates, or their egg branchiopods, because females are the heterogametic production is substantially higher (see Fig. 2b, where sex, and because different W* chromosomes in the it can be seen that low vc implies the females cannot hermaphrodites never meet, we might expect l to be invade); neither of these scenarios seems very likely. greater than zero as a result of W* degeneration (see Section 1). But is l>0.5? Weeks et al. (2001a) estimated the relative fitnesses of monogenics and (iii) Maintenance of males with hermaphrodites amphigenics under controlled conditions in the lab- In their model, Otto et al. (1993) included a term for oratory to be 0.87, corresponding to an estimate inbreeding depression that reduced the fitness of all of l=0.13. However, we might expect the expression self-fertilized progeny relative to their outcrossed of inbreeding depression to be higher under field counterparts. That model predicted that inbreeding conditions than in the laboratory (Schemske, 1983; depression might play an important role in the main- Dudash, 1990), so a value of l>0.5 cannot yet be tenance of males with hermaphrodites, because her- ruled out. Indeed, higher values of l probably need to maphrodites can only outcross with males. In other be invoked to explain the observed deficit of mono- models of androdioecy, directed largely at under- genics in natural populations (Weeks et al., 2001a). standing the sexual system in plants (e.g. Lloyd, 1975; Given the potential importance of l in explaining Charlesworth & Charlesworth, 1978; Charlesworth, male persistence in branchiopods, efforts to estimate 1984), males must compete with hermaphrodites for it in the wild would be worthwhile. outcrossing opportunities, and these models predict Lineage selection is another possible explanation that androdioecy is unlikely to occur in species with for the long-term maintenance of males. Although much self-fertilization, regardless of the level of males cannot be lost selectively under the model with inbreeding depression suffered by the progeny. This l>0.5, they can be lost as a result of drift, which is probably why androdioecy is so much rarer than might be an important force in species that suffer re- gynodioecy in plants, given that the evolution of peated colonization bottlenecks or density fluctua- gynodioecy is favoured when the product of the self- tions (Whitlock & Barton, 1997). This possibility is ing rate and the level of inbreeding depression is >0.5 borne out by the many male-less populations of (e.g. Charlesworth & Charlesworth, 1978). Eulimnadia and other androdioecious branchiopod Although inbreeding depression should help to species. In such situations, males might then be maintain males with hermaphrodites in clam shrimps, maintained within the species as a whole if male-less males may nevertheless be lost if male–hermaphrodite (and thus effectively asexual) populations suffer encounter rates fall, for example when population higher extinction probabilities than those with males. densities are low (Otto et al., 1993). Given the com- Increased extinction of hermaphrodite-only versus mon observation of hermaphrodite-only populations androdioecious populations has indeed been observed in otherwise androdioecious species (see above), this under experimental conditions (Weeks, 2004). By would seem to be a frequent occurrence for these extension, species in which males have been lost en- animals. It is thus all the more remarkable that tirely might be less likely to persist in the long term androdioecy appears to have persisted in the genus than those in which males have been maintained. The Eulimnadia for at least 24 million years, and in the evolutionary longevity of androdioecy in branchi- Limnadiidae family for probably much longer still opods could thus be seen as a result of the long-term (Weeks et al., 2006a, b). disadvantages of asexual reproduction by obligately By incorporating the term l that accounts for the selfing hermaphrodites. potential effects of W*-linked genetic load, the model here provides one possible explanation for the long- (iv) Implications of the evolution of inbreeding term evolutionary maintenance of androdioecy in depression branchiopod crustaceans. Not only does inbreeding depression at sex-linked loci increase the frequency of The model presented here assumes fixed values for d males generally; when l>0.5, in particular, males will and l. This is probably reasonable in the case of l,

