Behavioural dynamics

Interspecific and intraspecific Taylor's laws for frog skin microbes

Amphibians are known to have an abundance of microorganisms colonizing their skin, and these symbionts often protect the host from disease. There are now many comprehensive studies on amphibian skin microbes, but the interspecific and intraspecific abundance distributions (or abundance heterogeneity) of amphibian skin microbes remain unclear. Furthermore, we have a very limited understanding of how the abundance and heterogeneity of microbial communities relate to the body size (or more specifically, skin surface area) of amphibian hosts. In this study, we evaluated the interspecific and intraspecific abundance distribution patterns of amphibian skin microbes and evaluated whether the symbiotic skin microbes of different anuran species share a fundamental heterogeneity scaling parameter. If scaling invariance exists, we hypothesize that a fundamental heterogeneity scaling value also exists. A total of 358 specimens of 10 amphibian host species were collected, and we used Type-I and III Taylor's power law expansions (TPLE) to assess amphibian skin microbial heterogeneity at the community and mixed-species population levels, respectively. The obtained results showed that, at the community scale, a high aggregation of the microbial abundance distribution on the skin barely changed with host size. In a mixed-species population (i.e., a community context), the abundance distribution pattern of mixed microbial species populations also does not change with host size and always remains highly aggregated. These findings suggest that while amphibian skin microbiomes located in different hosts may have different environmental conditions, they share a fundamental heterogeneity scaling parameter, and thus, scale invariance exists. Finally, we found that microhabitat area provided by the host skin is vital to the stability of the symbiotic microbial community.

Power law analysis of the human milk microbiome

The human breast milk microbiome (HMM) has far reached health implications for both mothers and infants, and understanding the structure and dynamics of milk microbial communities is therefore of critical biomedical importance. Community heterogeneity, which has certain commonalities with familiar diversity but also with certain fundamental differences, is an important aspect of community structure and dynamics. Taylor's (1961) power law (TPL) (Nature, 1961) was discovered to govern the mean-variance power function relationship of population abundances and can be used to characterize population spatial aggregation (heterogeneity) and/or temporal stability. TPL was further extended to the community level to measure community spatial heterogeneity and/or temporal stability (Ma 2015, Molecular Ecology). Here, we applied TPL extensions (TPLE) to analyze the heterogeneity of the human milk microbiome by reanalyzing 12 datasets (2115 samples) of the healthy human milk microbiome. Our analysis revealed that the TPLE heterogeneity parameter (b) is rather stable across the 12 datasets, and there were approximately no statistically significant differences among ¾ of the datasets, which is consistent with the hypothesis that the heterogeneity scaling (i.e., change across individuals) of the human microbiome, including HMM, is rather stable or even constant. For this, we built a TPLE model for the pooled 12 datasets (b = 1.906), which can therefore represent the scaling rate of community-level spatial heterogeneity of HMM across individuals. Similarly, we also analyzed mixed-species ("averaged virtual species") level heterogeneity of HMM, and it was found that the mixed-species level heterogeneity was smaller than the heterogeneity at the previously mentioned community level (1.620 vs. 1.906).

Spatial heterogeneity analysis of the human virome with Taylor's power law

Spatial heterogeneity is a fundamental characteristic of organisms from viruses to humans. Measuring heterogeneity is challenging, especially for naked-eye invisible viruses, but of obvious importance. For example, spatial heterogeneity of virus distribution may strongly influence infection spreading and outbreaks in the case of pathogenic viruses; the spatial distribution (i.e., the inter-subject heterogeneity) of commensal viruses within/on our bodies can influence the competition, coexistence, and dispersal of viruses within or between our bodies. Taylor's power law (TPL) was first discovered in the 1960s to describe the spatial distributions of plant and/or animal populations, and since then it has been verified by numerous experimental and theoretical studies. Recently, TPL has been extended from population to community level and applied to bacterial communities. Here we report the first comprehensive testing of the TPL fitted to human virome datasets. It was found that the human virome follows the TPL as bacterial communities do. Furthermore, the TPL heterogeneity scaling parameter of human virome is virtually the same as that of the human bacterial microbiome (1.916 vs. 1.926). We postulate that the extreme closeness of human viruses and bacteria in heterogeneity scaling coefficients could be attributed to the fact that most of the viruses that were annotated in this study actually belong to bacteriophages (86% viral OTUs) that "piggyback" on their bacterial hosts, and their distributions are likely host-dependent. The scaling parameter, which measures the inter-subject heterogeneity changes, should be an innate property of human microbiomes including both bacteria and viruses. It is similar to the acceleration coefficient of the gravity (g = 9.8) as specified by Newton's law, which is invariant on the earth. Nevertheless, we caution that our postulation is contingent on an implicit assumption that the proportion of bacteriophages to total virome may not change significantly when more virus species can be identified in future.

