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Invited Special Paper |
2Department of Biology, Indiana University, Bloomington, Indiana 47405-3700 USA 3Department of Botany and Plant Sciences, University of California, Riverside, California 92521-0124 USA
Received for publication July 18, 2000. Accepted for publication March 8, 2001.
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ABSTRACT |
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Key Words: dead-end hypothesis • evolutionary irreversibility • mating-system evolution • outcrossing • phylogenetic approach • self-fertilization
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REPRODUCTIVE ASSURANCE AND THE TWOFOLD ADVANTAGE OF SELF-FERTILIZATION |
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TOPABSTRACTREPRODUCTIVE ASSURANCE AND THE...IS SELFING AN EVOLUTIONARY...MACROEVOLUTIONARY APPROACHES...PROBLEMS ENCOUNTERED IN EXISTING...CONCLUSIONSLITERATURE CITED |
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; Grant, 1981
). Selfing has two primary advantages over outcrossing: (1) reproductive assurance and (2) twofold transmission of genes. Selfing assures reproduction by eliminating reliance on pollinators, which increases colonization potential (Baker, 1955
). The second advantage is intrinsic to selfing; a selfer transmits two sets of genes to each of its offspring, while an outcrosser transmits a single set (Fisher, 1941
; Nagylaki, 1976
; Lloyd, 1979
). Theoretical models of mating-system evolution predict that modifier alleles that enhance self-fertilization will rapidly increase in frequency due to the transmission advantage of selfing (Fisher, 1941
; Nagylaki, 1976
; Lloyd, 1979
). These studies also predict that reduced fitness of selfed progeny due to inbreeding depression can counteract transmission advantage if the fitness of outcrossed progeny is more than twice that of selfed progeny (reviewed in Uyenoyama, Holsinger, and Waller, 1993
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IS SELFING AN EVOLUTIONARY DEAD END? |
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). One line of reasoning suggests that selfing is an "evolutionary dead end"; selfing lineages continually go extinct and new lineages are founded from outcrossing progenitors (Stebbins, 1957, 1974
; Grant, 1958
; Wyatt, 1988
).
This appears to be a simple claim. However, the phrase "evolutionary dead end" implies two major components: (1) selfing cannot persist as a long-term strategy (i.e., selfing lineages have limited potential for adaptation and speciation and will eventually go extinct), and (2) selfing lineages cannot revert to outcrossing. The first component, extinction of selfing lineages, is supported by two theoretical constructs: a theory predicting the loss of evolutionary flexibility and a theory predicting accumulation of deleterious mutations in selfing populations of finite size. However, increased extinction of selfing lineages does not necessarily mean that selfers are an evolutionary dead end. If selfers can revert to outcrossing, the theories predicting extinction of selfers no longer apply, and selfers, like outcrossers, have the potential to found major evolutionary lineages. Irreversibility of mating-system evolution is a necessary condition of the dead-end hypothesis. However, it is a commonly neglected component of what is implied by Stebbins' (1957)
proposal.
Extinction of selfers: loss of adaptive potential
Stebbins' original argument is that selfing results in the loss of genetic diversity, which consequently precludes adaptation to new or changing environments (Stebbins, 1957
). Most populations are regularly exposed to temporal and spatial variation in physical and biotic features of the environment. Although most organisms are equipped with physiological and/or developmental mechanisms (e.g., phenotypic plasticity) to dampen the effects of short-term environmental variation, the ability of these mechanisms to reduce the effects of environmental stochasticity are confined to the range of environmental conditions that the organisms have experienced in recent evolutionary time. A population's evolutionary flexibility (the ability to respond to novel selective challenges) is proportional to its additive genetic variance (Falconer, 1989
, p. 128). The maintenance of additive genetic variation within populations is thought to be essential to the long-term persistence of species.
