# Estimating Taxon-Environment Relationships: Environmental Limits

## Environmental Limits

Taxon-environment relationships expressed in terms of *environmental limits* attempt to capture the maximum or the minimum level of an environmental variable under which a taxon can persist. Environmental limits can be estimated by computing cumulative percentiles (CPs) from field data. An empirical CP is estimated for a given value of the environmental variable, *x _{0 }*, as follows (Equation 2):

*x _{i}*

_{ }<

*x*and I = 0 if

_{0}*x*

_{i}_{ }>

*x*, and other variables are as defined in Equation 1 (see the Central Tendencies link to in the Quick Links box). For presence/absence data, the numerator is the number of occurrences of taxon

_{0 }*j*at sites in which the value of the environmental variable is less than the cutoff value, and the denominator is the total number of occurrences of taxon

*j*. Plots of CP as a function of

*x*are shown in Figure 4 for two genera. An environmental limit would be estimated by fixing CP at a prescribed value and then computing the

_{0}*x*that corresponds to that value of CP for each taxon. Then,

_{0}*x*quantifies the limiting conditions for that taxon. To estimate the maximum level of an environmental variable under which a taxon could persist, CP would be fixed at a relatively high value (e.g., 0.75).

_{0 }