Heterogeneity-disease relationship in the human microbiome-associated diseases

Space is a critical and also challenging frontier in human microbiome research. It has been found that lack of consideration of scales beyond individual and ignoring of microbe dispersal are two crucial roadblocks in preventing deep understanding of the spatial heterogeneity of human microbiome. Assessing and interpreting the heterogeneity and dispersal in microbiomes explicitly are particularly challenging, but implicit approaches such as Taylor's power law (TPL) can be rather effective. Based on TPL, which achieved a rare status of ecological laws, we introduce a general methodology for characterizing the spatial heterogeneity of microbiome (i.e. characterization of microbial spatial distribution) and further apply it for investigating the heterogeneity-disease relationship (HDR) via analyzing a big dataset of 26 MAD (microbiome-associated disease) studies covering nearly all high-profile MADs including obesity, diabetes and gout. It was found that in majority of the MAD cases, the microbiome was sufficiently resilient to endure the disease disturbances. Specifically, in ∼10-16% cases, disease effects were significant-the healthy and diseased cohorts exhibited statistically significant differences in the TPL heterogeneity parameters. We further compared HDR with classic diversity-disease relationship (DDR) and explained their mechanistic differences. Both HDR and DDR cross-verified remarkable resilience of the human microbiomes against MADs.

Predicting the Outbreak Risks and Inflection Points of COVID-19 Pandemic with Classic Ecological Theories

Predicting the outbreak risks and/or the inflection (turning or tipping) points of COVID-19 can be rather challenging. Here, it is addressed by modeling and simulation approaches guided by classic ecological theories and by treating the COVID-19 pandemic as a metapopulation dynamics problem. Three classic ecological theories are harnessed, including TPL (Taylor's power-law) and Ma's population aggregation critical density (PACD) for spatiotemporal aggregation/stability scaling, approximating virus metapopulation dynamics with Hubbell's neutral theory, and Ma's diversity-time relationship adapted for the infection-time relationship. Fisher-Information for detecting critical transitions and tipping points are also attempted. It is discovered that: (i) TPL aggregation/stability scaling parameter (b > 2), being significantly higher than the b-values of most macrobial and microbial species including SARS, may interpret the chaotic pandemic of COVID-19. (ii) The infection aggregation critical threshold (M 0) adapted from PACD varies with time (outbreak-stage), space (region) and public-health interventions. Exceeding M 0, local contagions may become aggregated and connected regionally, leading to epidemic/pandemic. (iii) The ratio of fundamental dispersal to contagion numbers can gauge the relative importance between local contagions vs. regional migrations in spreading infections. (iv) The inflection (turning) points, pair of maximal infection number and corresponding time, are successfully predicted in more than 80% of Chinese provinces and 68 countries worldwide, with a precision >80% generally.

Estimating the Optimum Coverage and Quality of Amplicon Sequencing With Taylor's Power Law Extensions

