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a Department of Botany, Department of Genetics and Cell Biology, Washington State University, Pullman, Washington 99164-4238
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Key Words: Claytonia virginica • fertility per flower • Portulacaceae • resource allocation • size and number trade-off
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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The explanations for low fertility per flower share assumptions, either stated or implied by the fitness maximization economy (Lloyd, 1985; Charnov, 1997), about trade-offs between net (male and female) fertility gain and reproductive allocation at flowering and fruiting (Smith and Fretwell, 1974; Lloyd, 1987; Morgan, 1993a). The essential assumptions, captured by sex allocation theory (Charnov, Maynard Smith, and Bull, 1976; Charnov, 1982) and summarized in Fig. 1, are: (1) an individual manufacturing more costly flowers can only do so by decreasing total flower number; and (2) the relationship between flower cost and net (male and female) fertility is sigmoid. The model is similar to Smith and Fretwell's (1974) classic explanation for offspring number, but includes fertility gain through both male and female functions, and accommodates separate (sequential) resource allocation decisions to flowering and fruiting (Morgan, 1993a). Analysis of the model shows that, perhaps surprisingly, flowering investments that result in less than complete fertility per flower maximize Darwinian (whole plant, male and female) fitness (Morgan, 1993a).
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Theoretical context
Figure 2 illustrates the assumptions and prediction to be evaluated here. The upper panel shows the assumption that plants possess limited resources for reproduction, so that there is a trade-off between the size and the number of flowers produced. In the figure flower number is inversely proportional to flower size. The middle panel shows the assumption that fertility increases in a sigmoid fashion with flower investment. Fertility gains of flowers above a critical size follow a power function with exponent less than one [e.g., fertility = (size - sizeminimum); 
< 1].
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The assumptions of the model of fertility per flower require testing at the within-population level. This is because the assumptions of trade-off and fertility gain, and the method of analysis (evolutionary stable strategy, or ESS, analysis), refer to constraints experienced by individual plants and comparisons of fertility within a single population. The predictions of the model are made at the population level, identifying how the relationship between population average allocation patterns and female fertility per flower changes in response to between-population differences in trade-offs and opportunities for fertility gain.
A previous theoretical study (Morgan, 1993a) assumed that "fertility per flower" corresponds to fruit set, but a second mechanism for changing fertility per flower is through regulation of seed production per flower. Plants may adjust fertility per flower through both mechanisms. Here, however, logistic considerations (discussed below) dictate that fruit per flower be used for testing assumptions within populations, while seed production per flower be used for evaluating between-population predictions.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Testing assumptions within populations
Two independent data sets are used to test assumptions and predictions of the model. The central assumptions are the trade-off between flower size and flower number arising because of limited resources available for reproduction, and the diminishing opportunities of female fertility gain associated with larger flower size. To test these assumptions, I identified two populations of C. virginica in old-growth forest at the McGill University research station, Mont St. Hilaire, Quebec. Approximately 100 individuals in each population were chosen arbitrarily from the plants flowering on 17 May 1994. The plants were marked and numbered using plastic bands obtained by cutting a spiral binding into individual loops.
Measures of overall plant size and of per flower resource investment were taken early in the flowering season. Plant size was measured as height (soil surface to inflorescence tip). The chronological sequence of the most recently opened flower was noted (e.g., second flower produced by the plant), and the width of the corolla of this flower was recorded as a measure of flower size.
Approximately 2 wk later, measures were made of plant size, total flower number, and the fraction of flowers producing fruits. Most plants in both populations were no longer producing flowers, and the flowers measured during the previous visit were in the latter stages of fruit maturation. Plant size was again measured as the height of the plant; this second measure of plant size differs from the first, because the inflorescence of C. virginica is partially indeterminate so that internodes and terminal buds expand over the period of flower production. As fruit maturation starts, flower production and inflorescence growth cease. This allows measurement of total inflorescence flower production and fraction of flowers retained as fruit.
