Individual Size Distribution Research Articles

Bayesian hierarchical modelling of size spectra

Abstract A fundamental pattern in ecology is that smaller organisms are more abundant than larger organisms. This pattern is known as the individual size distribution (ISD), which is the frequency distribution of all individual body sizes in an ecosystem. The ISD is described by a power law and a major goal of size spectra analyses is to estimate the exponent of the power law, λ. However, while numerous methods have been developed to do this, they have focused almost exclusively on estimating λ from single samples. Here, we develop an extension of the truncated Pareto distribution within the probabilistic modelling language Stan. We use it to estimate multiple λs simultaneously in a hierarchical modelling approach. The most important result is the ability to examine hypotheses related to size spectra, including the assessment of fixed and random effects, within a single Bayesian generalized mixed model. While the example here uses size spectra, the technique can also be generalized to any data that follow a power law distribution.

Maximum likelihood outperforms binning methods for detecting differences in abundance size spectra across environmental gradients.

Individual body size distributions (ISD) within communities are remarkably consistent across habitats and spatiotemporal scales and can be represented by size spectra, which are described by a power law. The focus of size spectra analysis is to estimate the exponent ( ) of the power law. A common application of size spectra studies is to detect anthropogenic pressures. Many methods have been proposed for estimating most of which involve binning the data, counting the abundance within bins, and then fitting an ordinary least squares regression in log-log space. However, recent work has shown that binning procedures return biased estimates of compared to procedures that directly estimate using maximum likelihood estimation (MLE). While it is clear that MLE produces less biased estimates of site-specific λ's, it is less clear how this bias affects the ability to test for changes in λ across space and time, a common question in the ecological literature. Here, we used simulation to compare the ability of two normalised binning methods (equal logarithmic and log2 bins) and MLE to (1) recapture known values of , and (2) recapture parameters in a linear regression measuring the change in across a hypothetical environmental gradient. We also compared the methods using two previously published body size datasets across a natural temperature gradient and an anthropogenic pollution gradient. Maximum likelihood methods always performed better than common binning methods, which demonstrated consistent bias depending on the simulated values of . This bias carried over to the regressions, which were more accurate when was estimated using MLE compared to the binning procedures. Additionally, the variance in estimates using MLE methods is markedly reduced when compared to binning methods. The error induced by binning methods can be of similar magnitudes as the variation previously published in experimental and observational studies, bringing into question the effect sizes of previously published results. However, while the methods produced different regression slope estimates, they were in qualitative agreement on the sign of those slopes (i.e. all negative or all positive). Our results provide further support for the direct estimation of and its relative variation across environmental gradients using MLE over the more common methods of binning.

DNA Sizing with pg/μL Sensitivity for Cell-Free DNA Analysis with the μLAS Technology.

The μLAS technology enables in-line DNA concentration and separation in a microchannel. Here, we describe its operation to analyze the size profile of cell-free DNA (cfDNA) extracted from blood plasma. Operated on commercial systems for capillary electrophoresis, we provide the size distribution of healthy individuals or patients using an input of 10μL.

Temporal changes in the individual size distribution modulate the long‐term trends of biomass and energy use of North American breeding bird communities

AbstractAimThe frequency of different body sizes in an ecological community (the individual size distribution, or ISD) is a key link between the number of individual organisms present in a community and community function—total biomass or total energy use. If the ISD changes over time, the dynamics of community function may become decoupled from trends in abundance. Understanding how, and how often, the ISD modulates the relationship between abundance, biomass and energy use is of critical importance to understand biodiversity trends in the Anthropocene. Here, we conduct the first macroecological‐scale analysis of this type for avian communities.LocationNorth America, north of Mexico.Time Period1989–2018.Major Taxa StudiedBreeding birds.MethodsWe used species' traits to generate annual ISDs for bird communities in the North American Breeding Bird Survey. We compared the long‐term trends in total biomass and energy use to the trends generated from a null model of an unchanging ISD.ResultsTrends in biomass have been evenly split between increases and decreases, but the trends predicted by the null model were dominated by decreases. A substantial number of communities have undergone a shift in the ISD favouring larger bodied species, resulting in a less negative trend in biomass than would be expected had the ISD remained static. Trends in energy use more closely paralleled the null model.Main ConclusionsTaking changes in the ISD into account qualitatively changes the continental‐scale picture of how biomass and energy use have changed over the past 30 years. For North American breeding birds, shifts in species composition favouring larger bodied species may have partially offset declines in standing biomass driven by losses of individuals over the past 30 years.

