Data Analysis
To evaluate overall patterns of microbiome alpha diversity, t-tests and Mann-Whitney U tests were performed to compare total observed eukaryotic or bacterial OTUs across site types (island vs. mainland) or MHC IIB genotypes (homozygote vs. heterozygote) in SPSS (vrs. 22). Analyses of microbiome community structure (beta diversity) were conducted using Mantel tests of community dissimilarity vs. geographic distance or genetic distance (F­ST­) implemented in the ade4 package of R (vrs. 1.7-11) (44–47).
To examine associations between microbial communities and geography or host frog MHC IIB genotype, data were statistically analyzed and visualized using packages implemented in Python (vrs. 2.7.13) and Matplotlib (48,49). Associations between microbial communities and geography or frog MHC IIB genotype were determined by simulating an expected null distribution of host frog microbiomes. To create the null distribution, a two-column data table was first created with column 1 being the site type (island or coastal) or MHC IIB genotype (heterozygous or homozygous) of a host frog and column 2 being one microbial OTU found on that frog. After the data table was populated for all frogs and microbes in the dataset, column 2 (microbial OTU) was held constant while column 1 (site type or frog genotype) was shuffled randomly. This was repeated 1000 times to create two sets of random microbial occurrence distributions, one for analysis of microbial associations with site type and a second for analysis of microbial associations with host frog genotype.
Co-occurrence between microbial OTUs within and among domains (Bacteria vs. Eukaryotes) was analyzed with a third null distribution of microbial communities. Because of potential site effects on microbial presence and community structure (e.g ., some microbes only co-occur on frogs because the microbes themselves solely occur at the same subset of sites) and site-MHC IIB genotype interactions (as homozygotes and heterozygotes are not evenly distributed across sites or site types; Table 1), an expected null distribution of microbes accounting for site-specific presence/absence of each microbe was created. This null distribution of microbes was achieved through within-site randomization using MCMC edge swapping, a standard method for network datasets (50–52). This method allows any configuration to be reached from any starting point, and allows for even sampling along all allowed states as forward and backward swaps are equally likely. To achieve this, first, two microbe-frog pairs were randomly selected (each pair consisting of a single randomly selected microbial OTU found on a single randomly selected frog). Microbial OTUs were then swapped between the selected frogs when three criteria were met: (1) the frogs were different individuals with the same MHC IIB genotype (either both homozygous or both heterozygous); (2) the OTUs were different from one another; and (3) neither frog already hosted the microbe it would receive via the swap. Microbe swapping was performed with 1000 repetitions for each frog-microbe pair.
To test whether hypothesized bacterial effects on Bd extend to diverse microeukaryotic members of the microbiome, bacterial OTUs that matched the Woodhams et al. (2015) database were binned according to their hypothesized ecological significance with regard to Bd(Bd inhibitory, Bd enhancing, or no effect on Bd ). The co-occurrences of bacteria within each category with microbiome eukaryotes were then compared with the third null distribution of microbial OTUs.
For all microbial association/co-occurrence analyses, the probability of non-random microbial association/co-occurrence (p ) was calculated by comparing observed versus expected counts of microbial association/co-occurrence. P -values were evaluated at a significance level of α = 0.05. Using the results of the tests of co-occurrences within and among all microbial taxa, network analyses were performed and visualized in SciPy (53).