Hutchinson defined species' realized niche as the set of environmental conditions in which populations can persist in the presence of competitors. In terms of demography, the realized niche corresponds to the environments where the intrinsic growth rate (r) of populations is positive. Observed species occurrences should reflect the realized niche when additional processes like dispersal and local extinction lags do not have overwhelming effects. Despite the foundational nature of these ideas, quantitative assessments of the relationship between range-wide demographic performance and occurrence probability have not been made. This assessment is needed both to improve our conceptual understanding of species' niches and ranges and to develop reliable mechanistic models of species geographic distributions that incorporate demography and species interactions.

The objective of this study is to analyse how demographic parameters (intrinsic growth rate r and carrying capacity K ) and population density (N ) relate to occurrence probability (P_occ ). We hypothesized that these relationships vary with species' competitive ability. Demographic parameters, density, and occurrence probability were estimated for 108 tree species from four temperate forest inventory surveys (Québec, western USA, France and Switzerland). We used published information of shade tolerance as indicators of light competition strategy, assuming that high tolerance denotes high competitive capacity in stable forest environments.

Interestingly, relationships between demographic parameters and occurrence probability did not vary substantially across degrees of shade tolerance and regions. Although they were influenced by the uncertainty in the estimation of the demographic parameters, we found that r was generally negatively correlated with P_occ, while N, and for most regions K, was generally positively correlated with P_occ. Thus, in temperate forest trees the regions of highest occurrence probability are those with high densities but slow intrinsic population growth rates. The uncertain relationships between demography and occurrence probability suggests caution when linking species distribution and demographic models.