Biological and statistical processes jointly drive population aggregation: using host-parasite interactions to understand Taylor's power law

Abstract

The macroecological pattern known as Taylor's power law (TPL) represents the pervasive tendency of the variance in population density to increase as a power function of the mean. Despite empirical illustrations in systems ranging from viruses to vertebrates, the biological significance of this relationship continues to be debated. Here we combined collection of a unique dataset involving 11 987 amphibian hosts and 332 684 trematode parasites with experimental measurements of core epidemiological outcomes to explicitly test the contributions of hypothesized biological processes in driving aggregation. After using feasible set theory to account for mechanisms acting indirectly on aggregation and statistical constraints inherent to the data, we detected strongly consistent influences of host and parasite species identity over 7 years of sampling. Incorporation of field-based measurements of host body size, its variance and spatial heterogeneity in host density accounted for host identity effects, while experimental quantification of infection competence (and especially virulence from the 20 most common host-parasite combinations) revealed the role of species-by-environment interactions. By uniting constraint-based theory, controlled experiments and community-based field surveys, we illustrate the joint influences of biological and statistical processes on parasite aggregation and emphasize their importance for understanding population regulation and ecological stability across a range of systems, both infectious and free-living.

Keywords: community ecology; disease ecology; feasible sets; macroecology; population regulation; superspreaders.

Figure 1.

Conceptual diagrams displaying the two steps used in our analysis of Taylor's power law, which focuses on the scaling relationship between the sample mean and its variance. (a) Ecological mechanisms can affect the variance of a distribution either indirectly through the mean (arrows 1 and 2; P = total number of individuals in a sample, e.g. parasites; H = total number of units sampled, e.g. hosts, or directly; arrow 3). Feasible set theory removes these indirect effects to focus on mechanisms that directly affect variance. (b) Taylor's power law is often represented as the positive, linear relationship between log-transformed values of the mean and the variance. Ecological mechanisms can change the intercept, the slope or both parameters in this relationship. (Online version in colour.)

Figure 2.

Using feasible set theory to account for constraints in empirical patterns of parasite aggregation within amphibian hosts. (a) The observed relationship between the log-mean and log-variance of infection for 971 host–parasite distributions (white and red points), for which each point corresponds to a unique combination of host species, parasite species, wetland identity and sample year. Black points represent the predicted log-variance values from feasible set theory. White points fall within the 95% confidence interval (CI) of the feasible set-predicted log variance and red points fall outside this interval (95% CIs are based on 1000 draws of feasible set-predicted log variance given P and H). Note that the quadratic shape is a prediction from feasible set theory. (b) The feasible set-predicted log-variance values plotted against the observed log-variance for all 971 populations. The black dashed line is the one-to-one line, along which all points would fall if feasible set theory perfectly predicted the observed log variance. (c) The residual variation (observed–predicted) in the data after accounting for the feasible set; each point is coloured according to amphibian host species identity. The lines give the best-fit regressions. While host species have different intercepts, the slopes are not significantly different (intercept , p < 0.001; slope, p = 0.072). (d) Same as (c) but points are coloured according to parasite species. Parasite species identity affects both the intercept and slope of the residual variation (intercept , p < 0.01; slope, p < 0.01).

Figure 3.

The effects of host and parasite species identity on Taylor's power law across the 7-year sampling period. While (a) parasite species and (b) host species had differing effects on the estimated slope or intercept of the log-mean–log-variance relationship, these effects were broadly consistent over time. Symbol shapes correspond to the identity of parasite or host species and colour indicates the sample year. For a given host or parasite, points are staggered with respect to the x-axis for visual clarity. Effect sizes and standard errors were extracted from a linear mixed-effects model.

Figure 4.

Effects of infection (a) competence and (b) virulence on the slope of Taylor's power law (TPL). Competence and virulence for each host–parasite combination were measured experimentally using controlled exposure dosages. Laboratory-derived estimates of (standardized) virulence and competence for each host-parasite combination are plotted against the empirically observed slope of the log-mean–log-variance relationship from sampled field sites. Each point represents the estimated TPL slope based on a linear mixed effect model with year, host and parasite species. The colour and shapes of each point indicates the host and parasite species, respectively. Multiple points of the same shape and colour correspond to multiple years of observation. The size of each point reflects the number of data points for that combination of host, parasite and year. The black line represents the best-fit line from a weighted least-squares regression with virulence or competence as the predictor variable with the 95% confidence interval indicated by the grey region. On the upper right of each plot is the estimated coefficient from this regression and its corresponding p-value. (Online version in colour.)