Appendix A. Additional analyses of DECEMS simulations.

Additional analyses of DECEMS simulations

Host species level variance covariance matrix and random effect posteriors.

Diagonal elements display the among host species standard deviation in abundance for parasite species. Upper triangular elements show among-species correlation parameters. Black indicates correlations that are probably positive or probably negative (95% of posterior probability mass greater than or less than zero); grey indicates otherwise. Lower triangular elements show bivariate smoothed scatter plots of species-level random effects, with host species codes printed at the posterior means. The smoothed grey portions represent the posterior densities of the species-level random effects.</p

Individual level variance covariance matrix and random effect posteriors.

<p>Diagonal elements display the among host individual standard deviation in abundance for parasite species. Upper triangular elements show among-individual correlation parameters. Black indicates correlations that are probably positive or probably negative (95% of posterior probability mass greater than or less than zero); grey indicates otherwise. Lower triangular elements show bivariate scatter plots of the posterior means of the individual-level random effects corresponding to the intersection of the species in the rows and columns, such that each host individual is represented by one point in each panel.</p

The relationship between community R₀ and host species richness for six example scenarios.

<p>Panels <i>A</i>–<i>D</i> show results from simulations based on the four different assumptions of the underlying relationship between host community abundance and richness (depicted as inset Figures) with density-dependent transmission. Panels <i>E</i> and <i>F</i> are two examples with frequency-dependent transmission. Boxplots summarize the findings of 1000 simulations for each panel. LOESS smoothers with 95% confidence bands were added for visual interpretation of average trends. Not all iterations of frequency-dependent transmission are shown because they show the same qualitative trends. (Parameters used to generate these data: <i>Y₀</i> = 10, <i>z</i> = 0.10, <i>M</i> = 3, <i>a</i> = 2, <i>b</i> = 1, <i>m</i> = 1.5, ε = 10, <i>k</i> = 0.3, <i>ψ</i> = 3, <i>c_ij</i> = 0.05).</p

Bivariate posterior distributions of the effective variance and dependence for the multivariate random effects.

Each point represents a simulated draw from the posterior. Effective variance measures the magnitude of spread in any direction of the random effects, and effective dependence measures the magnitude of among-species correlation.</p

The Scaling of Host Density with Richness Affects the Direction, Shape, and Detectability of Diversity-Disease Relationships

<div><p>Pathogen transmission responds differently to host richness and abundance, two unique components of host diversity. However, the heated debate around whether biodiversity generally increases or decreases disease has not considered the relationships between host richness and abundance that may exist in natural systems. Here we use a multi-species model to study how the scaling of total host community abundance with species richness mediates diversity-disease relationships. For pathogens with density-dependent transmission, non-monotonic trends emerge between pathogen transmission and host richness when host community abundance saturates with richness. Further, host species identity drives high variability in pathogen transmission in depauperate communities, but this effect diminishes as host richness accumulates. Using simulation we show that high variability in low richness communities and the non-monotonic relationship observed with host community saturation may reduce the detectability of trends in empirical data. Our study emphasizes that understanding the patterns and predictability of host community composition and pathogen transmission mode will be crucial for predicting where and when specific diversity-disease relationships should occur in natural systems.</p></div

Site level variance covariance matrix and random effect posteriors.

Diagonal elements display the among-site standard deviation in abundance for all host and parasite species (Anbo = Anaxyrus boreas, Psre = Pseudacris regilla, Lica = Lithobates catesbeianus, Tagr = Taricha granulosa, Tato = Taricha torosa, Rib = Ribeiroia ondatrae, Echino = Echinostoma sp., Cephalo = Cephalogonimus sp., Alaria = Alaria sp., Rv = Ranavirus sp., Bd = Batrachochytrium dendrobatidis). Green indicates hosts and blue, parasites. Upper triangular elements show among-species correlation parameters. Black indicates correlations that are probably positive or probably negative (95% of posterior probability mass greater than or less than zero); grey indicates otherwise. Lower triangular elements show bivariate scatter plots of the posterior means of the site-level random effects corresponding to the intersection of the species in the rows and columns, such that each site is represented by one point in each panel.</p

Multilevel Models for the Distribution of Hosts and Symbionts

<div><p>Symbiont occurrence is influenced by host occurrence and vice versa, which leads to correlations in host-symbiont distributions at multiple levels. Interactions between co-infecting symbionts within host individuals can cause correlations in the abundance of two symbiont species across individual hosts. Similarly, interactions between symbiont transmission and host population dynamics can drive correlations between symbiont and host abundance across habitat patches. If ignored, these interactions can confound estimated responses of hosts and symbionts to other factors. Here, we present a general hierarchical modeling framework for distributions of hosts and symbionts, estimating correlations in host-symbiont distributions at the among-site, within-site, among-species, and among-individual levels. We present an empirical example from a multi-host multi-parasite system involving amphibians and their micro- and macroparasites. Amphibian hosts and their parasites were correlated at multiple levels of organization. Macroparasites often co-infected individual hosts, but rarely co-infected with the amphibian chytrid fungus. Such correlations may result from interactions among parasites and hosts, joint responses to environmental factors, or sampling bias. Joint host-symbiont models account for environmental constraints and species interactions while partitioning variance and dependence in abundance at multiple levels. This framework can be adapted to a wide variety of study systems and sampling designs.</p></div

Survey level variance covariance matrix and random effect posteriors.

<p>Diagonal elements display the among-survey standard deviation in abundance for host species. Upper triangular elements show among-species correlation parameters. Black indicates correlations that are probably positive or probably negative (95% of posterior probability mass greater than or less than zero); grey indicates otherwise. Lower triangular elements show bivariate scatter plots of the posterior means of the survey-level random effects corresponding to the intersection of the species in the rows and columns, such that each survey is represented by one point in each panel.</p

Results of GAM to test the effect of community abundance-richness relationships and pathogen transmission mode on community R₀-richness relationships across a range of sample sizes.

<p><i>A</i>–<i>C</i>, Proportion of simulations where the GAM was significant versus sample size, for the three treatments: <i>A</i>, “additive” method with density-dependent transmission; <i>B</i>, “additive” method with frequency-dependent transmission; and <i>C</i>, “saturating” method with density-dependent transmission. The horizontal dashed lines in <i>A–C</i> show the total proportion of significant cases across all sample sizes (i.e. out of 820 simulations) for each of the three treatments. Parameters of generated local communities follow those specified in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0097812#pone-0097812-g002" target="_blank">Figure 2</a>.</p