It computes the proportion of the variation of the response variable as estimated using the generated regression compared to the variation of the response variable computed using the null model, i.e., the mean of the values [29].
First, we generated 10,000 random matrices using the null model Patefield [35], in which the interaction frequency between two species is proportional to their total sum of interactions.
First, we generated 1,000 random matrices from the original matrix, using the null model 2 [10] (null model Ce in Aninhado), in which the probability of interaction between a bat and a plant species is proportional to their total number of interactions (i.e. their degree).
The branch-site test 2 was performed using the null model, ω2 = 1 fixed (using the parameters fix omega = 1 and omega = 1).
The coil model (8) is treated simply as a model that describes a segment of a protein raw, using the null model approach described above in Section 3.1.
We calculated the intra-class correlation (ICC) (Merlo et al. 2005a) (a measure of the degree of clustering at the country level) and the proportional change in variance (PCV) (Merlo et al. 2005b) for each variable that was added to a respective model using the null model (M0) (a model without predictors) as a reference.
An overall test for positive selection (Test Overall; TO) was carried out using the null model M1a (Nearly-neutral) and the alternative model M2a (Positive selection) [ 60]; this test identifies genes under positive selection in any or all of the branches of a given phylogeny.
Two types of tests were implemented in PAML to identify genes under positive selection: Test 1 was carried out using the null model M1a (Nearly-neutral) and the alternative model M2a (positive selection) [ 52], whereas Test 2 was carried out to identify genes under positive selection in specific branches of C. trachomatis (branch-site test2 described by Zhang et al. [ 53]).
The second LRT uses the null model M7 (beta) that assumes the ω ratio is drawn from a beta distribution defined between 0 and 1.
To test the hypothesis that Muller's ratchet does not threaten the Amazon molly with extinction during the known time of its existence, we used the null model for quantifying the threat of extinction from Muller's ratchet, as described elsewhere in detail [ 7].