Reduced genetic variation in selfers: theoretical support
Long-standing debates among evolutionary geneticists have produced a number of hypotheses to explain the maintenance of quantitative genetic variation within populations. These mechanisms include: (1) overdominance in fitness at the loci underlying the variation (Robertson, 1955
), (2) a balance between recurrent nearly neutral mutations and random genetic drift (Lynch and Hill, 1986
; Lynch, 1988
), and (3) an equilibrium between stabilizing or directional selection and recurrent mutations causing deviation from the optimum genotype (Lande, 1975
; Turelli, 1984
; Kondrashov and Turelli, 1992
). Generally, most of the theories predict that selfing should eventually reduce genetic variation (summarized in Charlesworth and Charlesworth, 1995
), qualitatively supporting the dead-end hypothesis. However, under some assumptions, the reduction of genetic diversity in selfers will be limited (details in Charlesworth and Charlesworth, 1995
). In this case, selfing is not likely to have a strong influence on adaptability. Unfortunately little empirical evidence is available to determine which of the proposed mechanisms is most relevant in natural populations, limiting our ability to use these theories to evaluate Stebbins' claim.
Reduced genetic variation in selfers: empirical support
In contrast to the wealth of theoretical studies, empirical data supporting the reduction of quantitative genetic variation due to selfing are scarce. Molecular markers have facilitated the accumulation of data on molecular genetic diversity within populations. The consensus is that inbreeding will lead to reduced molecular diversity (reviewed in Hamrick and Godt, 1989
). However, molecular marker-based estimates of genetic diversity may not be representative of quantitative-genetic variation (Cheverud, Routman, and Jaquish, 1994
; Lynch, 1995
; Storfer, 1996
). Reviewing estimates of quantitative genetic parameters in plants, Charlesworth and Charlesworth (1995)
suggest that few studies contain appropriate data to assess the effects of mating system on quantitative genetic variation. However, in the small number of appropriate studies, there was some evidence that highly inbreeding populations had reduced additive genetic coefficients of variation (Charlesworth and Charlesworth, 1995
), a more satisfactory index for comparing the evolvability of different populations than heritabilities (Houle, 1992
).
In summary, theory and a limited amount of empirical data seem to support the claim that selfing results in reduced quantitative genetic variation. However, it is premature to assess whether genetic variation is sufficiently reduced to eliminate adaptive potential and drive populations to extinction.
Genetic degradation
Another line of argument for increased extinction of selfing lineages concerns the accumulation of deleterious mutations in finite populations. Assuming that most mutations are deleterious, Muller (1964)
suggested that deleterious mutations would irreversibly accumulate in finite asexual populations (Muller's ratchet). In the absence of recombination or segregation, an individual can never produce offspring with fewer deleterious mutations than it carries. In sexual populations, recombination can slow the ratchet process. Progeny with fewer mutations than either parent can be produced by combining the best portions of two parental chromosomes (Charlesworth, Morgan, and Charlesworth, 1993
). In selfing populations, where most individuals are homozygous, recombination has little effect. Hence, highly selfing populations may experience the ratchet process (Heller and Maynard Smith, 1979
). Assuming plausible mutation rates in computer simulations, Lynch, Conery, and Burger (1995)
showed that mean time to extinction in obligatory selfing populations is much shorter than in outcrossing populations. Although this model assumes small populations, occasional reduction in effective population size may be enough to click the ratchet, even in otherwise large populations (Lynch, Conery, and Burger, 1995
).
Irreversibility of mating-system evolution
The two ideas discussed above (loss of variation and genetic degradation) are the primary reasons that selfing may not persist as a long-term strategy. If selfers can revert to outcrossing, none of the arguments for their predilection toward extinction apply. One widely cited genetic theory from the study of mating-system evolution seems to preclude the evolution of outcrossers from selfers. Recall that in the simplest model, inbreeding depression has to be greater than 0.5 for outcrossers to evolve from selfers (Kimura, 1959
; Lloyd, 1979
; Charlesworth, 1980
; Feldman and Christiansen, 1984
). Assuming inbreeding depression is due to deleterious recessive mutations at segregating loci, Lande and Schemske (1985)
predicted that once a population evolves toward self-fertilization, inbreeding depression will decrease. In other words, increased selfing will increase the frequency of homozygotes for deleterious mutations and the opportunity for selection to act against them. Hence, the number of loci segregating for deleterious mutations will decrease (purging effect) (Lande and Schemske, 1985
, but see Byers and Waller 1999
). In a selfing population of infinite size, where inbreeding depression (the cost of selfing) has been purged, outcrossers cannot evolve because there is no advantage that can overcome a selfer's twofold transmission advantage. Thus the model suggests that the evolution of mating systems is one-way, from outcrossing to selfing.
