Frequency-Dependent Inbreeding Depression in Amsinckia

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1 vol. 16, no. 6 the american naturalist december 003 Frequency-Dependent Inbreeding Depression in Amsinckia Pierre-Olivier Cheptou * and Daniel J. Schoen Department of Biology, McGill University, 105 Dr. Penfield Avenue, Montreal, Quebec H3A 1B1, Canada Submitted September 3, 00; Accepted June 10, 003; Electronically published December 19, 003 abstract: If the competitive ability of plants produced by selfpollination differs from that of plants derived by outcrossing, then the magnitude of inbreeding depression may be influenced by the composition of the competitive environment (i.e., the frequency of plants that have arisen from selfing and outcrossing in the neighborhood of target plants in which inbreeding depression is expressed). Here, we report the results of experiments designed to examine whether inbreeding depression is influenced by the frequency of inbred plants in the competitive neighborhood. Two species of the annual plant genus Amsinckia were studied, one a nearcomplete selfer (Amsinckia gloriosa) and the other a partial outcrosser (Amsinckia douglasiana). Competition experiments were conducted in artificial stands composed of different mixtures of inbred and outbred progeny. The fitnesses of progeny were found to be significantly influenced by the composition of the competing neighborhood. The fitness of target plants, however, did not vary monotonically with the frequency of inbred plants in the neighborhood. Rather, for A. gloriosa, maximum performance was observed when there was an intermediate frequency of inbred neighbors. For A. douglasiana, the opposite pattern was found. The results suggest that competition among progeny has the potential to play a role in the selection of self-fertilization and possibly in the maintenance of mixed mating systems. Keywords: self-pollination, competition, mating system evolution. Individual fitness is a fundamental parameter in population dynamics. It is a property of the individual s genetic makeup and also its physical and biotic environment (Heino et al. 1998). In natural populations, one important aspect of the biotic environment arises from interactions * Present address: Centre d Ecologie Fonctionnelle et Evolutive, Centre National de la Recherche Scientifique, 1919 Route de Mende, F-3493 Montpellier Cedex 05, France; cheptou@cefe.cnrs-mop.fr. dan.schoen@mcgill.ca. Am. Nat Vol. 16, pp by The University of Chicago /003/ $ All rights reserved. with conspecifics, particularly competition for limiting resources. Consequently, meaningful measures of fitness may need to take into account competitive interactions among neighboring plants as well as the density- and frequencydependent effects that arise from such interactions (Brommer 000). Many hermaphroditic plants have the potential to produce progeny through self-fertilization and outcrossing. Individuals produced by selfing often exhibit a reduction in fitness (i.e., inbreeding depression). A number of empirical studies have investigated the magnitude of inbreeding depression as assessed through measurements of components of fitness such as survival and fecundity. This is typically done using isolated plants grown in the greenhouse or growth chamber (Husband and Schemske 1996). The reasons for conducting such studies include learning about the genetic basis of inbreeding depression (Byers and Waller 1999) and how inbreeding depression acts to oppose the selection of selfing (Lloyd 1979). Despite findings from experiments with Drosophila that demonstrate that competitive ability may be strongly influenced by inbreeding (Lynch and Walsh 1998), only a few studies of inbreeding depression have explicitly addressed the contribution of the competitive environment (Schmitt and Ehrhardt 1990; Cheptou 001). If inbreeding influences competitive ability, then it follows that inbreeding depression itself may vary depending on whether the competing individuals are outbred or inbred. This aspect of the biotic competitive environment is expected to be a function of the population s selfing rate. While some studies have recognized that ecological determinants may modify the effect of inbreeding on fitness (Uyenoyama et al. 1993; Pray et al. 1994), the interplay between the population selfing rate, inbreeding depression, and the influence of intraspecific interactions has not been intentively studied. Cheptou and Dieckmann (00) proposed a phenotypic model that explicitly considered density regulation in a population with partial selfing. They showed that when the competitive abilities of inbred and outbred progeny differ, inbreeding depression is modified by the frequency of inbred plants, and therefore, the population s selfing rate itself influences (or feeds back on) the evolution of selfing. In demographically stable pop-

