Species mean elevational range size pattern
Species elevational range size is defined as the range from the lowest to highest elevation of a given species. Species only recorded in one site (elevational range size is zero) were considered to occur in the entire 100-m elevational band (Stevens, 1992); elevational range sizes less than 100 m were also adjusted to 100 m considering the mobility of bird species. Three different methods were used to calculate the mean elevational range size of species in each 100-m elevational bands respectively: (1) the average range size of all species within each elevational band (the Steven’s method, Stevens, 1992); (2) the average range size of species whose midpoints occur in each elevational band (the midpoint method, Rohde et al., 1993); (3) the average range size of species whose abundance center (Equation 1) occur in each elevational band (the specimen method, Almeida-Neto et al., 2006); abundance center is calculated as the weighted average midpoint of each species, as follows:
\(WA_{i}=\frac{\sum_{i=1}^{i=n}{E_{i}N_{i}}}{\sum_{i=1}^{i=n}N_{i}}\)(Equation 1)
where \(WA_{i}\ \)is the weighted average midpoint of species \(i\);\(E_{i}\) is the elevation of each band where species \(i\) is present; and \(N_{i}\) is the number of individuals of species \(i\) at each elevational band (Almeida-Neto et al., 2006).