At first examination, the theory predicting the accumulation of mutations in a selfing population and the theory postulating that selfing will purge inbreeding depression (thus causing irreversible evolution of the mating system) seem to be in conflict. However, there is an important difference in one of the assumptions used in the two models. Lynch, Conery, and Burger (1995)
predict that genetic degradation, caused by the fixation of deleterious mutations, proceeds much more rapidly in selfing populations of finite size. Lande and Schemske (1985)
assumed an infinite population size, where fixation of deleterious alleles is impossible. The conclusions of Lande and Schemske (1985)
should still hold under the assumption of finite population size. However, the term purging is misleading. The essence of the purging effect examined by Lande and Schemske (1985)
is that selfing decreases the number (or proportion) of segregating loci. Note that inbreeding depression is caused only by segregating loci. That is, once deleterious mutations at certain loci are fixed in the population, the fixed loci do not contribute further to inbreeding depression. The fixed loci may contribute to heterosis in crosses among populations, which is sometimes regarded as inbreeding depression in conservation biology. However, in the context of mating-system evolution, heterosis should be distinguished from inbreeding depression within populations. Thus the purging effect eliminates segregating alleles contributing to inbreeding depression but may not slow genetic degradation; hence these two models are not mutually exclusive.
The point can be illustrated by noting that there are two alternative fates for a new deleterious mutant allele at any given locus: the allele will eventually be fixed by genetic drift or be eliminated by selection in a finite population. Thus, a locus can have one of three possible states: (1) fixation of the wild-type allele, (2) segregation of the wild-type and the mutant allele, or (3) fixation of the deleterious mutation. Selfing increases the probability of the transition from state (1) to state (3) (Lynch, Conery, and Burger, 1995
). However, the expected time spent in state (2) is lower in selfing populations (Lande and Schemske, 1985
), and the level of inbreeding depression is therefore decreased. The results of a simulation study support this scenario (Table 4 in Charlesworth, Morgan, and Charlesworth, 1993
).
As reviewed above, there are two important components of the dead-end hypothesis: extinction of selfing lineages and irreversibility of mating-system evolution. These two processes when taken together reach one conclusion, that selfers are continually spinning off from outcrossers and going extinct. Thus current evolutionary genetic theory seems to support the hypothesis originally proposed by Stebbins (1957)
.
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MACROEVOLUTIONARY APPROACHES EXAMINING THE IRREVERSIBILITY OF MATING-SYSTEM EVOLUTION |
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; Maddison, 1994
). We briefly review studies that have used phylogenetic analyses to examine evolution of mating systems and discuss potential problems encountered in such studies.
Characterization of mating systems
At first, we discuss the types of traits used to characterize mating systems. Although selfing-rate estimation methods using isozyme or other genetic markers are readily available (Ritland, 1990
), estimating selfing rates for more than a few populations is still labor intensive. Most studies do not use direct estimates of selfing rates for each taxon. Instead, morphological characters indicative of mating system are used. For example, in a study of the Neotropical vine Dalechampia, anther–stigma separation was treated as a continuous character and mapped on a morphology-based phylogenetic tree that included 45 taxa (Armbruster, 1993
). Anther–stigma distance was negatively correlated with autonomous seed set (Armbruster, 1988
). Armbruster concluded that facultatively autogamous lineages (anther–stigma separation between 2 and 6 mm) gave rise to new allogamous species (separation >6 mm) 13 times and to more autogamous species (separation <2 mm) 11 times. Armbruster suggested that the facultatively autogamous species in Dalechampia may outcross sufficiently in nature that the 13 occasions of allogamous lineages arising from facultatively autogamous lineages do not represent a strong counterexample to the dead-end hypothesis.