2 Selfing and Frequency-Dependent Fitness 745 ulations, Cheptou and Dieckmann s model suggests that the functional relationship between inbreeding depression and the frequency of inbred plants is sufficient for predicting the evolution of selfing. Moreover, when inbreeding depression increases with the proportion of selfed plants, their model suggests that (under a broad range of population densities) a stable mixed selfing system can be maintained. This article reports the results of experiments designed to determine how fitnesses of progeny derived from selfing and outcrossing are influenced by the frequency of inbred and outbred plants in the competing neighborhood. Two related species of the genus Amsinckia (Boraginaceae) with contrasting mating systems were studied. The principal aim was to determine whether the potential exists for the population s selfing rate (through its influence on inbreeding depression) to produce the hypothetical feedback effect on evolution of the mating system, as envisioned by Cheptou and Dieckmann (00). To address this question, we studied the relationship between inbreeding depression and the frequency of inbred plants in the competitive environment. To our knowledge, the experiment reported here is the first attempt to address this relationship in either artificial or natural populations. Material and Methods Study Populations Amsinckia (Boraginaceae) is a genus of annual plant species centered in western North America. Populations of the species often consist of large, dense stands of several thousand individuals. The group exhibits striking floral morphological variation, with heterostyly and homostyly found among closely related pairs of species (e.g., Amsinckia douglasiana and Amsinckia gloriosa) as well as among varieties within single species (e.g., Amsinckia spectabilis; Ray and Chisaki 1957; Schoen et al. 1997). Selfing rates are highly variable among taxa, ranging from predominantly outcrossing in several heterostylous taxa to near-complete selfing in several homostylous taxa (Johnston and Schoen 1996; Schoen et al. 1997). The evolution of self-fertilization may have occurred independently in at least four separate lineages within the genus (Schoen et al. 1997). Two species were studied: A. douglasiana, which is heterostylous and predominantly outcrossing, and A. gloriosa, which is homostylous and predominantly selfing. While A. gloriosa is an allotetraploid sister taxon of A. douglasiana, segregation analyses of allozyme loci suggest that it has a disomic mode of inheritance (Johnston and Schoen 1996). The populations occur together in Palomo Creek Canyon in Monterrey County, California, and the materials studied here derive from collections described by Johnston and Schoen (1996). Johnston and Schoen (1996) used progeny array analysis to estimate natural selfing rates in these populations as 0.5 (95% confidence interval [CI] ) for A. douglasiana and 0.99 (95% CI ) for A. gloriosa. That there is some selfing in A. douglasiana is likely to be connected with the fact that heterostyly in this species not coupled with self- or intramorph sterility. Earlier experiments conducted under noncompetitive conditions with these same populations yielded low estimates of inbreeding depression ( d 0.1; Johnston and Schoen 1996). Controlled Pollinations and Determination of Seed Weights Seventy-five seeds of A. douglasiana and 85 seeds of A. gloriosa, each produced originally by separate plants in natural populations, were sown in growth chambers in the McGill University Phytotron. For A. douglasiana, controlled pollinations were conducted using emasculated flowers by brushing either self or outcross pollen from a single anther across the stigmatic surface. For A. gloriosa, selfed seeds were obtained by leaving a proportion of the flowers on each plant intact and later collecting the seeds produced. Outcrossed seeds were obtained by emasculating flowers in bud and brushing pollen across the stigma as described above. When flowers were emasculated but no pollen was added, no seeds were produced. For both species, the pollen donor for outcrossing was chosen at random from the population sample. Seed weights were estimated by weighing a random sample of seeds per cross. Experimental Design for Frequency-Dependent Fitness Measurements To analyze the effect of interactions between inbred and outbred progeny on fitness, plants were grown at constant densities (310 plants/m ) but with varying frequencies of inbred and outbred neighbors. This density was determined empirically in a preliminary experiment designed to establish the density at which two neighboring rosettes overlap and compete for light at the time when plants begin to flower and, moreover, is characteristic of densities observed in natural populations. The same planting design (used with both species) consisted of dividing plants into two groups: targets (the measured plants) and neighbors (the nonmeasured plants). Each target was surrounded by six neighbors arrayed in a hexagonal pattern (fig. 1a). Several types of competition stands were created, each one by planting 0 target plants and 58 neighbors. Frequency of inbred neighboring plants

