Anthelmintic Treatment and the Stability of Parasite Distribution in Ruminants

Parasites are generally overdispersed among their hosts, with far-reaching implications for their population dynamics and control. The factors determining parasite overdispersion have long been debated. In particular, stochastic parasite acquisition and individual host variation in density-dependent regulation through acquired host immunity have been identified as key factors, but their relative roles and possible interactions have seen little empirical exploration in parasite populations. Here, Taylor's power law is applied to test the hypothesis that periodic parasite removal destabilises the host-parasite relationship and increases variance in parasite burden around the mean. The slope of the power relationship was compared by analysis of covariance among 325 nematode populations in wild and domestic ruminants, exploiting that domestic ruminants are often routinely treated against parasite infections. In Haemonchus spp. and Trichostrongylus axei in domestic livestock, the slope increased with the frequency of anthelmintic treatment, supporting this hypothesis. In Nematodirus spp., against which acquired immunity is known to be strong, the slope was significantly greater in post-mortem worm burden data than in faecal egg counts, while this relationship did not hold for the less immunogenic genus Marshallagia. Considered together, these findings suggest that immunity acting through an exposure-dependent reduction in parasite fecundity stabilises variance in faecal egg counts, reducing overdispersion, and that periodic anthelmintic treatment interferes with this process and increases overdispersion. The results have implications for the diagnosis and control of parasitic infections in domestic animals, which are complicated by overdispersion, and for our understanding of parasite distribution in free-living wildlife. Parasite-host systems, in which treatment and immunity effectively mimic metapopulation processes of patch extinction and density dependence, could also yield general insights into the spatio-temporal stability of animal distributions.

Spatial variance-mass allometry of population density in felids from camera-trapping studies worldwide

Power laws are cornerstone relationships in ecology and evolutionary biology. The density-mass allometry (DMA), which predicts an allometric scaling of population abundance, and Taylor’s law (TL), which predicts a decrease in the population abundance variation along with a decrease in population density, have enhanced our knowledge of inter- and intra-specific variation in population abundance. When combined, these two power laws led to the variance-mass allometry (VMA), which states that larger species have lower spatial variation in population density than smaller species. The VMA has been predicted through theoretical models, however few studies have investigated if this law is also supported by empirical data. Here, to formally test the VMA, we have used the population density estimates obtained through worldwide camera trapping studies for an emblematic and ecologically important carnivorous taxa, the Felidae family. Our results showed that the VMA law hold in felids, as well as the TL and the DMA laws; bigger cat species showed less variation for the population density than smaller species. These results have important implications for the conservation of wildlife population and confirm the validity of important ecological concepts, like the allometric scaling of population growth rate and the slow-fast continuum of life history strategies.

The inherent multidimensionality of temporal variability: how common and rare species shape stability patterns

Empirical knowledge of diversity-stability relationships is mostly based on the analysis of temporal variability. Variability, however, often depends on external factors that act as disturbances, which makes comparisons across systems difficult to interpret. Here, we show how variability can reveal inherent stability properties of ecological communities. This requires that we abandon one-dimensional representations, in which a single variability measurement is taken as a proxy for how stable a system is, and instead consider the whole set of variability values generated by all possible stochastic perturbations. Despite this complexity, in species-rich systems, a generic pattern emerges from community assembly, relating variability to the abundance of perturbed species. Strikingly, the contrasting contributions of different species abundance classes to variability, driven by different types of perturbations, can lead to opposite diversity-stability patterns. We conclude that a multidimensional perspective on variability helps reveal the dynamical richness of ecological systems and the underlying meaning of their stability patterns.

Synchrony affects Taylor's law in theory and data

Taylor's law (TL) is a widely observed empirical pattern that relates the variances to the means of groups of nonnegative measurements via an approximate power law: variance _g ≈ a [Formula: see text] mean _g^b , where g indexes the group of measurements. When each group of measurements is distributed in space, the exponent b of this power law is conjectured to reflect aggregation in the spatial distribution. TL has had practical application in many areas since its initial demonstrations for the population density of spatially distributed species in population ecology. Another widely observed aspect of populations is spatial synchrony, which is the tendency for time series of population densities measured in different locations to be correlated through time. Recent studies showed that patterns of population synchrony are changing, possibly as a consequence of climate change. We use mathematical, numerical, and empirical approaches to show that synchrony affects the validity and parameters of TL. Greater synchrony typically decreases the exponent b of TL. Synchrony influenced TL in essentially all of our analytic, numerical, randomization-based, and empirical examples. Given the near ubiquity of synchrony in nature, it seems likely that synchrony influences the exponent of TL widely in ecologically and economically important systems.