The interpretation of character evolution can be sensitive to the methods used to define the mating systems. For example, if the Dalechampia data are reanalyzed with the mating system categorized dichotomously (the seven extant taxa with <2 mm of anther–stigma separation as selfers and the rest as outcrossers), the most parsimonious reconstruction yields five independent origins of selfing from outcrossing and no origins of outcrossing from selfing. Likewise, the interpretation may be influenced by where the threshold is set between selfers and outcrossers. The use of marker-based outcrossing estimates does not resolve the problem of determining the threshold unless it produces a cleanly bimodal distribution of selfing rates. However, it can offer a more direct representation of mating systems than estimates of autonomous seed set. Some species with delayed selfing mechanisms may have a high rate of outcrossing in natural populations (Kalisz et al., 1999
). This may occur despite high autonomous seed set in a pollinator-free greenhouse. Therefore, it is desirable to estimate actual outcrossing rates in the field and to assess how individual characters under study influence the mating system.
Another problem related to indirect characterization of mating systems is that selfing rate may be controlled by more than one character. This problem is well illustrated by studies of the Scutellaria angustifolia complex (Olmstead, 1989
). Corolla length was used as the primary indicator of mating system. A parsimony interpretation of character evolution suggests that the three long-corolla species (>22 mm) are derived independently on three occasions from short-corolla species (12–22 mm). This seems to suggest several independent origins of outcrossers from more selfing species. However, further study of isozyme genetic variation within populations showed that two white-flowered, short-corolla species had lower Wright's inbreeding coefficients (F) than would be expected in highly selfing species (Olmstead, 1990
). Olmstead postulated that corolla color, in addition to corolla size, may influence the mating systems. If these revised mating systems (two white, short-corolla species and the three long-corolla species as outcrossers and the rest as selfers) are mapped on the two hypothesized trees using equally weighted parsimony, the majority of ancestral nodes become equivocal. However, if the two characters (corolla size and flower color) are mapped independently, the most parsimonious explanation is that all five of the outcrossing species are independently derived from short-corolla selfing ancestors with blue flowers.
This illustrates the problem with ancestral reconstruction when more than one trait influences selfing rate. Since increased outcrossing can be achieved by many different mechanisms, the character states (outcrossing vs. selfing) may not be homologous. The problems of homology can be magnified when many taxa are included. For example, the Polemoniaceae includes a broad mix of selfing and outcrossing species, with outcrossing promoted by sporophytic self-incompatibility, herkogamy, and dichogamy (Grant and Grant, 1965
). In a phylogenetic study of mating-system evolution in the family, Barrett, Harder, and Worley (1996)
categorized the mating systems dichotomously as selfing or outcrossing primarily based on morphology. Phylogenetic relationships among 77 species were estimated using matK sequences. The authors concluded that the dead-end hypothesis seems to be supported because most of the selfers were on terminal branches, and there were no unequivocal transitions from selfers to outcrossers. In this case, it is worth investigating whether a different conclusion would be reached if the individual traits that promote outcrossing were separately mapped on the tree.
In the same study, Barrett, Harder, and Worley (1996)
noted a possibility that self-incompatibility (SI) may have arisen multiple times within the Polemoniaceae. This is based on observations of SI in several species scattered among eight genera in the family (Cobaea, Gilia, Ipomopsis, Loeselia, Linanthus, Leptodactylon, Phlox, Polemonium; discussed in Grant and Grant, 1965
, p. 160). While some species were confirmed to have genetic SI systems (Levin, 1993
; Goodwillie, 1997
), other species reported to be SI in Grant and Grant (1965)
may actually have reduced seed set because of high levels of inbreeding depression during seed maturation, rather than true SI (Charlesworth, 1985
; Krebs and Hancock, 1990
). For example, Gilia caruifolia is reported to be SI based on hand pollinations where 15 self-pollinated flowers set no seeds, whereas sibling crosses were fully fertile (Grant and Grant, 1965
, p. 69). Confirmation of multiple origins of SI in the Polemoniaceae will require a phylogenetic analysis including a finer scale taxonomic sampling of all lineages reported to include SI taxa. Nonetheless, this study demonstrates the phylogenetic scale necessary to examine change in complex mating systems. As discussed below, smaller scale studies examining genera or closely related species can generally only report the breakdown of complex genetic systems that promote outcrossing.