3 746 The American Naturalist Figure 1: Design of the competition experiments. a, Stands were composed of 0 target plants, each at the center of a hexagon of neighboring plants (58 total). Plants derived from selfing denoted by open circles, and plants derived from outcrossing denoted by filled circles. b, Five different stand types were employed. The target individual (gray) was surrounded by six nonmeasured neighbors. Stands differed from one another by varying the frequency of inbred neighbors from zero inbred/six total, two inbred/six total, three inbred/six total, four inbred/six total, and six inbred/six total. was modified among types of competition stands by varying the number of inbred neighbors per hexagon (fig. 1b). A stand type was characterized by one of five inbred neighbor frequency treatments: zero inbred and six outbred, two inbred and four outbred, three inbred and three outbred, four inbred and two outbred, and six inbred and zero outbred. The five stand types were placed in a single growth chamber, with a second replicate set of five placed in a separate growth chamber. The stands were each grown in 68.5 # 46 # 16-cm containers filled with 48 L of 3 : 1 sand to black earth. The distance between plants was kept constant at 6. cm. All seeds in a single chamber were sown on one day. Growth chambers are thus treated as replicate blocks in the data analysis. This design has several apparent disadvantages. For instance, there is the possibility that two targets may influence one another though indirect competition effects with their shared neighbors. As well, this design requires many plants to create the different experimental units. There are, nevertheless, several compelling reasons for choosing this design. First, an alternative design, employing a single target plant per pot with each type of pot having a different frequency of inbred plants, failed in an earlier pilot study to produce competition sufficient to impose an effect on the target the neighbor plants tended to grow over the edge of the pot, thereby exerting little competitive influence on the target. Second, despite the possibility for interactions among targets, the relatively large plantings used in the experiments mimic the sorts of conditions that plants in natural stands would also encounter, that is, where higher order competitive interactions could also potentially occur. To produce target plants, 10 randomly chosen maternal parent families were used as sources of seed. Planting position was assigned randomly for each family. Likewise, the maternal parents used to provide the neighboring plants (selfed or outcrossed) were selected at random. The random sampling of seed together with the large number of families available meant that the probability of two neighbors belonging to the same family was negligible.

4 Selfing and Frequency-Dependent Fitness 747 Table 1: ANCOVA for competition experiments with Amsinckia douglasiana Source of variation df Mean leaf length (7 d) Type III SS F P Rosette size (14 d) Type III SS F P Final dried biomass Type III SS F P No. flowers Type III SS F P Frequency (linear term) , , !.0001 Frequency (quadratic term) , ! ,91 9.8!.0001 Block , ! , !.0001 Family , , Cross , , Family # cross , , Residual, ,843, ,81 Note: For random factors, family is tested with family # cross interactions, and family # cross is tested with the residual error. This reduces the chance that sib competition is a significant source of variation in target plant performance. The growth chambers were maintained in the dark at 4 C for the first week. Following that, the temperature was maintained at 0 C under a 14L : 10D cycle until the end of the life cycle (8 wk later). Seed germination was synchronous, so that variation in germination time was not considered to contribute to variation in performance. When seeds did not germinate (approximately 8%), additional (replacement) seedlings were planted in the same growth chamber from a pool of seedlings derived from seeds sown at the same date. Stands were rotated randomly every week within the growth chamber. Fitness Component Measures Two indirect (nondestructive) estimates of the biomass were made at two stages before the plants flowered. Digital photos of seedlings were taken 1 wk after germination (when four leaves per plants were present) and analyzed by calculating the mean leaf length at 7 d. Two weeks after germination, the number of leaves and the mean diameter of the rosettes were determined and the product (number of leaves # mean diameter) was used to estimate the ro- sette size at 14 d. At the end of the life cycle, the final dried aboveground biomass and the number of flowers were determined. Statistical Analysis The effect of cross type (i.e., self vs. outcross) on seed mass was analyzed using a mixed model ANOVA (SAS 1990), with cross type as a fixed factor and maternal plant as a random factor. Statistical analysis of the four measures of fitness was carried out using the generalized linear model (SAS GLM procedure; SAS Institute 1990) with Type III sums of square. Three categorical factors were included in the model: block, family, and cross. Family and the family # cross interaction were treated as random effects and tested with the appropriate error structure (tables 1, ), whereas the block and cross were treated as fixed effects. The frequency of inbred neighbors, an ordinal treatment in the experiments, was treated as a covariate. Since the effect of frequency was found to be nonlinear, it was characterized using both linear and quadratic terms. Thus, the model was Y p freq freq block cross family family # cross error term. Error was assumed to be normally distributed. The quadratic and the linear terms