Taylor's law and related allometric power laws in New Zealand mountain beech forests: the roles of space, time and environment

Yeast facilitates the multiplication of Drosophila bacterial symbionts but has no effect on the form or parameters of Taylor's law

Interactions between microbial symbionts influence their demography and that of their hosts. Taylor’s power law (TL)–a well-established relationship between population size mean and variance across space and time–may help to unveil the factors and processes that determine symbiont multiplications. Recent studies suggest pervasive interactions between symbionts in Drosophila melanogaster. We used this system to investigate theoretical predictions regarding the effects of interspecific interactions on TL parameters. We assayed twenty natural strains of bacteria in the presence and absence of a strain of yeast using an ecologically realistic set-up with D. melanogaster larvae reared in natural fruit. Yeast presence led to a small increase in bacterial cell numbers; bacterial strain identity largely affected yeast multiplication. The spatial version of TL held among bacterial and yeast populations with slopes of 2. However, contrary to theoretical prediction, the facilitation of bacterial symbionts by yeast had no detectable effect on TL’s parameters. These results shed new light on the nature of D. melanogaster’s symbiosis with yeast and bacteria. They further reveal the complexity of investigating TL with microorganisms.

Comparative power law analysis for the spatial heterogeneity scaling of the hot-spring microbiomes

Spatial heterogeneity is a fundamental property of any natural ecosystems, including hot spring and human microbiomes. Two important scales that spatial heterogeneity exhibits are population and community scales, and Taylor's power law (PL) and its extensions (PLEs) offer ideal quantitative models to assess population- and community-level heterogeneities. Here we analyse 165 hot spring microbiome samples at the global scale that cover a wide range of temperatures (7.5-99°C) and pH levels (3.3-9). We explore a question of fundamental importance for measuring the spatial heterogeneity of the hot-spring microbiome and further discuss their ecological implications: How do critical environmental factors such as temperature and pH influence the scaling of community spatial heterogeneity? We are particularly interested in the existence of a universal scaling model that is independent of environmental gradients. By applying PL and PLEs, we were able to obtain such scaling parameters of the hot spring at both community and population levels, which are temperature- and pH-invariant. These findings suggest that while the hot-spring microbiomes located at different regions may have different environmental conditions, they share a fundamental heterogeneity scaling parameter, analogically similar to the gravitational acceleration on Earth, which may vary slightly depending on altitude and latitude, but is invariant overall. In contrast, similar to the physics of the Moon and Earth, which have different gravitational accelerations, the hot spring and human microbiomes can have different scaling parameters as demonstrated in this study.

Proximate determinants of Taylor's law slopes

Taylor's law (TL), a commonly observed and applied pattern in ecology, describes variances of population densities as related to mean densities via log(variance) = log(a) + b*log(mean). Variations among datasets in the slope, b, have been associated with multiple factors of central importance in ecology, including strength of competitive interactions and demographic rates. But these associations are not transparent, and the relative importance of these and other factors for TL slope variation is poorly studied. TL is thus a ubiquitously used indicator in ecology, the understanding of which is still opaque. The goal of this study was to provide tools to help fill this gap in understanding by providing proximate determinants of TL slopes, statistical quantities that are correlated to TL slopes but are simpler than the slope itself and are more readily linked to ecological factors. Using numeric simulations and 82 multi-decadal population datasets, we here propose, test and apply two proximate statistical determinants of TL slopes which we argue can become key tools for understanding the nature and ecological causes of TL slope variation. We find that measures based on population skewness, coefficient of variation and synchrony are effective proximate determinants. We demonstrate their potential for application by using them to help explain covariation in slopes of spatial and temporal TL (two common types of TL). This study provides tools for understanding TL, and demonstrates their usefulness.

Taylor's power law captures the effects of environmental variability on community structure: An example from fishes in the North Sea

Taylor's power law (TPL) describes the relationship between the mean and variance in abundance of populations, with the power law exponent considered a measure of aggregation. However, the usefulness of TPL exponents as an ecological metric has been questioned, largely due to its apparent ubiquity in various complex systems. The aim of this study was to test whether TPL exponents vary systematically with potential drivers of animal aggregation in time and space and therefore capture useful ecological information of the system of interest. We derived community TPL exponents from a long-term, standardised and spatially dense data series of abundance and body size data for a strongly size-structured fish community in the North Sea. We then compared TPL exponents between regions of contrasting environmental characteristics. We find that, in general, TPL exponents vary more than expected under random conditions in the North Sea for size-based populations compared to communities considered by species. Further, size-based temporal TPL exponents are systematically higher (implying more temporally aggregated distributions) along hydrographic boundaries. Time series of size-based spatial TPL exponents also differ between hydrographically distinct basins. These findings support the notion that TPL exponents contain ecological information, capturing community spatio-temporal dynamics as influenced by external drivers.

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

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.

Chagas disease vector control and Taylor's law

BACKGROUND

Large spatial and temporal fluctuations in the population density of living organisms have profound consequences for biodiversity conservation, food production, pest control and disease control, especially vector-borne disease control. Chagas disease vector control based on insecticide spraying could benefit from improved concepts and methods to deal with spatial variations in vector population density.

METHODOLOGY/PRINCIPAL FINDINGS

We show that Taylor's law (TL) of fluctuation scaling describes accurately the mean and variance over space of relative abundance, by habitat, of four insect vectors of Chagas disease (Triatoma infestans, Triatoma guasayana, Triatoma garciabesi and Triatoma sordida) in 33,908 searches of people's dwellings and associated habitats in 79 field surveys in four districts in the Argentine Chaco region, before and after insecticide spraying. As TL predicts, the logarithm of the sample variance of bug relative abundance closely approximates a linear function of the logarithm of the sample mean of abundance in different habitats. Slopes of TL indicate spatial aggregation or variation in habitat suitability. Predictions of new mathematical models of the effect of vector control measures on TL agree overall with field data before and after community-wide spraying of insecticide.

CONCLUSIONS/SIGNIFICANCE

A spatial Taylor's law identifies key habitats with high average infestation and spatially highly variable infestation, providing a new instrument for the control and elimination of the vectors of a major human disease.

Linking parasite populations in hosts to parasite populations in space through Taylor's law and the negative binomial distribution

The spatial distribution of individuals of any species is a basic concern of ecology. The spatial distribution of parasites matters to control and conservation of parasites that affect human and nonhuman populations. This paper develops a quantitative theory to predict the spatial distribution of parasites based on the distribution of parasites in hosts and the spatial distribution of hosts. Four models are tested against observations of metazoan hosts and their parasites in littoral zones of four lakes in Otago, New Zealand. These models differ in two dichotomous assumptions, constituting a 2 × 2 theoretical design. One assumption specifies whether the variance function of the number of parasites per host individual is described by Taylor's law (TL) or the negative binomial distribution (NBD). The other assumption specifies whether the numbers of parasite individuals within each host in a square meter of habitat are independent or perfectly correlated among host individuals. We find empirically that the variance-mean relationship of the numbers of parasites per square meter is very well described by TL but is not well described by NBD. Two models that posit perfect correlation of the parasite loads of hosts in a square meter of habitat approximate observations much better than two models that posit independence of parasite loads of hosts in a square meter, regardless of whether the variance-mean relationship of parasites per host individual obeys TL or NBD. We infer that high local interhost correlations in parasite load strongly influence the spatial distribution of parasites. Local hotspots could influence control and conservation of parasites.