Studies involving gain or loss of complex mechanisms
In other studies, researchers have investigated the evolution of mating systems with discrete-state characters such as genetic self-incompatibility or heterostyly, where a complex suite of characters has evolved to prevent self-fertilization. It is generally assumed that complex traits are more readily lost than gained. This contrasts with the studies examined above, where there is no a priori expectation of bias toward either increase or decrease in stigma–anther distance or corolla length.
Several studies support the view that complex characters promoting increased outcrossing seem to have broken down frequently and that derived selfers are generally limited to terminal clades. For example, a phylogenetic analysis of the genus Amsinckia, based on chloroplast DNA restriction site variation, supports four independent origins of homostylous selfing species from heterostylous outcrossers when distyly was assumed to be ancestral or when the loss of distyly was assumed to be more likely than the gain (Schoen et al., 1997
). The determination of the ancestral mating system, and choice of an appropriate outgroup were major complicating factors in this study, as phylogenetic relationships in the Boraginaceae (outside Amsinckia) are unclear. Similarly, an ITS-based phylogeny of Linanthus section Leptosiphon suggests three to four independent origins of self-compatible lineages from sporophytic self-incompatibility progenitors (Goodwillie, 1999
).
Although these data appear to support the dead-end hypothesis, conclusions should be drawn cautiously. Studies of congeners or sections of genera are useful to estimate the number of times outcrossing was lost, but the gain of complex traits is less likely to be observed than their loss within a short period of evolutionary time. In a larger scale study, Kohn et al. (1996)
observed the origins of complex traits such as self-incompatibility and enantiostyly (a floral polymorphism in which flowers possess either left- or right-bending styles) in the family Pontederiaceae. Kohn et al. (1996)
also concluded that the breakdown of heterostyly appeared to be more frequent than its gain. As noted previously, a large scale study of Polemoniaceae suggested the possibility of several independent origins of SI (Barrett, Harder, and Worley, 1996
).
Although the studies of Pontederiaceae and Polemoniaceae demonstrated the possible evolution of characters that reduce selfing, these studies did not indicate that outcrossing species were derived from habitually selfing species. Thus overall, there has been no single study that unequivocally demonstrates the transition from highly selfing to outcrossing lineages. Possible exceptions are a study of Asarum (Aristolochiaceae) and a study of Medicago (Fabaceae). Kelly (1997)
suggested that in Asarum, herkogamy and other floral traits for insect–pollinator attraction may have evolved from within a predominantly autogamous group. However, this may not be an example of evolution of an outcrossing lineage from selfers because limited data indicated that the derived herkogamous species still undergo very little outcrossing (Kelly, 1997
). A molecular phylogeny of Medicago was estimated with combined sequences of external and internal transcribed spacer regions of nuclear ribosomal DNA (nrDNA) (Bena et al., 1998
). On the basis of published descriptions, 35 species were defined as annual selfers, 4 as perennial selfers and 8 as perennial outcrossers. The most parsimonious reconstruction suggests that annual habit and self-fertilization are the ancestral trait in Medicago, with outcrossing evolving twice from selfing and with one subsequent reversion to selfing. However, this reconstruction contradicts traditional morphology-based hypotheses of relationships in Medicago. Outcrossing species in the genus and some closely related taxa have elaborate floral mechanisms that promote outcrossing. In selfing species, the outcrossing mechanisms have degenerated or self-fertilization occurs before they are operational. Therefore, based on morphological comparisons, outcrossing was believed to be ancestral. A 6 : 1 weighting scheme favoring evolution from outcrossing to selfing was needed to force the original morphology-based hypothesis of mating-system evolution to map as expected on the nrDNA-based phylogeny (Bena et al., 1998
). With the 6 : 1 weighting scheme, selfing would have evolved nine times independently with no reversals. Regardless of the weighting scheme or associated phylogenetic pattern, the diversity of selfing species in Medicago suggests that selfers have been capable of extensive speciation.