where inbreeding depression at W*-linked loci is sequences be found on both chromosomes close to the hypothesized to be due to the fixation of deleterious sex-determining locus, and to what extent are they mutations. In contrast, the assumption is an over- functional? If the sex-determining locus is as ancient simplification for d because inbreeding depression at as the hypothesis proposed here supposes, then it is autosomal loci can evolve through the purging of remarkable that WW homozygous hermaphrodites genetic load under partial selfing (Lande & Schemske, are as viable as they apparently are, i.e. that W 1985; Barrett & Charlesworth, 1991; Byers & Waller, degeneration has not progressed further. The lower 1999; Crnokrak & Barrett, 2002). Predictions of the fitness of the WW genotype in branchiopods poses model here for the invasion of hermaphrodites into fascinating questions that bear on the advantages a dioecious population will not be affected by this of sexual reproduction and recombination, the evol- assumption, because high inbreeding depression ution of sex chromosomes, and on the process by should be maintained in an ancestral dioecious which deleterious mutations accumulate and are ex- population (Lande & Schemske, 1985; Charlesworth pressed. & Charlesworth, 1987; Lande et al., 1994; Crnokrak Finally, it is worth recalling that androdioecious & Barrett, 2002). However, should partially selfing branchiopod species typically comprise a mixture hermaphrodites invade a population, we expect in- of androdioecious populations and populations in breeding depression to decline over time. This will which males are absent, i.e. populations in which the make the re-invasion of females even more difficult hypothesized effects of overdominance at the sex- than predicted (see above). The assumption of fixed determining locus have not been sufficient for the inbreeding depression at autosomal loci thus means local maintenance of males. These populations may that the predicted stability of androdioecy to the in- well have been founded by monogenic hermaphro- vasion of females is probably conservative. dites, or males and amphigenic hermaphrodites may have been lost locally by drift. The model considered here is deterministic, and it would therefore be valu- (v) Conclusions able to extend it by considering the dynamics of the The model of Otto et al. (1993) has been extensively sex-determining locus under the joint influence of tested in a series of papers that aimed chiefly to selection and drift, particularly in the context of a measure its parameters. These studies, which have metapopulation in which populations are linked by recently been reviewed by Weeks et al. (2006a), have migration and colonization. highlighted two key issues. First, it is difficult to ac- I am grateful to Stephen Weeks for his detailed answers to count for the high frequency of amphigenics observed my many questions about clam shrimps, to Spencer Barrett in populations of Eulimnadia texana on the basis of and Marcel Dorken for helpful comments on the manu- the original model of Otto et al. (1993). And second, script, and particularly to Sally Otto for numerous useful the original model does not adequately account for suggestions and for advising on the stability analysis to derive more general conditions for mutant invasion in the expression of inbreeding depression observed in equations (4) and (5). Deborah Charlesworth established Eulimnadia texana, part of which is sex-linked. The important foundations for the study of androdioecy by new model presented here incorporates the observed clarifying several critical empirical and theoretical issues. I sex-linked inbreeding depression, which, when suf- thank her for her generosity over the years and for the ficiently high, might account for the high frequencies very positive influence she has had on my own research. The insights she has shared regarding deleterious mutations, of amphigenics in natural populations. It also pro- inbreeding depression, mating systems and sex-chromosome vides a plausible explanation for the extraordinarily evolution stimulated my own interest in these topics and long persistence of males in Eulimnadia and probably contributed to the foundation on which the model presented the Limnadiidae family more generally. here was built. Testing the new model will require better estimates of l. The current estimate of l=0.13 is too low to be References able to explain the high frequency of amphigenics, Akimoto, J., Fukuhara, T. & Kikuzawa, K. (1999). and it falls below the 0.5 threshold that would Sex ratios and genetic variation in a functionally guarantee the indefinite selective maintenance of an- androdioecious species, Schizopepon bryoniaefolius drodioecy. The current estimate of l was made under (Cucurbitaceae). American Journal of Botany 86, 880–886. laboratory conditions and is likely to differ from l in Baker, H. G. (1955). Self-compatibility and establishment the field. Although no doubt logistically challenging, after ‘long-distance’ dispersal. Evolution 9, 347–348. estimates of l from experiments carried out under Barrett, S. C. H. & Charlesworth, D. (1991). Effects of a field conditions would therefore be very useful. change in the level of inbreeding on the genetic load. It would also be valuable to characterize DNA se- Nature 352, 522–524. Bergero, R., Forrest, A., Kamau, E. & Charlesworth, D. quence variation at or close to the sex-determining (2007). Evolutionary strata on the X chromosomes of locus of these animals on both the W and the Z the dioecious plant Silene latifolia: evidence from new chromosomes. To what extent can homologous sex-linked genes. Genetics 175, 1945–1954.

