Application of Charnov ’ s model to two hypothetical species with pollen – ovule ratios of 10,000 and 1000 and seed sizes of 1000 and 100, respectively. The scheme illustrates the assumptions and consequences of the model. See text for further details. Note that the intercept is arbitrary in this example. 

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... pollen–ovule ratio is an important floral trait that reflects the mating system of a plant (e.g. Cruden, 1977; Preston, 1986; Bennett, 2001; Bosch et al ., 2001; Jürgens et al ., 2002) (following Neal and Anderson (2005), we will use the term ‘mating system’ instead of ‘breeding system’ throughout this article). Cruden (1977) was the first to observe that outbreeding plants tend to have higher pollen–ovule ratios. He explained this finding by the ‘efficiency of pollin- ation’: self-pollinating plants (i.e. autogamous mating system) need less pollen grains for efficient pollination than plants dependent on agents such as wind or animals for pollination (i.e. xenogamous mating system). Charnov (1982) criticized this view for its bias towards seeds as the means to gain fitness (i.e. that the pollen only serves as a means to maximize seed set in a plant). He proposed that seeds and pollen should be equivalent means towards fitness gain. The model he developed based on sex allocation theory hypothe- sizes an isometric negative relationship between the log pollen – ovule ratio and log pollen grain size, and an isometric positive relationship between the log pollen – ovule ratio and log seed size. For the former relationship, he presented a regression analysis of data from Cruden and Millerward (1981) to support his hypothesis. In contrast, Gallardo et al. (1994) found no relationship between pollen – ovule ratio and pollen grain size but held inaccuracy in Charnov ’ s model responsible for this result. When controlling for additional factors in the model, an increase in the pollen – ovule ratio did indeed coincide with a decrease in pollen size. Both hypothesized relationships received support based on theoretical consider- ations (Queller, 1984) . Also, support for the hypothesized positive relationship between seed size and the pollen – ovule ratio has previously been reported by several authors (Uma Shaanker and Ganeshaiah, 1984; Preston, 1986; Mione and Anderson, 1992; Lopez et al. , 2000; Bosch et al. , 2001) . However, these studies were conducted within the taxonomical limitations of single families (Brassicaceae), tribes (Delphinieae, Genisteae), or genera ( Phyllantus, Solanum ). To test the general applicability of Charnov ’ s model, a broad taxonomic range of species needs to be analysed. Furthermore, the phylogenetic relationship of the studied species should be accounted for because closely related species are likely to have similar phenotypes and data across species are therefore not independent (Felsenstein, 1985; Harvey and Pagel, 1991) . In the present study, we included nearly 300 species of the German flora, belonging to 45 families. The phylogenetic relatedness was incorporated by using phylogenetically independent contrasts (Harvey and Pagel, 1991) . The main objectives were: (1) to test the validity of Charnov ’ s model by conducting a comparative analysis on the relationship between seed size and the pollen – ovule ratio, and (2) to evaluate if this relationship is different among various mating systems and taxa (families). Charnov ’ s model (Fig. 1) is simplified, as it relies only on the number and size of pollen grains and ovules. Any other factors of allocation of resources to male and female functions are omitted. If we let r be the proportion of resource ( R ) given to pollen, 1 – r the proportion of resource ( R ) given to seeds (as an equivalent for female function and assuming that the number of seeds = the number of ovules), and C 2 and C 1 the cost for one single seed or pollen grain respectively, we can write the number of pollen grains ( P ) ...