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PROBLEMS ENCOUNTERED IN EXISTING STUDIES AND ALTERNATIVE METHODS OF ANALYSIS |
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), resulting in very different outcomes. Therefore, sensitivity analyses that explore various weighting schemes are useful in deriving a range of possible ancestral reconstructions from a given tree (Armbruster, 1992
; Omland, 1997
; Ree and Donoghue, 1998
). However, it may not be possible to draw a conclusive interpretation of the evolutionary history if the results are widely variable and the optimal weighting scheme is not known for the character, as observed in the Medicago study discussed above (Bena et al., 1998
). For some types of characters such as gain vs. loss of a restriction site (Albert, Mishler, and Chase, 1992
), it may be possible to determine optimal weighting schemes. However, universal weighting schemes are unlikely to be found for the evolution of mating systems (discussed in Omland, 1999
). Therefore, conclusions should not be based solely on ancestral reconstructions. Rather, in-depth knowledge of characters under study, including their functional morphology and genetic and developmental basis, is needed to choose the most probable reconstructions (Cunningham, Omland, and Oakley, 1998
). Nonetheless, sensitivity analyses or other posthoc tests should generally be performed to assess the robustness of conclusions (for examples of the methods and assumptions of posthoc hypothesis testing, see Armbruster, 1992, 1993
).
Uncertainties involved in ancestral state reconstructions
In addition to the difficulty of determining appropriate weighting schemes when using parsimony, most studies do not consider the statistical uncertainty of estimated ancestral states (Schluter, 1995
). All the studies reviewed here used maximum parsimony criteria to reconstruct the ancestral states and draw conclusions directly from the reconstructions. Comparison of parsimony results with a maximum likelihood (ML) approach developed to estimate ancestral states of discrete characters suggests that parsimony reconstructions deep in the tree can often produce uncertainty, especially when the rate of character change is high (Schluter et al., 1997
). Maximum likelihood approaches offer the advantage of considering reconstructions other than those based on an absolute minimum of state change because the ML method takes branch lengths into account while parsimony ignores them (Schluter et al., 1997
). The total number of state changes may generally be underestimated by parsimony (minimum change) reconstructions. These results suggest that caution should be used when testing evolutionary hypotheses with ancestral state reconstructions. Although both parsimony and ML ancestral reconstructions have limitations (discussed in Cunningham, Omland, and Oakley, 1998
), ML methods, along with parsimony, should be employed when evaluating rapidly evolving characters such as components of mating-system change.
Testing irreversibility using ancestral reconstructions
When ancestral state reconstructions are robust, they are useful for visualizing potential patterns of evolutionary history and provide information about the frequency of state changes and where changes occurred within a group of organisms. However, they do not provide clear-cut criteria for accepting or rejecting the dead-end hypothesis. Is one known reversal from selfing to outcrossing sufficient to reject the hypothesis? Can we accept the hypothesis based on the observations that most, if not all, transitions occur from outcrossing to selfing or that selfers are limited to terminal clades? Irreversibility, an essential component of the hypothesis, can be directly quantified by the transition bias, i.e., the relative probability of gain vs. loss of a character state (in this case selfing). Sanderson (1993)
developed a method of testing the irreversibility of character evolution by incorporating information about the frequency of state changes and where the changes occurred on the tree. For example, an ancestral reconstruction where selfing evolved once, deep in the tree, conveys stronger support for irreversibility than a tree where a selfing taxon is derived once in a terminal clade.
The transition bias in the estimated ancestral reconstruction can be tested with a likelihood ratio test (LRT) (Sanderson, 1993
). Likelihood ratio tests have been a useful tool to address many evolutionary questions in phylogenetic analyses (Huelsenbeck and Rannala, 1997
). For a given ancestral reconstruction, probabilities of gain or loss of a character are estimated using a model describing the transitions of a two-state character (0 or 1). The likelihood of a model where the probability of gain (
01) and probability of loss (01) are estimated separately is compared with the likelihood of a constrained model where these two probabilities are equal, 01 = 10. For a given ancestral reconstruction, the ratio of these two likelihoods can be used to reject the hypothesis of equal frequency of state change; a large difference in the two likelihoods means that the constrained model (01 = 10) does not fit to the data as well as the model with two parameters (01, 10), suggesting that the probability of gain is not equal to the probability of loss. This test appears to be useful to address the question of irreversibility in mating systems. However, the power of the LRT is very low when the evolution of a single character is studied (Sanderson, 1993
). Therefore, utility of the test may be limited.