Theoretical analysis of DNA sequencing coverage problem has been investigated with complex mathematical models such as Lander-Waterman expectation theory and Stevens' theorem for randomly covering a domain. In the field of metagenomics sequencing, several approaches have been developed to estimate the coverage of whole-genome shotgun sequencing, but surprisingly few studies addressed the coverage problem for marker-gene amplicon sequencing, for which arguably the biggest challenge is the complexity or heterogeneity of microbial communities. Overall, much of the practice still relies variously on speculation, semi-empirical and ad hoc heuristic models. Conservatively raising coverage may ensure the success of sequencing project, but often with unduly cost. In this study, we borrow the principles and approaches of optimum sampling methodology originated in applied entomology, achieved equal success in plant pathology and parasitology, and plays a critical role in the decision-making for global crop and forest protection against economic pests since 1970s when the pesticide crisis and food safety concerns forced the reduction of pesticide usages, which in turn requires reliable sampling techniques for monitoring pest populations. We realized that sequencing coverage is essentially an optimum sampling problem. Perhaps the only essential difference between sampling insects and sampling microbiome is the "instrument" used. In traditional entomology, it is usually humans that visually count the numbers of insects, occasionally aided by binocular microscope. In the metagenomics research, it is the DNA sequencers that count the number of DNA reads. Furthermore, a key theoretical foundation for sampling insect pest populations, i.e., Taylor's power law, which achieved rare status of ecological law and captures the population aggregation, has been recently extended to the community level for describing community heterogeneity and stability, namely, Taylor's power law extensions (TPLEs). This theoretical advance enabled us to develop a novel approach to assessing the quality and determining optimum reads (coverage) of amplicon sequencing operations. Specifically, two applications were developed: one is, in hindsight, to assess the quality of amplicon sequencing operation in terms of the precision and confidence levels. Another is, prior to sequencing operation, to determine the minimum sequencing efforts for a sequencing project to achieve preset precision and confidence levels.

Assessing and Interpreting the Metagenome Heterogeneity With Power Law

There are two major sequencing technologies for investigating the microbiome: the amplicon sequencing that generates the OTU (operational taxonomic unit) tables of marker genes (e.g., bacterial 16S-rRNA), and the metagenomic shotgun sequencing that generates metagenomic gene abundance (MGA) tables. The OTU table is the counterpart of species abundance tables in macrobial ecology of plants and animals, and has been the target of numerous ecological and network analyses in recent gold rush for microbiome research and in great efforts for establishing an inclusive theoretical ecology. Nevertheless, MGA analyses have been largely limited to bioinformatics pipelines and ad hoc statistical methods, and systematic approaches to MGAs guided by classic ecological theories are still few. Here, we argue that, the difference between “gene kinds” and “gene species” are nominal, and the metagenome that a microbiota carries is essentially a ‘community’ of metagenomic genes (MGs). Each row of a MGA table represents a metagenome of a microbiota, and the whole MGA table represents a ‘meta-metagenome’ (or an assemblage of metagenomes) of N microbiotas (microbiome samples). Consequently, the same ecological/network analyses used in OTU analyses should be equally applicable to MGA tables. Here we choose to analyze the heterogeneity of metagenome by introducing classic Taylor’s power law (TPL) and its recent extensions in community ecology. Heterogeneity is a fundamental property of metagenome, particularly in the context of human microbiomes. Recent studies have shown that the heterogeneity of human metagenomes is far more significant than that of human genomes. Therefore, without deep understanding of the human metagenome heterogeneity, personalized medicine of the human microbiome-associated diseases is hardly feasible. The TPL extensions have been successfully applied to measure the heterogeneity of human microbiome based on amplicon-sequencing reads of marker genes (e.g., 16s-rRNA). In this article, we demonstrate the analysis of the metagenomic heterogeneity of human gut microbiome at whole metagenome scale (with type-I power law extension) and metagenomic gene scale (type-III), as well as the heterogeneity of gene clusters, respectively. We further examine the influences of obesity, IBD and diabetes on the heterogeneity, which is of important ramifications for the diagnosis and treatment of human microbiome-associated diseases.

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.

Twenty-Five Years of the Binary Power Law for Characterizing Heterogeneity of Disease Incidence

Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range of methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor's power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parameter estimates from over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units.