Optimal heat emissivity control of n population system based on individual size-distribution

This paper generalizes a class of controllability problems based on the scale structure population system model. Based on the comparison principle of linear systems, the solution of the nonlinear system model is obtained by referring to the fixed point theorem. The non-negative, boundedness, existence, and uniqueness of the solution of the system model are established. The optimality condition is described in detail by means of a normal cone and conjugate system under the condition of proving the continuous dependence of the state environment on the solution to control variables.

Earthquake disturbance shifts metabolic energy use and partitioning in a monodominant forest

AbstractAimBoth macroecology and disturbance ecology have long been used to characterize population‐ and community‐level patterns across scales, but the integration of both approaches in characterizing disturbed ecosystems is rare. Here, we use the maximum entropy theory of ecology (METE) to model the individual size distribution (ISD) of trees in pre‐ and post‐disturbance tree populations and estimate the corresponding metabolic scaling exponents.LocationNew Zealand.Time Period1987–1999.Major Taxa StudiedMountain beech (Fuscospora cliffortioides Nothofagaceae).MethodsMETE uses information entropy and empirical macro‐state variables to constrain predictions of ecological distributions related to biodiversity. METE has successfully predicted a range of biodiversity metrics in static or relatively undisturbed conditions. However, METE can fail to accurately model ecological patterns in disturbed ecosystems. We extend existing theoretical predictions to a highly disturbed ecosystem by treating the metabolic scaling exponent and Lagrange multipliers as free parameters in METE.ResultsWe showed that the fully parameterized METE (FP‐METE) model reasonably predicted the ISD of mountain beech populations in a monodominant forest after a strong earthquake, which restructured the forest. Furthermore, the FP‐METE model revealed that decreasing metabolic scaling exponent drove the substantial decline of total metabolic rate energy and the redistribution of energy towards smaller trees after the earthquake. Increased number of small trees was not sufficient to capture the full impact of disturbance on forest energy use.Main ConclusionsOur FP‐METE model applies an informatics approach to estimate the metabolic scaling relationship. We find that instead of maintaining a fixed value, the metabolic scaling exponent is variable among populations, and declines significantly after an earthquake disturbance. This leads to major shifts in the total population metabolic energy and energy distribution. With this approach, we now have the opportunity to advance beyond categorizing forms of mathematical distributions that describe biodiversity patterns and move into a predictive framework where the true constraints on ecosystems and their dynamics emerge.

Zooplankton community size structure across lakes within a semi-arid landscape: the effect of temperature and salinity

AbstractBody size is a master trait controlling biological communities and ecosystem functioning. Mean population size not only depends on the size of individuals, but also on the size distribution of individuals within the population. Mean community size is additionally influenced by the composition of species (larger- or smaller-sized species). Shallow lakes within semi-arid landscapes are prone to experience large changes in temperature and salinity, which affect the zooplankton size structure. Higher temperatures are expected to result in smaller average body size, while the effect of salinity appears to depend on the range under study. Here we analyze zooplankton body size patterns across shallow lakes from the semi-arid central region of Argentina. All community size descriptors point to decreasing size and a narrow size range at higher temperatures. On the other hand, the maximum average community body size occurred at intermediate (~30 gL−1) salinity levels. The combined effect of both variables resulted in a bell-shaped pattern, with maximum community body size toward lower temperatures and intermediate salinities. Based on future temperature scenarios, one may anticipate an overall decrease in community body size. But such prediction is strongly conditioned by regional and local trends in salinity.