Hypothesis testing without ancestral reconstructions
Sanderson's method discussed above requires ancestral reconstructions before the hypothesis testing and does not account for uncertainty in the reconstruction. To avoid this problem, a specific hypothesis may be addressed with Pagel's Markov transition-rate model for estimating the rate of change in dichotomous traits (Pagel, 1994, 1999
; Ree and Donoghue, 1999
). The procedure of hypothesis testing is similar to Sanderson's. The likelihood of a full model, where the rates of change to and from selfing are estimated, is compared to the likelihood from a constrained or null model. By comparing these two likelihoods, the null hypothesis can be rejected if a more complex model provides a better fit to the tree topology and character state data for extant taxa than the null model. Note that this test does not require any ancestral reconstructions of the character. The difference between Sanderson's (1993)
and Pagel's (1994, 1999)
models is that in Pagel's model the likelihoods are summed over the range of all possible sets of ancestral states (a phylogeny with N terminal taxa has 2N–1 possible sets), while Sanderson's method calculates a likelihood for a given single set of reconstructed ancestral states. In other words, Pagel's method estimates the rates of change given character states of the extant taxa while Sanderson's method makes an estimation given that reconstructed ancestral states at all nodes are known. Both methods assume that the estimated phylogenetic tree is true; that is, the uncertainty in the phylogenetic tree estimation is not considered.
For our purposes of testing irreversibility of mating-system evolution, the constrained or null model can be defined either as equiprobable transition to and from selfing (model A), or complete irreversibility of selfing, that is, the transition rate of selfers to outcrossers is restricted to zero (model B). These two tests address slightly different aspects of the dead-end hypothesis. Rejection of model A suggests some degree of irreversibility in mating-system evolution (i.e., biased transition probabilities to and from selfing). On the other hand, rejection of model B suggests that transition to selfing is not completely irreversible, and outcrossers may have derived from selfing lineage. However, failure to reject model B does not necessarily support the dead-end hypothesis (or complete irreversibility); the failure may simply indicate the low power of the statistical test due to limited amount of data (number of species), as is in any statistical hypothesis testing. A similar LRT was used to test for significant differences in the transition probabilities between hermaphroditism and other polymorphic breeding systems such as dioecy and gynodioecy in monocotyledons (Weiblen, Oyama, and Donoghue, 2000
).
Using the program Discrete 1.01a, we applied Pagel's method to the studies of mating-system evolution reviewed above (Table 1). In most studies, the branch lengths were not available, so branch lengths were assumed to be a unit length and tests were performed using only topological information. The effect of this assumption is discussed in Cunningham (1999)
. A 
2 approximation to the LRT or Monte Carlo simulations can be useful to judge whether the full model fits significantly better than the constrained, null model. Under the 2 approximation, the full model with one extra parameter is preferred over the simpler model when the difference in log-likelihoods (or improvement in fit) is half as large as the critical value for a 2 distribution with one degree of freedom. However, further justification of the approximation procedure is needed (Mooers and Schluter, 1999
), and we use the difference between log-likelihoods 
2.0 as a conservative value for judging whether the full model fits significantly better than the constrained, null model (Mooers and Schluter, 1999
). This criterion corresponds to a significance level of 
= 0.045 in a 2 approximation with 1 df. With this criterion, the studies of Polemoniaceae (and possibly the study of Linanthus, where Lfull – LA was 1.97) are the only cases where the full model with unequal transition rates fits significantly better than model A, where equiprobable transition to and from selfing is assumed. These results do not necessarily mean that the transition rates to and from selfing are equal. Rather it may suggest that for most data sets, the number of species used is too small to reliably estimate forward and backward transition rates simultaneously (Mooers and Schluter, 1999
). The full model requires estimation of an extra parameter compared with the constrained model, and consequently more data are needed to maintain accuracy. Therefore, we did not detect the improvement of fit in the full model with medium-sized trees.