1/ f Noise and multifractality from bristlecone pine growth explained by the statistical convergence of random data

Tree-ring growth records from bristlecone pines reveal an irregular pattern of fluctuations that have been linked to climatic change but otherwise have remained poorly understood. We find within these records evidence for a temporally related variance to mean power law, 1/ f noise and multifractality that empirically resembles a fractal stochastic process and could be attributed to self-organized criticality. These growth records, however, also conformed to a non-Gaussian statistical distribution (the Tweedie compound Poisson distribution) characterized by an inherent variance to mean power law, that by itself implies 1/ f noise. This distribution has a fundamental role in statistical theory as a focus of convergence for many types of random data, much like the Gaussian distribution has with the central limit theorem. The growth records were also multifractal, with the dimensional exponent of the Tweedie distribution critically balanced near the transition point between fractal stochastic processes and gamma distributed data, possibly consequent to a related convergence effect. Non-Gaussian random systems, like those related to bristlecone pine tree growth, may express 1/ f noise and multifractality through mathematical convergence effects alone, without the dynamical assumptions of self-organized criticality.

Distribution and Feeding Behavior of Omorgus suberosus (Coleoptera: Trogidae) in Lepidochelys olivacea Turtle Nests

Omorgus suberosus (Fabricius, 1775) has been identified as a potential predator of the eggs of the turtle Lepidochelys olivacea (Eschscholtz, 1829) on one of the main turtle nesting beaches in the world, La Escobilla in Oaxaca, Mexico. This study presents an analysis of the spatio–temporal distribution of the beetle on this beach (in areas of high and low density of L. olivacea nests over two arrival seasons) and an evaluation, under laboratory conditions, of the probability of damage to the turtle eggs by this beetle. O. suberosus adults and larvae exhibited an aggregated pattern at both turtle nest densities; however, aggregation was greater in areas of low nest density, where we found the highest proportion of damaged eggs. Also, there were fluctuations in the temporal distribution of the adult beetles following the arrival of the turtles on the beach. Under laboratory conditions, the beetles quickly damaged both dead eggs and a mixture of live and dead eggs, but were found to consume live eggs more slowly. This suggests that O. suberosus may be recycling organic material; however, its consumption of live eggs may be sufficient in some cases to interrupt the incubation period of the turtle. We intend to apply these results when making decisions regarding the L. olivacea nests on La Escobilla Beach, one of the most important sites for the conservation of this species.

A Process-Independent Explanation for the General Form of Taylor's Law

Taylor's law (TL) describes the scaling relationship between the mean and variance of populations as a power law. TL is widely observed in ecological systems across space and time, with exponents varying largely between 1 and 2. Many ecological explanations have been proposed for TL, but it is also commonly observed outside ecology. We propose that TL arises from the constraining influence of two primary variables: the number of individuals and the number of censuses or sites. We show that most possible configurations of individuals among censuses or sites produce the power-law form of TL, with exponents between 1 and 2. This "feasible set" approach suggests that TL is a statistical pattern driven by two constraints, providing an a priori explanation for this ubiquitous pattern. However, the exact form of any specific mean-variance relationship cannot be predicted in this way, that is, this approach does a poor job of predicting variation in the exponent, suggesting that TL may still contain ecological information.

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.

Taylor's power law and fluctuation scaling explained by a central-limit-like convergence

A power function relationship observed between the variance and the mean of many types of biological and physical systems has generated much debate as to its origins. This Taylor's law (or fluctuation scaling) has been recently hypothesized to result from the second law of thermodynamics and the behavior of the density of states. This hypothesis is predicated on physical quantities like free energy and an external field; the correspondence of these quantities with biological systems, though, remains unproven. Questions can be posed as to the applicability of this hypothesis to the diversity of observed phenomena as well as the range of spatial and temporal scales observed with Taylor's law. We note that the cumulant generating functions derived from this thermodynamic model correspond to those derived over a quarter century earlier for a class of probabilistic models known as the Tweedie exponential dispersion models. These latter models are characterized by variance-to-mean power functions; their phenomenological basis rests with a central-limit-theorem-like property that causes many statistical systems to converge mathematically toward a Tweedie form. We review evaluations of the Tweedie Poisson-gamma model for Taylor's law and provide three further cases to test: the clustering of single nucleotide polymorphisms (SNPs) within the horse chromosome 1, the clustering of genes within human chromosome 8, and the Mertens function. This latter case is a number theoretic function for which a thermodynamic model cannot explain Taylor's law, but where Tweedie convergence remains applicable. The Tweedie models are applicable to diverse biological, physical, and mathematical phenomena that express power variance functions over a wide range of measurement scales; they provide a probabilistic description for Taylor's law that allows mechanistic insight into complex systems without the assumption of a thermodynamic mechanism.