were fitted using the stepwise procedure; that is, fitting the largest polynomial functions (Zar 1996). When the quadratic term was nonsignificant, it was removed from the model. To determine whether the effect of frequency differed between cross types, we checked whether the slope of the quadratic and the linear terms differed significantly between the two types of crosses. This was done by introducing a term for interaction between the covariate and cross (SAS Institute 1990). When this interaction term was nonsignificant (i.e., when slopes were similar for both cross type) it was removed from the model. When the interaction term was significant, the slopes were estimated separately for each cross type. Results Seed Weights and Germination In Amsinckia douglasiana, mean seed weight following cross-fertilization was # 10 g ( SE p 0.97 # 10 ),

5 748 The American Naturalist Table : ANCOVA for competition experiment with Amsinckia gloriosa Source of variation df Mean leaf length (7 d) Type III SS F P Rosette size (14 d) Type III SS F P Final dried biomass Type III SS F P No. flowers Type III SS F P Frequency (linear term) , , Frequency (quadratic term) , Block ! , , Family , , Cross , Family # cross , , Slope heterogeneity freq # cross Residual 1, ,799, ,351.1 Note: For random factors, family is tested with family # cross interactions, and family # cross is tested with the residual error. whereas following selfing it was 30.9 # 10 g ( SE p 0.7 # 10, F p 1.84, df p 1, 101, P!.0001), with a significant maternal parent effect. For Amsinckia gloriosa, the opposite result was found, with mean seed weight following cross-fertilization of 36.9 # 10 g ( SE p 0.64 # 10 ), and following selfing of 4.38 # 10 g ( SE p 0.58 # 10, F p 48.88, df p 1, 131, P!.0001), again with a significant maternal parent effect. The germination rate for A. gloriosa was 99% for selfed seed and 88% for outcrossed seed. For A. douglasiana, 88% seed produced by selfing germinated versus 95% of seed produced by outcrossing. There was no effect on germination of the neighbor frequency treatment. Four Fitness Measures The assumptions of normality of the residuals and homocedasticity of the data were checked for each fitness measure. Homocedasticity was fulfilled, but the residuals for the number of flowers in A. douglasiana deviated slightly from normality. General linear model-based analyses are, however, known to be robust to the violation of this assumption, and the slight departure from normality should not affect the conclusions (Sokal and Rolf 1995). For A. douglasiana, analysis of mean leaf length at 7 d showed that seedlings derived from selfing were significantly smaller than those from outcrossing (table 1; fig. ). While the effect was small, the frequency of inbred neighbors significantly influenced mean leaf length at 7 d, and there was a significant positive quadratic term (table 1). Thus, the poorest performance occurred at an intermediate frequency of inbred neighbors. Neither the block nor the family and family # cross interaction were significant for mean leaf length at 7 d (table 1). The three others fitness measures (rosette size, final dried biomass, and number of flowers) showed a similar pattern (table 1). The effect of frequency of selfed neighbors was significant for both the linear and quadratic terms (table 1; fig. ), as was the effect of cross type. The block effect was also significant, suggesting environmental heterogeneity among growth chambers. The family effect as well as the family # cross interactions were not significant. For all four fitness measures, the effect of frequency of inbred neighbors did not differ between the cross types (i.e., there was no interaction between the frequency treatment and cross type). Analysis of mean leaf length at 7 d in the A. gloriosa indicated that inbred seedlings were significantly larger than outbred seedlings (table ; fig. ). The quadratic effect of neighbor frequency was nonsignificant and was removed from the analysis. The linear effect, however, was highly significant (table ), indicating that performance decreased with the frequency of inbred competitors. The block effect was significant, but neither family nor the family # cross interaction were significant (table ). Rosette size at 14 d showed the same trend (fig. ), but the effect of cross was nonsignificant (table ), while the family effect was significant (table ). Contrary to what was observed with A. douglasiana, the two late lifecycle fitness measures did not consistently show the same pattern as the earlier measures. In the case of final dried biomass, the slope of the quadratic effect associated with frequency of selfed neighbors differed for progeny derived from selfing versus progeny from outcrossing (sig- nificant freq # cross interaction, table ), and so two separate regression coefficients for the quadratic term (both negative) were estimated. Progeny from selfing were larger than progeny from outcrossing in neighbor-

6 Figure : Means and SE of fitness measures as a function of frequency of inbred neighbors, as calculated from the linear model (see text). Solid lines represent progeny from outcrossing. Dotted lines represent progeny from selfing. Left, Amsinckia douglasiana; right, Amsinckia gloriosa.

