| Introduction | More realistic models will include non-neutral processes, such as interactions that depend on species identity [32, 33], but neutral theory can act as a null model for assessing the weight of evidence for such processes. |
| Introduction | As the dynamics are made more non-neutral, the deviations from the SNM should become stronger, and we expect the power of the test of the neutral null model to increase. |
| Power calculation for fixed non-neutral model parameters | Because, for the non-neutral model in this limit, I is nothing more than a sample size—a community of size 2 I can be constructed by adding two communities of size I—this non-monotonic relationship between power and I must be due to the nonlinear role played by I in the community dynamics in the neutral null model . |
| Power calculation for large forest surveys | For related reasons, the probability of rejecting the neutral null model was low for model IF/ LOGS when fitted to the empirical data. |
| Power calculations for particular experiments | For each forest, and separately for each survey year, we tested the null model that the data were generated by the SNM using the parametric bootstrap method described above. |
| Statistical power calculation for fixed non-neutral model parameters | For each data set, perform a test of the neutral null model using the parametric bootstrap method described above. |
| Statistical power calculation for fixed non-neutral model parameters | the neutral null model was rejected). |
| Testing the neutral null model | Testing the neutral null model |
| Testing the neutral null model | To calculate the p-value of our test, we compare the value of a test statistic for the test data set with values of the test statistic for data sets generated by the null model . |
| E 3 A A g Time s 'r r a E A AA Time Time | For a dataset generated from this null model , the p-values should be uniformly distributed from 0 to 1, exclusive: the highest Kendall’s 1‘ out of N tests should have a p-value of 1 / (N + 1), the second highest test statistic has a p-value of 2/ (N + 1), and the ith highest test statistic has a p-value of i/ (N + 1) [35]. |
| Overview | The domain of test statistics increases very quickly with the number of data points, however, so Monte Carlo (MC) sampling, in which representations of the null model are randomly generated and evaluated, is required to estimate p-values if there are more than approximately 20 time points due to the computational cost of the generating function. |
| Simulated data benchmarks | While the empirical calculation approximates the null model well, it does not fully prevent multiple hypothesis testing from weakening the ability to identify rhythmic time series. |