Origins of Taylor's power law for fluctuation scaling in complex systems

Taylor's fluctuation scaling (FS) has been observed in many natural and man-made systems revealing an amazing universality of the law. Here, we give a reliable explanation for the origins and abundance of Taylor's FS in different complex systems. The universality of our approach is validated against real world data ranging from bird and insect populations through human chromosomes and traffic intensity in transportation networks to stock market dynamics. Using fundamental principles of statistical physics (both equilibrium and nonequilibrium) we prove that Taylor's law results from the well-defined number of states of a system characterized by the same value of a macroscopic parameter (i.e., the number of birds observed in a given area, traffic intensity measured as a number of cars passing trough a given observation point or daily activity in the stock market measured in millions of dollars).

Spatial and temporal stability of the estimated parameters of the binary power law

The incidence of hop powdery mildew on leaves, caused by Podosphaera macularis, collected from 1,606 transects in 77 commercial hop yards in Oregon and Washington over 9 years was used to assess variability in heterogeneity of disease and the estimated binary power law parameters. Spatial analyses of data sets were conducted at the level of individual rows (row level) and multiple rows within a yard (yard level). The binary power law provided a good fit to all data sets, with R(2) values ranging from 0.933 to 0.993. At the row level, the intercept parameter ln(A(x)) was >0 for 8 years, but was not significantly greater than 0 in 2006. The parameter b was greater than 1 for all row-level data sets collected from 1999 to 2005, but was <1 in 2006 and not significantly different from 1 in 2007. Covariance analysis indicated the factor 'region' affected ln(A(x)) in 3 years, and b in 2 years. 'Cultivar' had an effect on ln(A(x)) in 3 years and b in year. At the yard level, ln(A(x)) was greater than 0 for 6 years, but in 2006 and 2007, ln(A(x)) was not significantly different from 0. The slope parameter b was greater than 1 in 6 years, but was not significantly different from 1 in 2006 and 2007. Differences in b among years were large enough to have practical implications for sample sizes and precision of fixed and sequential sampling. Although the binary power law parameter tended to be relatively stable, variability of the estimated parameters may have practical consequences for sampling precision and costs.

Highlighting ontogenetic shifts in habitat use by nocturnal coral reef fish

The lagoon of Moorea Island was characterised by 12 distinct reef zones. Visual censuses allowed us to document the spatial distributions of recently settled juveniles vs adults of 17 nocturnal fish species among the 12 reef zones. Five distinct patterns in habitat use were found: an increase in the number of reef zones used during the adult stage (four species); a decrease in the number of reef zones adults used compared to recently settled juveniles (two species); the use of different reef zones (one species); the use of same reef zones but with relative densities different (one species); and no change in habitat use (nine species). Overall, this study is the first to explore the use of space by a broad range of nocturnal fish taxa to document the patterns and determinism of habitat shifts between juvenile and adult life stages.

A spatially explicit approach to estimating species occupancy and spatial correlation

1. Understanding and predicting the form of species distributions, or occupancy patterns, is fundamental to macroecology and is dependent on the identification of scaling relationships that underlie the patterns observed. 2. Occupancy-abundance models based on the negative binomial distribution and Taylor's power law are spatially implicit, rather than explicit, as they include no information on the relative positions of individuals. Here we present a spatially explicit model, the spatial scaling occupancy (SSO) model, to estimate species occupancy and spatial correlation, based on join-count statistics, or a pair approximation, approach. This model provides a spatially explicit description of species range size and aspects of range structure. 3. Occupancy data from Drosophilidae species inhabiting a decaying fruit mesocosm were used to test the SSO model. Predictions from the spatially implicit and explicit models were largely equally accurate. The SSO model is thus more efficient as it is less data demanding, and more informative as it provides an estimation of spatial correlation. 4. The results also showed that species distribution patterns differ when examined with spatially implicit vs. explicit approaches; the scaling relationship between occupancy and local density identifies a focal grain for studying the scale-dependent nature of ecological relationships; and the longer the length of the sample edge, the higher the occupancy observed under conditions of spatial aggregation. 5. The SSO model presents a step towards a general scaling model for occupancy, and demonstrates that the inclusion of spatially explicit information in macroecological models warrants further attention.