Bull, J. J. (1983). Evolution of Sex Determining Mechanisms. Liston, A., Rieseberg, L. H. & Elias, T. S. (1990). Menlo Park, CA: Benjamin/Cummings. Functional androdioecy in the flowering plant Datisca Byers, D. L. & Waller, D. M. (1999). Do plant populations glomerata. Nature 343, 641–642. purge their genetic load? Effects of population size Lloyd, D. G. (1975). The maintenance of gynodioecy and and mating history on inbreeding depression. Annual androdioecy in angiosperms. Genetica 45, 325–339. Review of Ecology and Systematics 30, 479–513. Longhurst, A. R. (1955). Evolution in the Notostraca. Charlesworth, B. & Charlesworth, D. (2000). The Evolution 9, 84–86. degeneration of Y chromosomes. Philosophical Trans- Maurice, S. & Fleming, T. H. (1995). The effect of pollen actions of the Royal Society of London, Series B 355, limitation on plant reproductive systems and the main- 1563–1572. tenance of sexual polymorphisms. Oikos 74, 55–60. Charlesworth, D. (1984). Androdioecy and the evolution of Medland, V. L., Zucker, N. & Weeks, S. C. (2000). dioecy. Biological Journal of the Linnean Society 23, Implications for the maintenance of androdioecy in 333–348. the freshwater shrimp, Eulimnadia texana Packard: Charlesworth, D. (1999). Theories of the evolution of di- encounters between males and hermaphrodites are not oecy. In Gender and Sexual Dimorphism in Flowering random. Ethology 106, 839–848. Plants, pp. 33–60. Berlin: Springer. Nei, M. (1969). Linkage modification and sex difference in Charlesworth, D. & Charlesworth, B. (1978). A model for recombination. Genetics 63, 681–699. the evolution of dioecy and gynodioecy. American Nei, M. (1970). Accumulation of nonfunctional genes Naturalist 112, 975–997. on sheltered chromosomes. American Naturalist 104, Charlesworth, D. & Charlesworth, B. (1987). Inbreeding 311–322. depression and its evolutionary consequences. Annual Nicolas, M., Marais, G., Hykelova, V., Janousek, B., Review of Ecology and Systematics 18, 273–288. Laporte, V., Vyskot, B., et al. (2005). A gradual process Charlesworth, D., Charlesworth, B. & Marais, G. (2005). of recombination restriction in the evolutionary history Steps in the evolution of heteromorphic sex chromo- of the sex chromosomes in dioecious plants. PLoS somes. Heredity 95, 118–128. Biology 3, 47–56. Connor, H. E. (1996). Breeding systems in Indomalaysian Obbard, D. J., Harris, S. A., Buggs, R. J. A. & Pannell, Spinifex (Paniceae: Gramineae). Blumea 41, 445–454. J. R. (2006). Hybridization, polyploidy, and the evolution Crnokrak, P. & Barrett, S. C. H. (2002). Purging the genetic of sexual systems in Mercurialis (Euphorbiaceae). load: a review of the experimental evidence. Evolution 56, Evolution 60, 1801–1815. 2347–2358. Otto, S. P. & Day, T. (2007). A Biologist’s Guide to Darwin, C. (1877). The Different Forms of Flowers on Plants Mathematical Modeling in Ecology and Evolution. of the Same Species. New York: Appleton. Princeton: Princeton University Press. Dudash, M. R. (1990). Relative fitness of selfed and Otto, S. P., Sassaman, C. & Feldman, M. W. (1993). outcrossed progeny in a self-compatible, protandrous Evolution of sex determination in the conchostracan species, Sabatia angularis L (Gentianaceae): a com- shrimp Eulimnadia texana. American Naturalist 141, parison in three environments. Evolution 44, 1129–1139. 329–337. Duesing, C. (1884). Die Regulierung des Geschle- Pannell, J. (1997a). The maintenance of gynodioecy and chtsverha¨ltnisses bei der Vermehrung der Menschen, androdioecy in a metapopulation. Evolution 51, 10–20. Tiere und Pflanzen. Jenaer Zeitschrift fu¨r Nat- Pannell, J. (1997b). Widespread functional androdioecy in urwissenschaft 17, 593–940. Mercurialis annua L. (Euphorbiaceae). Biological Journal Eder, E., Richer, S., Gottwald, R. & Hodle, W. (2000). First of the Linnean Society 61, 95–116. record of Limnadia lenticularis males in Europe Pannell, J. R. (2001). A hypothesis for the evolution of (Branchiopoda: Conchostraca). Journal of Crustacean androdioecy: the joint influence of reproductive Biology 20, 657–662. assurance and local mate competition in a metapopu- Fisher, R. A. (1930). The Genetical Theory of Natural lation. Evolutionary Ecology 14, 195–211. Selection. Oxford: Oxford University Press. Pannell, J. R. (2002). The evolution and maintenance of Fisher, R. A. (1941). Average excess and average effect of a androdioecy. Annual Review of Ecology and Systematics gene substitution. Annals of Eugenics 11, 53–63. 33, 397–425. Hollenbeck, V. G., Weeks, S. C., Gould, W. & Zucker, Pannell, J. R. & Barrett, S. C. H. (1998). Baker’s Law N. (2002). Maintenance of androdioecy in the revisited: reproductive assurance in a metapopulation. freshwater shrimp Eulimnadia texana: sexual encounter Evolution 52, 657–668. rates and outcrossing success. Behavioral Ecology 13, Rieseberg, L. H., Hanson, M. A. & Philbrick, C. T. (1992). 561–570. Androdioecy is derived from dioecy in Datiscaceae: Knoll, L. & Zucker, N. (1995). Selfing versus outcrossing evidence from restriction site mapping of PCR-amplified in the androdioecious clam shrimp, Eulimnadia texana chloroplast DNA fragments. Systematic Botany 17, (Crustacea, Conchostraca). Hydrobiologia 298, 83–86. 324–336. Krahenbuhl, M., Yuan, Y. M. & Kupfer, P. (2002). Sakai, S. (2001). Thrips pollination of androdioecious Chromosome and breeding system evolution of the genus Castilla elastica (Moraceae) in a seasonal tropical forest. Mercurialis (Euphorbiaceae): implications of ITS mol- American Journal of Botany 88, 1527–1534. ecular phylogeny. Plant Systematic and Evolution 234, Sassaman, C. (1989). Inbreeding and sex ratio variation in 155–170. female-biased populations of a clam shrimp, Eulimnada Lande, R. & Schemske, D. W. (1985). The evolution of self- texana. Bulletin of Marine Science 45, 425–432. fertilization and inbreeding depression in plants. I. Sassaman, C. (1991). Sex ratio variation in female- Genetic models. Evolution 39, 24–40. biased populations of Notostracans. Hydrobiologia 212, Lande, R., Schemske, D. W. & Schultz, S. T. (1994). 169–179. High inbreeding depression, selective interference Sassaman, C. (1995). Sex determination and the evolution among loci, and the threshold selfing rate for purging of unisexuality in the Conchostraca. Hydrobiologia 298, recessive lethal mutations. Evolution 48, 965–978. 45–65.