Maximum entropy models reveal spatial variation of metabolic scaling in stream fish communities.

Metabolic scaling provides valuable information about the physiological and ecological functions of organisms, although few studies have quantified the metabolic scaling exponent (b) of communities under natural conditions. Maximum entropy theory of ecology (METE) is a constraint-based unified theory with the potential to empirically assess the spatial variation of the metabolic scaling. Our main goal is to develop a novel method of estimating b within a community by integrating metabolic scaling and METE. We also aim to study the relationships between the estimated b and environmental variables across communities. We developed a new METE framework to estimate b in 118 stream fish communities in the north-eastern Iberian Peninsula. We first extended the original maximum entropy model by parameterizing b in the model prediction of the community-level individual size distributions and compared our results with empirical and theoretical predictions. We then tested the effects of abiotic conditions, species composition and human disturbance on the spatial variation of community-level b. We found that community-level b of the best maximum entropy models showed great spatial variability, ranging from 0.25 to 2.38. The mean exponent (b = 0.93) resembled the community-aggregated mean values from three previous metabolic scaling meta-analyses, all of which were greater than the theoretical predictions of 0.67 and 0.75. Furthermore, the generalized additive model showed that b reached maximum at the intermediate mean annual precipitation level and declined significantly as human disturbance intensified. The parameterized METE is proposed here as a novel framework for estimating the metabolic pace of life of stream fish communities. The large spatial variation of b may reflect the combined effects of environmental constraints and species interactions, which likely have important feedback on the structure and function of natural communities. Our newly developed framework can also be applied to study the impact of global environmental pressures on metabolic scaling and energy use in other ecosystems.

A pilot tagging program on southern rays bream (Brama australis): methodology and preliminary recaptures

The southern rays bream (Brama australis) is a highly migratory, epi-mesopelagic species supporting an important artisanal fishery off central-southern Chile. Despite its importance, several questions exist about this species's demography and migratory routes. The first step in understanding the migratory behavior of B. australis is to test the feasibility of a conventional tagging program, a standard mark-recapture method, to infer migration in fish. Between February 2020 and December 2021, conventional tagging was conducted during 21 fishing trips on board artisanal vessels off Lebu harbor (Biobío Region, Chile) using gillnets, longlines, and handlines. Three thousand nine hundred forty-six individuals of B. australis between 30 and 55 cm fork length were tagged using external T-anchor bar labels (commonly known as "spaghetti"). Approximately 100 and 200 fish were tagged per fishing trip using longlines and gillnets, respectively. The size distribution of the tagged individuals was consistent with those retained in the catch, with 90% of tagged fish being longer than the fork length at 50% maturity. Eight tags have been recovered off the coast of Lebu up to May 2022. With times at liberty between 50 and 537 days. These preliminary recaptures are also analyzed in the context of the conceptual model for demography and migration proposed for this species in Chile. The main conclusion of this research is that a conventional tagging program is feasible for B. australis in Chile.

Life history traits of the deep-water medusa Periphylla periphylla as revealed through failure and recovery of recruitment

Extended recruitment failure and subsequent success of the coronate medusa Periphylla periphylla in a Norwegian fjord provided a unique opportunity to estimate age-related biological traits by combining individual size distribution in the population over time with previously published data. The average growth rate decreased exponentially with age, from 0.55% day−1 during the first year to <0.17% day−1 after four years. This species becomes mature at the third year, when females carry approximately 10 mature oocytes. At an age of 9 years, the medusa is on average 12 cm in diameter and carries over 1000 mature oocytes. Recruitment of juveniles, 0.5–1 cm diameter, was estimated to be 15 female−1 year−1 in Halsafjord; mortality from egg to juvenile 1 cm in diameter, using oocyte turnover times (T) of 1–12 months, was 93% (T = 12 months) to 99.95% (T = 1 month). Eggs and juveniles younger than 10 months are not capable of vertical migration and remain deeper than the sill depth where regular fjord circulation occurs. Therefore they are only vulnerable to deep-water renewal, and a fjord population of P. periphylla is estimated to gradually decrease recruitment with increased frequency of deep-water renewal and reach zero recruitment with renewal intervals of 10 months or less. It is hypothesized that differences in regular and intermittent deep-water renewal is the main factor causing variability in size (age) distribution between fjord populations.