Testing predictions between populations
The central prediction of the theory of size and number trade-offs is a positive correlation between population average flower size and population average fertility per flower. In the spring of 1992, I located 18 populations of C. virginica in the eastern central portion of Illinois, primarily in small woodlots in the vicinity of Urbana-Champaign. I chose ~30 plants haphazardly in each population, measuring the plant height and corolla diameter of the single open flower on the selected individual. I returned to the populations ~2 wk after the initial visit, to sample 30 different plants. At this point, I recorded a second measure of plant height, counting total flower production, and sampling the most mature fruit on each plant. These fruits were brought back to the laboratory, where the number of seeds (always 
6) were determined. The sampling strategy does not measure flowering and fruiting parameters on the same individuals, and uses seed set as a measure of fertility per flower. These methods allow more populations to be visited, and maximize statistical power for testing predictions between populations.
Statistical analysis
The form of statistical analysis is similar for tests of both assumptions and predictions. The model of trade-offs in size and number implicitly assumes that all individuals have the same amount of resource available for reproduction (see van Noordwijk and de Jong, 1986; Pease and Bull, 1988; Charlesworth, 1990; Houle, 1991). To accommodate variation in resource status present in the sample, I used measures of flower size, flower number, and female fertility that were corrected for overall plant size. In the test of assumptions, the corrected values were calculated as the residuals of independent analyses of variance using reproductive characters as the dependent variables and population of origin, plant size, and the interaction between population of origin and plant size as independnet variables. For testing predictions, residuals were calculated from regressions of population average reproductive characters on population average plant size. Using population means to test predictions is appropriate, since as outlined above predictions of the theory apply to between-population comparisons.
Tests of assumptions and predictions are simple linear regressions of the size-corrected measures of flower number and female fertility on flower size. In testing assumptions, the linear regression is not intended to evaluate the curvilinearity of the relationship required for evolutionary stability of hermaphroditism, but only the strength of selection acting on flower size. Alternative routes through statistical analysis (e.g., in the calculation of residuals, or use of weighted regression for population analysis) suggest themselves, but conclusions reached are identical qualitatively and very similar quantitatively to the results presented below.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Model assumptions met with mixed support (Fig. 3, upper and middle panels; compare with Fig. 2, upper and middle panels). The (size corrected) relationship between flower number and flower size is negative, but not statistically significant (P 
0.58). On the other hand, the association between fertility per flower and flower size is positive and statistically significant (P < 0.05), consistent with this model assumption.
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0.7, df = 1, 16, for measures of both flower diameter and fertility per flower).
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0.14). |
DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONREFERENCES |
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Self-fertilization
Claytonia virginica probably reproduces through partial self-fertilization, whereas the model of trade-offs in size and number assumes random mating. This difference may be unimportant, because the key components of the model rely on qualitative rather than quantitative description. For instance, self-fertilization changes the relative importance of the male and female transmission pathways (e.g., Lloyd, 1979), but since pollinator visits appear to be required for self-fertilization in C. virginica (Schemske, 1977) the assumption that female fertility increases with flower size (for instance through the effect of flower size on pollinator attraction) remains plausible. Variation in selfing rate associated with flower size might, however, influence the quantitative outcome of the model (Morgan, 1993b; although see Sakai, 1994). Estimates of the selfing rate and its association with flower size are not available. Regardless of the relationship between flower size and fertility, self-fertilization does not account for the absence of trade-off in size and number.