7 750 The American Naturalist hoods with low frequencies of inbred individuals, whereas progeny from outcrossing were larger than progeny from selfing in neighborhoods with high frequencies of inbred individuals (fig. ). The effect of block was significant, as was the effect of family. Neither cross, nor family # cross effects, were significant. The number of flowers produced per plant showed the same pattern as that of final dried biomass, but the effect of frequency on each cross type was statistically indistinguishable. Both covariables were significant, and the quadratic coefficient was negative, resulting in a maximum at intermediate frequencies of inbred neighbors. The family effect was highly significant, as was the block effect (table ). Again, neither cross nor family # cross interaction were significant. Discussion The primary aim of this study was to investigate how fitnesses of progeny arising from selfing and outcrossing are influenced by local competition across a range of frequencies of inbred and outbred neighbors. For both species of Amsinckia, our results show that fitnesses are significantly influenced by the frequency of inbred and outbred competitors in the local neighborhood. These results suggest that there is a potential for the population selfing rate, through its influence on the composition of the population, to modify individual fitnesses and thereby inbreeding depression. The nature of this effect and its possible significance to the evolution of selfing is discussed below. The Nature of Competitive Interactions in the Amsinckia Experiments Several models have been proposed to account for competitive interactions between different types of individuals (Bulmer 1994; Law and Watkinson 1987). The simplest ones assume two types of individuals that differ in their competitive abilities. If the effects of increasing the number of a neighboring individual of either type are additive, this should lead to a linear relationship between fitness of the target and neighbor frequency. If the effects are nonadditive but the change in frequency of a given type of neighbor either always increases or always decreases target fitness, a monotonic relationship between fitness and frequency is expected (Cheptou and Dieckmann 00). Thus, for example, if outbred plants are consistently better competitors than inbred plants, then as the frequency of inbred neighbors is decreased in the neighborhood of the target plants, monotonically decreasing performance of the targets is expected. This pattern, however, was not generally seen for either species. Instead, in Amsinckia douglasiana, fitness measures for the targets were larger when there were either low or high frequencies of inbred neighbors but reduced when inbred neighbors were present at intermediate frequencies. In Amsinckia gloriosa, on the other hand, final dried biomass and number of flowers were reduced at both low and high frequencies of inbred neighbors but maximal with intermediate frequencies. The biological basis of these results is unclear, though several factors may be involved. In the case of A. gloriosa, the nonmonotonic pattern of fitness change observed for both final biomass and number of flower could have arisen from a combination of dominance and suppression initiated early in life, coupled with inbreeding depression that become pronounced later in life (Husband and Schemske 1996). More specifically, because inbred seeds in this species are heavier than outbred seeds, the inbred neighbor seedlings may have had stronger early competitive abilities than outbred seedlings such that when the target had predominantly inbred neighbors, it became competitively suppressed in the later life-cycle stages. These early suppressive effects would be less pronounced when targets are surrounded by outbred neighbors. As well, if inbreeding depression is expressed primarily at later life-cycle stages, as observed by Johnston and Schoen (1996) in this species, then outbred neighbor plants would have exhibited increasingly stronger competitive ability in the later life-cycle stages (compared with inbred neighbors), and this could have led to low fitness in the case of targets surrounded predominantly by outbred plants. With both effects operating, the expected pattern is maximal target performance at intermediate frequencies of inbred neighbors, as observed. Dominance and suppression has been invoked to explain variation in inbreeding depression in