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... Charnov ’ s (1982) assumption that the allocated resources ( r ) and pollen grain size are constant, a linear relationship between log pollen – ovule ratio and log seed size is expected. Because the size of a single seed is dependent upon how many seeds can be produced by the plant, the log relationship is directly proportional – that is, the slope of the regression line is the unity slope (see Fig. 1). Mione and Anderson (1992) pointed out that the positive relationship between seed size and the pollen – ovule ratio could be a spurious correlation. Given negative correlations between seed size and ovule number and between the pollen – ovule ratio and ovule number, an increase in the pollen – ovule ratio with increasing seed size must follow. That plants with large seeds tend to produce few seeds and plants with light seeds produce many seeds is known as the ‘ seed size/seed number trade-off ’ (Shipley and Dion, 1992; Jakobsson and Eriksson, 2000) . A decrease in the pollen – ovule ratio with decreasing ovule numbers should be found because the ovule number itself is the denominator in the pollen – ovule ratio term. We calculated partial correlations for every combination of the three traits to control for possible inter- correlations. We obtained data for seed size, pollen – ovule ratio, and mating system from the database BIOLFLOR (Durka, 2002a; Otto, 2002) . This database provides ecological and biological data on the vascular plant species of Germany (Klotz et al. , 2002; K ü hn et al. , 2004) . We compiled pollen – ovule ratios for 77 additional species from the published literature to supplement the data available in the current version of the database. Germinule length, germinule width, and germinule height were taken from BIOLFLOR and used to calculate seed volume, assuming an ellipsoid shape of the seeds. When used in correlations and for calculating phylogenetically independent contrasts, ‘ mating system types ’ were recoded to positive integers ordered by increasing xenogamy (obligate autogamous = 1, facultative autogamous = 2, ‘ mixed mating system ’ = 3, facultative xenogamous = 4, xenogamous = 5). The mating systems are not absolutely identical to those used by Cruden (1977) . Cruden ’ s cleistogamous group is included in the obligate autogamous mating system. The ‘ mixed mating system ’ is not present in Cruden ’ s categories. It reflects the idea that mating systems are a continuous trait rather than a characteristic with only two states: predominant selfers and predominant outcrossers (Vogler and Kalisz, 2001; Barrett, 2003) . Appendix 1 provides an overview of the families studied, the number of species and genera, and the range of the data within these families. The working phylogeny used in this study is based on a supertree compiled by Durka (2002b) from over 200 literature sources for the 3679 species in the BIOLFLOR database. The 299 species included in the analyses are part of the German flora, but many of them have a wider distributional range. Because plant height is not available in BIOLFLOR, we compiled data for this trait from a national flora source (B ä ssler et al. , 1996) using the given maximal and minimal heights in the descriptions of the species. We present a phylogenetic tree of the studied species accompanied by a data table for seed size, pollen – ovule ratio, plant height, and mating system in the online appendix ( We tested the relationship between the pollen – ovule ratio and seed size by Pearson ’ s correlation in the case of (log)normally distributed, continuous variables, and by Kendall ’ s rank correlation in the non-parametric case (i.e. when mating system was one of the considered variables). Partial Kendall and Pearson correlation were used accordingly to test for the possible confounding effects of covariates that may lead to spurious correlations. We used Model II regression analyses to describe the functional relationship between seed size and the pollen – ovule ratio because Model I regression underestimates the slope coefficient when both X and Y variables are subject to a comparable magnitude of error. From the several available Model II regressions, we chose standardized major axis regression (SMA; also known as reduced major axis regression) because error variances and the ratio thereof were unknown (Sokal and Rohlf, 1995) and are difficult to estimate for phylogenetically independent contrasts (Nunn and Barton, 2000) . Under these conditions, standardized major axis regression was found to be better than major axis regression 2 (McArdle, 1987) . The r - and P -values presented with the SMA results stem from Pearson correlation tests. Because the intention of this study was to test Charnov ’ s theory in terms of a functional relationship instead of predicting pollen – ovule ratios from seed size, controlling for the possible effects of the phylogeny of the species was crucial (Harvey and Pagel, 1991; Desdevises et al. , 2003) . We present results for both cross-species analyses (CSA; i.e. species were treated as independent data points) and phylogenetically independent contrasts (PIC), so that it is possible to evaluate the effect of the phylogenetic relationship of the species on the relationship between the pollen – ovule ratio and seed size. A well-established approach to correct for the relatedness of the species in comparative ...