Sassaman, C. & Weeks, S. C. (1993). The genetic mech- androdioecious clam shrimp, Eulimnadia texana. Journal anism of sex determination in the conchostracan shrimp of Evolutionary Biology 14, 83–94. Eulimnadia texana. American Naturalist 141, 314–328. Weeks, S. C., Hutchison, J. A. & Zucker, N. (2001b). Schemske, D. W. (1983). Breeding system and habitat Maintenance of androdioecy in the freshwater shrimp, effects on fitness components in three neotropical Costas Eulimnadia texana: do hermaphrodites need males (Zingiberaceae). Evolution 37, 523–539. for complete fertilization? Evolutionary Ecology 15, Swensen, S. M., Luthi, J. N. & Rieseberg, L. H. (1998). 205–221. Datiscaceae revisited: monophyly and the sequence of Weeks, S. C., Benvenuto, C. & Reed, S. K. (2006a). When breeding system evolution. Systematic Botany 23, males and hermaphrodites coexist: a review of andro- 157–169. dioecy in animals. Integrative and Comparative Biology Turner, B. J., Davis, W. P. & Taylor, D. J. (1992). 46, 449–464. Abundant males in populations of a selfing hermaphro- Weeks, S. C., Sanderson, T. F., Reed, S. K., Zofkova, M., dite fish, Rivulus marmoratus, from some Belize cays. Knott, B., Balaraman, U., et al. (2006b). Ancient andro- Journal of Fish Biology 40, 307–310. dioecy in the freshwater crustacean Eulimnadia. Weeks, S. C. (2004). Seven generations of inbreeding does Proceedings of the Royal Society of London, Series B 273, not purge inbreeding depression in the clam shrimp, 725–734. Eulimnadia texana. Journal of Evolutionary Biology 17, Whitlock, M. C. & Barton, N. H. (1997). The effective size 475–484. of a subdivided population. Genetics 146, 427–441. Weeks, S. C. & Zucker, N. (1999). Rates of inbreeding in the Wolf, D. E. & Takebayashi, N. (2004). Pollen limitation androdioecious clam shrimp Eulimnadia texana. and the evolution of androdioecy from dioecy. American Canadian Journal of Zoology 77, 1402–1408. Naturalist 163, 122–137. Weeks, S. C., Marcus, V. & Crosser, B. R. (1999). Wolf, D. E., Satkoski, J. A., White, K. & Rieseberg, L. H. Inbreeding depression in a self-compatible, androdi- (2001). Sex determination in the androdioecious plant oecious crustacean, Eulimnadia texana. Evolution 53, Datisca glomerata and its dioecious sister species 472–483. D. cannabina. Genetics 159, 1243–1257. Weeks, S. C., Crosser, B. R., Bennett, R., Gray, M. & Zucker, N., Cunningham, M. & Adams, H. P. (1997). Zucker, N. (2000). Maintenance of androdioecy in the Anatomical evidence for androdioecy in the clam shrimp freshwater shrimp, Eulimnadia texana: estimates of in- Eulimnadia texana. Hydrobiologia 359, 171–175. breeding depression in two populations. Evolution 54, Zucker, N., Aguilar, G. A., Weeks, S. C. & McCandless, 878–887. L. G. (2002). Variation in reproductive cycle between Weeks, S. C., Crosser, B. R. & Gray, M. M. (2001a). selfing and outcrossing hermaphrodites in an androdi- Relative fitness of two hermaphroditic mating types in the oecious desert shrimp. Invertebrate Biology 121, 66–72.