other species (Schmitt et al. 1987; Cheptou et al. 001). A confounding factor that cannot be dismissed is the possibility that floral manipulation associated with the outcross pollination treatment resulted in damage to the developing outcrossed seed, though it may be noted that reduced seed weight of outcrossed compared with selfed seed has been reported in other studies (McCall et al. 1991). The pattern of target fitness variation observed in A. douglasiana, while also nonmonotonic, is qualitatively the reverse of that observed in A. gloriosa. That target plants performed best in the case where all neighbors were inbred is consistent with the expectation that progeny expressing inbreeding depression should be the poorest competitors. But the minimum performances at intermediate frequencies cannot be easily accounted for. Such patterns have been predicted under certain conditions in De Witt competition experiments, for example, when both types have detrimental influences on each other. Also, when one type of individual is a better competitor for the resource that limits the other, this results in lower performances in mixture (Braakhekke 1980). While other studies of competition between inbred

8 Selfing and Frequency-Dependent Fitness 751 and outbred progeny have yet to be conducted, Smith-Gill and Gill (1978) also found that competitive abilities of species vary with the relative proportion of competing types, a result that is qualitatively similar to our own findings (see also Law and Watkinson 1987). The Potential Significance of Frequency-Dependent Fitness Variation to the Evolution of Selfing Cheptou and Dieckmann (00) have shown that at equilibrium population density, inbred neighbor frequency, through its effect on inbreeding depression, may contribute to the evolution of the mating systems. As an illustration of how this approach may be applied to empirical findings that suggest a relationship between inbreeding depression and the population selfing rate, we can use the results for number of flowers (lifetime flower production). Because of the possibility of experimental artifacts (e.g., floral manipulation effects on seed size), it is important to note that conclusions drawn in the case of mating system evolution in Amsinckia must be viewed as preliminary. We present the analysis here mainly to illustrate the potential consequences of frequency-dependent inbreeding depression. We note that fitnesses of inbred and outbred target plants may be expressed as a function of relative frequency f of inbred neighbors: w inbred(f ) p af bf c, (1a) w outbred(f ) p af bf c, (1b) where a(a, b(b and c(c are the polynomial coefficients of inbred (outbred) fitness functions and f is the frequency of inbred neighbors (as in the experiments described above). As in the case of studies of the selection of selfing, we assume that a rare morph, with rate of selffertilization r, appears in an infinite population with selfing rate R (Lloyd 1979). Because of its rarity, the contribution of the rare morph to the pool of outcrossing pollen is proportional to its own frequency and the fraction of ovules available for outcrossing ( 1 R). In a large, unstructured population, the progeny of this rare morph will compete with progeny produced by the dominant reproductive strategy R the nature of competitive interactions and their effect on fitness is determined by the frequency of the dominant strategy R. Following Lloyd (1979), the fitness of the rare morph is ( ) 1 r 1 R Wr, ( R) p rwinbred ( R ) woutbred ( R ). () To convert the frequency of inbred neighbors (f ), as used in the experiments outlined above, to the proportion of plants arising from selfing in the natural population (with selfing rate R), one must take into account the frequency of all inbred plants in the population (i.e., targets plus neighbors). In these experiments there were 58 neighbors, 10 inbred targets, and 10 outbred targets per each stand, which yields the conversion formula R p (58f 10)/78. Contrary to the classical model (fitness independent of the population selfing rate), this model does not necessarily predict the evolution of complete outcrossing or complete selfing. Rather, mixed selfing rate can evolve under the condition that w inbred(r) p 0.5w outbred(r). An evo- lutionary stable selfing rate is predicted if inbreeding depression increases in the vicinity of R (app. A). When applied to the results obtained with A. gloriosa, we find that winbred 