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.

文件列表：R_code_for_piecewise_regression.r（MD5校验值：56713e387417b7364390e6095dad8fab） 数据集说明：分段回归（piecewise regression）是一种统计学方法，用于在数据序列中估计两段斜率，分别为分段点（breakpoint）前的斜率与分段点后的斜率。分段点可固定设定，也可通过模型估算得到。固定分段点的设定依据为环境变化；而在竞争研究中，估算分段点为必要选择，因为某一竞争者的增长必然发生在其他竞争者的下降之前。通过估算得到的分段点可以无偏地判断下降是否发生在增长之后。