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) in Scutellaria and Polemoniaceae are rather counterintuitive. For example, in Polemoniaceae, parsimony reconstruction suggested frequent evolution of selfing from outcrossing ancestors and no unambiguous instance of the reverse (Barrett, Harder, and Worley, 1996
). However, the estimated rate of transition from selfers to outcrossers ( = 1.21) is higher than the reverse (
= 0.70) (Table 1).
These counterintuitive results may be caused by a strong influence of the proportion of branch tips with selfing species (PS) on the transition rate estimates. Note that, in most cases, the values of PS are close to the ratios of the estimated transition rate, /( + ) (Table 1). State changes between outcrossing and selfing can be viewed as a first order Markov process, where the potential for change is determined by the present state. Under a continuous time Markov (or pure jump) process where the instantaneous transition rate from selfing to outcrossing is and the rate from outcrossing to selfing is ß, given sufficient time, the expected probability of being in the selfing state is /( + ß). Assuming that the evolution of mating system obeys this Markov process, if all species derived from a common ancestor evolved independently, forming a star phylogeny, the expected proportion of selfing clades (PS) in this star phylogeny would be /( + ß) after sufficient time. Therefore, our observation that /( + ) closely match PS may suggest that the ML estimators of transition rates are not very sensitive to the topological information of the phylogeny when a small- to medium-size phylogeny is analyzed. More detailed studies of the statistical nature of this procedure are needed.
As seen in our analysis, the LRT in its current implementation may have limited application to the question of irreversibility of mating system. One problem presently is that the scale of phylogenetic studies is too small to co-estimate both forward and backward transition rates. Furthermore, the statistical nature of this ML estimator needs to be explored in more detail.
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CONCLUSIONS |
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We did not discuss other components of the dead-end hypothesis in detail, such as differences in speciation or extinction rates between selfing and outcrossing species. Pagel (1997)
developed a LRT for the difference between speciation rates associated with discrete character states. This method may be useful in addressing the expected unequal speciation rates between selfing and outcrossing lineages. Differential extinction rates violate one assumption of the LRT employed here, i.e., that the character states themselves do not directly influence extinction rate. When selfing lineages go extinct more frequently than outcrossing lineages, the transition rate from outcrossing to selfing may be underestimated. This is because the transition will be undetected if the lineage goes extinct shortly after the transition to selfing. It may be theoretically possible to incorporate such differential extinction rates into the model; however, further complication of the model will result in a practically unusable method because the size of current data sets is generally not large enough to allow estimation of even two parameters.
Barrett (1995)
has pointed out that there are currently two distinct but complementary approaches in the field of mating-system evolution. First, using an extensive body of genetic theory, researchers have used manipulative experiments to test predictions and assumptions such as the characterization of inbreeding depression, male-siring strategy, and the quantitative genetics of floral traits influencing mating systems (reviewed in Wyatt, 1992
). For the past two decades, this approach has been very fruitful, increasing understanding of mating-system evolution. The second approach, reviewed in this paper, is to examine patterns of mating-system evolution by reconstructing the evolutionary history of plant reproductive traits associated with mating systems. Barrett (1995)
describes these two methods as micro- and macroevolutionary approaches and emphasizes the need for studies that use the macroevolutionary approach (also see Holsinger, 2000)
. It appears that phylogenetic studies of mating-system evolution in plants, while a promising avenue of research (see Weller and Sakai, 1999
), have not yet been successful in addressing the dead-end hypothesis. However, it seems likely that with data sets of appropriate resolution and improvements in objective data analyses, the macroevolutionary approach will yield fruitful results.
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FOOTNOTES |
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4 Author for correspondence, current address: Department of Biology, Box 90338, Duke University, Durham, North Carolina 27708-0338 USA. (ntakebay{at}duke.edu
).
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