1 0.5woutbred regardless of the frequency of inbred neighbors. Thus, if the empirical results reflect the situation in nature, the model predicts that this species should be self-fertilizing, a prediction that in fact agrees with high rate of selfing seen estimated in this species. For the A. douglasiana data, the observed fitness curves, if applied to this model, would predict two population selfing rates ( R1 p 0.4 and R p 0.63), but only R1 p 0.4 is an evolutionary stable mixed selfing rate (app. A). The stability of the mixed selfing R1 p 0.4 arises from the fact that inbreeding depression increases as R changes from 0 to 0.6. In this large range, natural selection tends to stabilize population selfing rate at R 1. It is important to note that the predicted selfing rate is sensitive to changes in the shape of the fitness curves. For instance, if higher mortality rates occur with an increase in overall population density, the predicted selfing rate would also probably change. Interestingly, the predicted stable selfing rate is consistent with the selfing rate measured in this population, whereas estimates of inbreeding depression made earlier in the absence of competition (Johnston and Schoen 1996) were, according to classical theory, too low to prevent the evolution of complete selfing in this species. Be- cause R p 0.63 is unstable, the model predicts that complete selfing would have evolved if the initial population selfing rate were higher than R p 0.63, which is not the case for the studied population. The major finding of this study is that the fitnesses of plants arising from selfing and outcrossing can not be characterized independently of the proportion of inbred and outbred plants in the population, and thus, the population selfing rate has potential to influence both the expression of inbreeding depression and the way in which selfing evolves. Frequency-dependent effects on mating system evolution arising from ecological aspects of mating system variation have also been reported in the case of the pollination system (i.e., frequency-dependent pollen discounting; Chang and Rausher 1998). The perspective

9 75 The American Naturalist that population ecological factors may contribute to inbreeding depression contrasts with the classical view that inbreeding depression reflects only genetical factors (e.g., as determined by mutation-selection balance). Clearly, the genetical perspective is important the potential for increased selfing to lead to purging of deleterious alleles can have important consequences on mating system evolution, and studies aimed at understanding mating system evolution would benefit from combining the study of both the genetic and ecological consequences that may arise from changes in the mating system. Acknowledgments We wish to thank I. Lessard for the quality of work she did with the experimental crosses. We also thank M. Johnston and M. Morgan for advice and criticism. C. Eckert made helpful comments that greatly improved the manuscript. This work was supported by a scholarship from the Government of Quebec to P.-O.C. and by a research grant from the Natural Science and Engineering Research Council of Canada to D.J.S. This article is dedicated to the memory of Paul Cheptou. APPENDIX A Unique Stable Mixed Selfing Rate under Two-Order Polynomial Fitness Function The evolutionarily stable mixed selfing rate is found when the selection gradient vanishes (Maynard Smith 198; Geritz et al. 1997): F W(r, R) g(r ) p p winbred ( R ) 0.5woutbred ( R ) p 0. (A1) r rprpr Assuming second-order polynomial functions for w inbred and w outbred, ( ) winbred R p ar br c, woutbred ( R) p ar br c. The two candidates for intermediate selfing rates are the roots of equation (A1): 0.5b 0.5b 0.5 ( b 0.5b 4 ( a 0.5a ( c 0.5c R1 p a 0.5a 0.5b 0.5b 0.5 ( b 0.5b 4 ( a 0.5a ( c 0.5c, R p for a 0.5a ( 0. a 0.5a The strategy is convergence stable (attainable) provided that the selection gradient decreases with R in al. 1997), that is, dg ( R) dr dg ( R) F RpR F dr RpR 1 dg ( R) F dr RpR p b ar 0.5 ( b ar )! 0, ( ( ( R (Geritz et p b 0.5b 4 a 0.5a c 0.5c, (A) ( ( ( p b 0.5b 4 a 0.5a c 0.5c. The two quantities have opposite signs, but only the first one satisfies the convergence criteria. R 1 is then the unique stable mixed selfing rate. For Amsinckia douglasiana, the fitness curves (after applying the equation for conversion of f to R; see text) are

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