Phenotypic integration: between zero and how much is too much

The hypothesis that flowers constitute mechanical devices designed by natural selection to ensure pollen donation/reception through the concerted action of a suite of correlated (integrated) traits is an appealing and broadly accepted idea (Bell, 1985). Two questions derive from this hypothesis. The first is whether flowers are, in fact, integrated modules. Most studies evaluating this question have found significant levels of floral integration and a marked heterogeneity among species (Armbruster et al., 1999, 2004; Pérez et al., 2007; Pérez-Barrales et al., 2007; Ordano et al., 2008). Thus, the available evidence already indicates that flowers are indeed integrated (Ordano et al., 2008). A different, but equally relevant, question is whether or not flowers exhibit relatively high levels of phenotypic integration. Because in most plant species flower functioning depends on the interaction between floral and pollinator morphologies, it has been suggested that flowers should have relatively high levels of phenotypic integration (Stebbins, 1950, 1970; Faegri & van der Pijl, 1966). Obviously, responses to these two questions require different approaches and rely on distinct biological reasons. In his letter to New Phytologist, Harder (2009; this issue, pp. 247–248) argues that our conclusion that flowering plants have lower floral integration than expected by a randomly generated distribution (Ordano et al., 2008, p. 1189) is flawed because of the inappropriateness of our analysis. He further concluded that: ‘floral integration is the rule, rather than the exception’. While we agree with his general conclusion regarding the ubiquity of floral integration, we believe that his criticism is based on confusing the two questions presented above. Accordingly, the disagreement presented by Harder (2009) merits a thorough discussion of these two questions. In doing so, we attempt to clarify possible sources of misinterpretation in the paper by Ordano et al. (2008). Since the seminal work of Berg (1960), evidence has accumulated supporting the expectation that flowers are integrated modules (Armbruster et al., 1999, 2004; Pérez et al., 2007; Pérez-Barrales et al., 2007; Ordano et al., 2008), a pattern observed for other functional modules in animal taxa (Wagner et al., 2007; Pavlicev et al., 2009). By using the observed distribution of integration values reported by Ordano et al. (2008), and the statistical approach developed by Wagner (1984) and Cheverud et al. (1989), Harder's analyses confirmed that flowers are significantly integrated. The null hypothesis used by Harder (2009) is that of no correlation among characters, and thus any integration level above the expected value, given by the sampling error E(V(λ)) = (M − 1)/N, would indicate that a correlation matrix is significantly integrated (Cheverud et al., 1989). Because the average integration value observed among flowering plants was 21.5% (Ordano et al., 2008), and the expected value obtained by Harder (2009) was only 2.76%, the null hypothesis is readily rejected (sampling error obtained from an approximated normal distribution of product–moment correlation coefficients). Accordingly, Harder's exercise (2009) just confirmed previous results supporting the expectation that flowers express significant levels of phenotypic integration. Moreover, we agree that the use of a uniform distribution of product–moment correlation coefficients to determine whether a given level of integration is significantly different from zero is not a valid procedure. So far, these results add to the mounting evidence showing that flowers, and many other functional modules in several organisms, express significant levels of integration. Harder's (2009) test evaluates whether a group of traits are indeed integrated, but it does not tell us if the magnitude of integration is low or high. In addition to the presence/absence question, one could also ask whether the special case of plant–pollinator interactions really favoured the evolution of high levels of phenotypic integration. The natural history of plants and pollinators is full of examples showing that efficient pollen transfer depends on the interaction between flower and pollinator morphologies (Faegri & van der Pijl, 1966; Fenster et al., 2004). Accordingly, answering if flowers are highly integrated modules requires a different null hypothesis from that used for testing question 1. In this sense, Ordano et al. (2008) looked for the appropriate null distribution that should be used to determine whether an observed level of integration was relatively low or high. To this end, Ordano et al. (2008) built an expected distribution of integration values based on randomly generated correlation matrices. These matrices, in turn, were obtained from randomly sampling product–moment correlation coefficients (ranging from −1 to 1). This procedure ensures that low, intermediate and high values have the same probability of being selected. Integration values were then calculated for each matrix (Wagner, 1984) and were used to build the expected distribution of integration. Such a distribution is centred on the average expected (significant) value of integration for a random association of independent correlation coefficients. Consequently, testing question 2 would determine whether a given integration value corresponds to a lower level or a higher level than that expected by chance. In fact, the expected distribution of integration values obtained by Ordano et al. (2008) can be used for any other functional module to determine what level of integration can be considered as low or high. A couple of examples suggests that there is a huge variation in the magnitude of integration. For instance, integration levels as high as 77.16% have been found for the wing in the northern goshawk (Accipiter gentilis; Pavlicev et al., 2009), while that of the fruit of Prunus persica is 21.79% (Badenes et al., 1998). Other modules, like the facial skull of papionins, can range from 33.33% in Papio cynocephalus to 18.33% in Macaca nemestrina (Cheverud, 1989). Thus, the low level of integration found among flowering plants may not be an exception. Overall, we agree with Harder (2009) in that floral integration is the rule. Having taken this position, we must also take another. Demonstrating that flowers are integrated organs does not mean that they are highly integrated. The analyses in Ordano et al. (2008) were intended to test question 2 and concluded that flowers have relatively low levels of floral integration, rejecting the expectation that flowers are highly integrated organs. Thus, besides understanding the causes of variation in the levels of floral integration, floral evolutionary biologists could go forward in exploring why flowers are apparently little integrated (Fornoni et al., 2008).