Supplement 1. R code for piecewise regression.

File List R_code_for_piecewise_regression.r (MD5: 56713e387417b7364390e6095dad8fab) Description Piecewise regression is a statistical method for estimationg two slopes in a series of data, one slope before a breakpoint and one slope after the breakpoint. The breakpoint can be fixed or estimated. Fixed breakpoints are based on changes in the environment. However, estimated breakpoints are necessary in competition studies, because an increase in one competitor must occur before the decline in the other competitor(s). Estimated breakpoints can determine, without bias, if the declines occurred after the increase.