An updated framework to account for inter-individual variability when quantifying phenotypic variation

In trait-based ecology, phenotypic variation (PVar) is often quantified with measures that express average differences between populations standardized in the range 0-1. A major problem with these measures is that they disregard the within-population trait variability. In addition, most of these measures cannot be decomposed across scales. This can alter their interpretation, thus limiting their applicability. To overcome these problems, we propose a new measure, the Phenotypic Dissimilarity Index (PhD) that is insensitive to the within-population interindividual trait variability. Likewise, PhD can be used to quantify PVar between individuals in a population while accounting for the PVar within individuals. Using simulated and real data, we showed that PhD index correctly quantifies PVar when the within-population trait variability is not negligible, as in many ecological studies. By accounting for within-population trait variability, the PhD index generally provides a more parsimonious quantification of PVar across an environmental gradient compared to other estimators. Traits sampled within a species have an inherent variability. Accounting for such variability is essential to understand species phenotypic responses to environmental cues. As such, the PhD index will provide ecologists with an asset to reliably quantify and compare PVar within and between species across environmental gradients at different scales. We also provide an R function to calculate the PhD index.


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Functional traits variability within species is a key determinant of species' ability to cope, and 4 5 eventually adapt, to environmental factor variations. Accounting for this variability is considered 4 6 essential to explain the success of a species under contrasting environmental conditions (Garnier et al., 4 7 2015). However, trait variability within species, or intraspecific trait variability (ITV), or phenotypic

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According to Valladares et al. (2006), in the simplest case of only two environmental states, k and 1 4 7 m, we can summarize the phenotypic variation of trait τ as the expected trait dissimilarity between two 1 4 8 individuals drawn at random, one from each environmental state:

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In the context of biodiversity theory, the same index was independently proposed by Rao (1982)

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The consequence of the dependence of RDPI from k D and m D is that RDPI violates the basic

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To overcome this problem, Rao (1982) (2014) proposed the following normalized version of the RDPI index: where the acronym PhD stands for Phenotypic Dissimilarity, an estimator of PVar that expresses the estimates only when the variability of a trait within each environmental state is zero (Fig. 2a), and 1 9 7 increasingly diverge as the trait standard deviation within environmental states increases ( Fig. 2b-d).

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Finally, a simple and intuitive way to generalize km PhD to more than two environmental states, which 2 0 8 is usually adopted in community ecology for calculating the beta diversity of a set of species states, the PhD index is independent on the trait variance within environmental states. We use an 2 1 7 example with simulated data to display such desirable property of the PhD index. As already described, alone, we generated four scenarios (Fig. 3a-d the PhD similar to the RDPI. In this scenario, the two indexes should be highly correlated.

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2) Scenario 2: within-population trait variance is high and of similar magnitude across all 2 3 1 populations (Fig. 3b). As the only difference with Scenario 1 is just an increase in the 2 3 2 magnitude of within-population trait variance, we expected the PhD index and the RDPI to be 2 3 3 still correlated.

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3) Scenario 3: within-population trait variance is relatively low across all populations, but not all 2 3 5 populations have the same trait variance (Fig. 3c). Under this scenario, we expected the indexes populations have the same trait variance (Fig. 3d). Similar to Scenario 3, we expected the two RDPI calculations). For this example, we selected only species that were present in at least four plots 2 5 8 along the considered gradient, as we considered four plots to be the minimum number data points than that of the most common PVar estimators ( Fig. 4a-d). This aspect is of particular interest as PVar 3 0 9 estimates are classically used to identify traits that are more responsive to environmental gradients, and represents an essential tool to reach such an overarching objective.

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The PhD index we propose is insensitive to the within-population interindividual trait variability