Spatial synchrony in population dynamics: The effects of demographic stochasticity and density regulation with a spatial scale

We generalize a previous simple result by Lande et al. (1999) on how spatial autocorrelated noise, dispersal rate and distance as well as strength of density regulation determine the spatial scale of synchrony in population density. It is shown how demographic noise can be incorporated, what effect it has on variance and spatial scale of synchrony, and how it interacts with the point process for locations of individuals under random sampling. Although the effect of demographic noise is a rather complex interaction with environmental noise, migration and density regulation, its effect on population fluctuations and scale of synchrony can be presented in a transparent way. This is achieved by defining a characteristic area dependent on demographic and environmental variances as well as population density, and subsequently using this area to define a spatial demographic coefficient. The demographic noise acts through this coefficient on the spatial synchrony, which may increase or decrease with increasing demographic noise depending on other parameters. A second generalization yields the modeling of density regulation taking into account that regulation at a given location does not only depend on the density at that site but also on densities in the whole territory or home range of individuals. It is shown that such density regulation with a spatial scale reduces the scale of synchrony in population fluctuations relative to the simpler model with density regulation at each location determined only by the local point density, and may even generate negative spatial autocorrelations.

Sample and population exponents of generalized Taylor's law

Taylor's law (TL) states that the variance V of a nonnegative random variable is a power function of its mean M; i.e., V = aM(b). TL has been verified extensively in ecology, where it applies to population abundance, physics, and other natural sciences. Its ubiquitous empirical verification suggests a context-independent mechanism. Sample exponents b measured empirically via the scaling of sample mean and variance typically cluster around the value b = 2. Some theoretical models of population growth, however, predict a broad range of values for the population exponent b pertaining to the mean and variance of population density, depending on details of the growth process. Is the widely reported sample exponent b ≃ 2 the result of ecological processes or could it be a statistical artifact? Here, we apply large deviations theory and finite-sample arguments to show exactly that in a broad class of growth models the sample exponent is b ≃ 2 regardless of the underlying population exponent. We derive a generalized TL in terms of sample and population exponents b(jk) for the scaling of the kth vs. the jth cumulants. The sample exponent b(jk) depends predictably on the number of samples and for finite samples we obtain b(jk) ≃ k = j asymptotically in time, a prediction that we verify in two empirical examples. Thus, the sample exponent b ≃ 2 may indeed be a statistical artifact and not dependent on population dynamics under conditions that we specify exactly. Given the broad class of models investigated, our results apply to many fields where TL is used although inadequately understood.

Stochastic multiplicative population growth predicts and interprets Taylor's power law of fluctuation scaling

Taylor's law (TL) asserts that the variance of the density (individuals per area or volume) of a set of comparable populations is a power-law function of the mean density of those populations. Despite the empirical confirmation of TL in hundreds of species, there is little consensus about why TL is so widely observed and how its estimated parameters should be interpreted. Here, we report that the Lewontin-Cohen (henceforth LC) model of stochastic population dynamics, which has been widely discussed and applied, leads to a spatial TL in the limit of large time and provides an explicit, exact interpretation of its parameters. The exponent of TL exceeds 2 if and only if the LC model is supercritical (growing on average), equals 2 if and only if the LC model is deterministic, and is less than 2 if and only if the LC model is subcritical (declining on average). TL and the LC model describe the spatial variability and the temporal dynamics of populations of trees on long-term plots censused over 75 years at the Black Rock Forest, Cornwall, NY, USA.

Seabird aggregative patterns: a new tool for offshore wind energy risk assessment

The emerging development of offshore wind energy has raised public concern over its impact on seabird communities. There is a need for an adequate methodology to determine its potential impacts on seabirds. Environmental Impact Assessments (EIAs) are mostly relying on a succession of plain density maps without integrated interpretation of seabird spatio-temporal variability. Using Taylor's power law coupled with mixed effect models, the spatio-temporal variability of species' distributions can be synthesized in a measure of the aggregation levels of individuals over time and space. Applying the method to a seabird aerial survey in the Ebro Delta, NW Mediterranean Sea, we were able to make an explicit distinction between transitional and feeding areas to define and map the potential impacts of an offshore wind farm project. We use the Ebro Delta study case to discuss the advantages of potential impacts maps over density maps, as well as to illustrate how these potential impact maps can be applied to inform on concern levels, optimal EIA design and monitoring in the assessment of local offshore wind energy projects.

Taylor's law and body size in exploited marine ecosystems

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density-mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance-mass allometry). Marine size spectra are known to exhibit density-mass allometry, but variance-mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size-at-entry fishing, in which only fish above a certain size may legally be caught.

Taylor's Law holds in experimental bacterial populations but competition does not influence the slope

Populations vary in time and in space, and temporal variation may differ from spatial variation. Yet, in the past half century, field data have confirmed both the temporal and spatial forms of Taylor's power Law, a linear relationship between log(variance) and log(mean) of population size. Recent theory predicted that competitive species interactions should reduce the slope of the temporal version of Taylor's Law. We tested whether this prediction applied to the spatial version of Taylor's Law using simple, well-controlled laboratory populations of two species of bacteria that were cultured either separately or together for 24 h in media of widely varying nutrient richness. Experimentally, the spatial form of Taylor's Law with a slope of 2 held for these simple bacterial communities, but competitive interactions between the two species did not reduce the spatial Taylor's Law slope. These results contribute to the widespread usefulness of Taylor's Law in population ecology, epidemiology and pest control.