Probabilistic approaches for investigating species co-occurrence from presence-absence maps

In this research, we propose probabilistic approaches to identify pairwise patterns of species co-occurrence by using presence-absence maps only. In particular, the two-by-two contingency table constructed from a presence-absence map of two species would be sufficient to compute the test statistics and perform the statistical tests proposed in this article. Some previous studies have investigated species co-occurrence through incidence data of different survey sites. We focus on using presence-absence maps for a specific study plot instead. The proposed methods are assessed by a thorough simulation study.

A Chi-squared test is used to determine whether the distributions of two species are independent. If the null hypothesis of independence is rejected, the Chi-squared method can not distinguish positive or negative association between two species. We propose six different approaches based on either the binomial or Poisson distribution to obtain p-values for testing the positive (or negative) association between two species. When we test to investigate a positive (or negative) association, if the p-value is below the predetermined level of significance, then we have enough evidence to support that the two species are positively (or negatively) associated.

A simulation study is conducted to demonstrate the type-I errors and the testing powers of our approaches. The probabilistic approach proposed by Veech (2013) is served as a benchmark for comparison. The results show that the type-I error of the Chi-squared test is close to the significance level when the presence rate is between 40% and 80%. For extremely low or high presence rate data, one of our approaches outperforms Veech (2013)'s in terms of the testing power and type-I error rate. The proposed methods are applied to a tree data of Barro Colorado Island in Panama and a tree data of Lansing Woods in USA. Both positive and negative associations are found among some species in these two real data.