Functional Diversity Measures Functional richness 0 10 15 0 10 15 10 15 –0.75 0.5 0.2 10 15 Niche overlap Functioal evenness Species richness 20 607 –0.1 0.25 –0.25 Mean annual temperature °C Mean annual temperature °C Figure 11 Relationships between functional diversity, niche overlap and mean annual temperature in French lacustrine fish communities 0.6 Beta Rao Alpha Rao 1.5 OLS R2 = 0.71 Jack-knifed R2 = 0.56 Jack- knifed P = 0.025 0.4 0.2 0.5 Alpha Rao Monte Carlo 0.5 600 300 900 600 300 = 0.86 OLS R2 Jack-knifed R2 = 0.75 Jack-knifed P = 0.003 Regional Rao 900 –0.5 –1 –1.5 900 300 600 Total soil P (mg kg–1) Figure 12 Observed Alpha Rao quadratic entropy and Alpha Rao relative to random expectation (Alpha Rao Monte Carlo) for each site along the chronosequence versus total soil P Each point represents a single site along the chronosequence OLS R2 is R-squared from ordinary least squares regression Other statistics are from Jack-knifed linear regression achieve high abundance became much more severe as soil P declined There was no relationship between regional (site) Rao and total soil P, but Beta Rao was significantly negatively correlated with total soil P (Figure 13) This indicates that 900 600 300 Total soil P (mg kg–1) Figure 13 Regional (site) and beta (between plots but within sites) Rao quadratic entropy for each site along the chronosequence versus total soil P Each point represents a single site along the chronosequence OLS R2 is R-squared from ordinary least squares regression Other statistics are from Jack-Knifed linear regression communities became functionally more homogeneous as nutrient stress increased The fact that a decline in local FD with declining soil P was only observed when raw Rao values were compared with