Pollen vs. resource limitation
A central assumption in the model of trade-offs in size and number is that resources limit opportunities for fertility gain, but it is not known whether C. virginica was pollen or resource limited in the populations used in this study. Empirical studies in other species find either resource or pollen limitation of female fertility (Young and Young, 1992; Burd, 1994). Such studies address limitation on an ecological time scale (e.g., over a single breeding season), but since a plant gains no fitness by having "excess" resources there is a strong argument for simultaneous resource and pollen limitation of fertility over evolutionarily relevant time periods (e.g., Levins, 1968; Charnov, 1982; Haig and Westoby, 1988). Nonetheless, a particularly favorable resource environment in the year of this study might account for the absence of observed trade-off between size and number. This would be consistent with a "bet-hedging" explanation for low fertility per flower, although bet hedging in this instance is based on resource status (Kozlowski and Stearns, 1989; Sakai, 1996) rather than pollinator availability. Evaluation of this hypothesis may be extremely difficult, because bet hedging may occur on a time scale spanning many years.
Perenniality
The major difference between the biology of C. virginica and the assumptions of the model of trade-offs in size and number is a perennial life cycle. Perenniality may represent a potential difficulty from theoretical and empirical perspectives. Zhang and Wang (1994; see also Charnov, Bull, and Mitchell-Olds, 1981; Kakehashi and Harada, 1987; Charnov, 1988; Olivieri, Couvet, and Slatkin, 1994) show that the common practice (also used in Morgan, 1993a) of separately analyzing "reproductive" (e.g., vegetative vs. reproductive) and "sex" (e.g., fruit vs. flower) allocation strategies is not always correct. For instance, plants with many large flowers may sacrifice future growth or survivorship; existing theory does not accommodate this possibility. Perenniality may explain the absence of trade-off between size and number observed in the present study.
Perenniality and indeterminate growth of C. virginica may mean that the distance from soil surface to inflorescence tip does not adequately characterize overall plant size. Perennials may use nutrients garnered the previous year and stored in underground organs for growth in the present year, suggesting that measurement of such underground storage organs may be appropriate. Unfortunately, many different measures of underground storage could be obtained (e.g., overall size, carbon or nutrient content) and there is no a priori guidance as to which, if any, of these measures truly assess "plant size." Identifying an appropriate measure of resource status represents a general problem of sex allocation and life history studies (Pease and Bull, 1988; Houle, 1991; Fry, 1993). Using plant height is no worse than measuring underground storage organs or other plant attributes, but because it represents the use (rather than storage) of resources it may better integrate the resource status of the plant into a single phytometric reading (Silvertown, 1982, p. 169).
The indeterminate inflorescences of C. virginica may mean that measures of plant size correlate more closely with number of flowers per plant or flower size than a true measure of size might warrant. This may reduce variation in residual flower size and number, limiting statistical power to reject the null hypothesis of no association between flower size and number and contributing to the absence of statistical significance shown in the upper panel of Fig. 3. The measure of plant size used here is therefore statistically conservative. Such conservativeness represents a strong point when analyses reject the null hypothesis, but it is unclear whether the result in the present instance is due to the measure of plant size or absence of trade-off between size and number.
Statistical power
Failure to detect statistically significant results is sometimes attributable to absence of biologically meaningful statistical power. Sample sizes for the within-population tests of assumptions are large and sufficient to detect a positive association between fertility per flower and flower size. Testing the between-population prediction involves a smaller sample size (18 populations), but each point represents a well-characterized population mean rather than a single observation. In addition, sample sizes are sufficient to detect significant between-population variation in measured parameters (Table 1). These observations suggest that the data contain at least moderate statistical power and reflect biologically meaningful variation. While larger samples increase power of statistical tests, results of the present study are likely to be robust to moderate increases in sampling effort.
Conclusions
The results presented here offer insight into paradoxically low female fertility per flower often observed in hermaphroditic flowering plants. Claytonia virginica does not exhibit a trade-off between flower size and flower number at the within-population level, a result that is at odds with assumptions underlying the theoretical description of fertility per flower. Resource uncertainty or perenniality may explain the discrepancy, although both explanations require further empirical and theoretical research. The present study shows that sex allocation theories are amenable to testing at the between-population level. This approach is underemployed in sex allocation studies, which often focus on the difficult task of estimating "gain curve" parameters.
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FOOTNOTES |
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