Host manipulation by Ligula intestinalis: a cause or consequence of parasite aggregation?

Previous investigations suggest that the infection of the cyprinid roach, Rutilus rutilus, with the larval plerocercoid forms of the cestode, Ligula intestinalis, creates behavioural and morphological changes in the fish host, potentially of adaptive significance to the parasite in promoting transmission to definitive avian hosts. Here we consider whether these behavioural changes are important in shaping the distribution of parasite individuals across the fish population. An examination of field data illustrates that fish infected with a single parasite were more scarce than expected under the negative binomial distribution, and in many months were more scarce than burdens of two, three or more, leading to a bimodal distribution of worm counts (peaks at 0 and >1). This scarcity of single-larval worm infections could be accounted for a priori by a predominance of multiple infection. However, experimental infections of roach gave no evidence for the establishment of multiple worms, even when the host was challenged with multiple intermediate crustacean hosts, each multiply infected. A second hypothesis assumes that host manipulation following an initial single infection leads to an increased probability of subsequent infection (thus creating a contagious distribution). If manipulated fish are more likely to encounter infected first-intermediate hosts (through microhabitat change, increased ingestion, or both), then host manipulation could act as a powerful cause of aggregation. A number of scenarios based on contagious distribution models of aggregation are explored, contrasted with alternative compound Poisson models, and compared with the empirical data on L. intestinalis aggregation in their roach intermediate hosts. Our results indicate that parasite-induced host manipulation in this system can function simultaneously as both a consequence and a cause of parasite aggregation. This mutual interaction between host manipulation and parasite aggregation points to a set of ecological interactions that are easily missed in most experimental studies of either phenomenon.

A quantitative study of day-night changes in the spatial distribution of insects in a stony stream

1

As many invertebrates are nocturnal, their spatial distribution may change from day to night. This behavioural aspect of their population dynamics has been ignored, but is now examined for the first time by testing the hypotheses: (i) a power function was a suitable model for the spatial distribution of common species of Ephemeroptera, Plecoptera and Trichoptera in a stony stream; (ii) the spatial distribution varied between species but was similar within species for larvae greater and smaller than half‐size; (iii) diurnal and nocturnal spatial distributions were significantly different for each species. To ensure that the conclusions were consistent, large samples (n = 30) were taken near midday and midnight in April, June and November over 4 years.

2

Twenty–one species were taken in sufficient numbers for the analyses; seven species were too sparse to be included. The first hypothesis was supported. A power function, relating spatial variance (s²) to mean (m), was an excellent fit in all the analyses (P < 0·001, r² > 0·95), i.e. the spatial variance was density–dependent. The power b, often used as an ‘index of aggregation’, varied in the range 0·88–2·50.

3

Most analyses supported the second hypothesis. For four species, the difference between the two size groups was just significant (P < 0·05), but was due to inadequate data for three species. Large larvae of the fourth species, the caddis Odontocerum albicorne, were less aggregated than small larvae at night, and were the only group with a b‐value less than one.

4

The third hypothesis was partially supported. The distribution did not change significantly (P > 0·05) for nine species; five burrowers in gravel, moss or mud, two highly mobile predators, one sedentary, case–building, Trichoptera species, and one net–spinning Trichoptera species. Aggregation was reduced significantly (P < 0·001) at night for four species, all case–building Trichoptera larvae. Aggregation increased significantly (P < 0·001) at night, except at low densities, for the remaining eight species, one being a nocturnal predator and the others being herbivorous species; all occurred frequently in night samples of invertebrate drift. Day–night changes in spatial distribution were therefore an essential part of the behavioural dynamics of 12 of the 21 species, and should be investigated in other species, including terrestrial species.