Fish size spectra from imaging sonar reveal variation in habitat use across nearshore coastal ecosystems

Structured coastal habitats provide foraging opportunities and refuge from predation for fish species of varying size and function. However, comprehensive assessments of fish communities among ecosystems are challenging because of biases arising across traditional sampling methods that target subsets of the community in different habitats (e.g. traps, seines, trawls, or visual census). Here, we used dual-frequency identification sonar (DIDSON) to examine shallow, nearshore habitat use by fishes in multiple structured habitats (seagrass, coral reefs, oyster reefs, rocky reefs, mangroves, woody debris, and docks) relative to soft-sediment habitat across 4 study locations ranging from tropical to temperate: Bocas del Toro, Panama, and Florida, Maryland, and California, USA. We then examined the distribution of individual fish sizes using size-spectra analysis. For temperate docks (Maryland) and eelgrass beds (California), size-spectra slopes were less steep than for soft-sediment habitats, indicating that larger fish associated with these structured habitats. No differences in slopes were identified for (sub)tropical Florida or Panama, although spectra intercepts from docks were higher in each location relative to soft sediment, denoting higher total abundance. Our results suggest geographically stratified habitat use with a tendency towards comparatively greater importance of structure in determining fish size distribution at higher latitudes, and greater importance of structured habitat in governing total abundance at lower latitudes. This study also demonstrates the potential of imaging sonar as a new tool for revealing variation in fish communities among habitats at local to continental scales.

Patterns of species richness, abundance and individual-size distributions in native stream-fish assemblages invaded by exotic and translocated fishes.

Predicting the impacts of species introductions long has attracted the attention of ecologists yet there still is limited insight into how impacts on native assemblages vary with the degree of shared evolutionary context. Here, we used data from 535 stream-fish surveys from 15 catchments in north-eastern Spain (99,700 km2) to explore whether the relative effects on native fishes differ between fish introductions from two different ecoregions (i.e., evolutionary contexts), namely, catchments within Iberian Peninsula (i.e., 'translocated species') and catchments beyond Iberian Peninsula (i.e., 'exotic fishes'). We used hierarchical Bayesian models to relate taxon richness, abundance, and the individual-size distributions (ISDs) of native fishes to the presence, abundance, and weighted trophic level (TL) of translocated and exotic fishes, conditional on geographic and habitat covariates. Environmental covariates dominated the percentage of explained variance (≥ 65%) for all responses. Translocated fishes accounted for more of the explained variance than did exotic fishes for ISDs and abundance, but not for native fish species richness. The presence of translocated fishes was associated with lower abundance and richness of native fishes, with individuals being smaller in the presence of translocated fishes of higher TL. The presence of exotic fishes was associated with a greater abundance and richness of native fishes, with individuals generally being larger in the presence of exotic fishes. Our study suggests that translocated fishes could be as problematic as exotic fishes when angling and water transfers among catchments to deal with climate change may increase the establishment of translocated fishes. We also discuss the difficulties of using fish body size as species-blind, transferable assemblage-level trait in fish monitoring.

Point pattern analysis as a tool for assessing disease spread and population features in remaining sanctuaries of the critically endangered bivalve Pinna nobilis

An emergent disease has relegated populations of the Mediterranean pen shell, Pinna nobilis L. critically endangered to sanctuaries featuring salinities outside the 36.5 to 39 range. Point pattern analysis was used in three areas of the Alfacs Bay (Ebro Delta) still hosting pen shells to assess the possible undergoing of disease spread by comparing the spatial distribution of live individuals vs. empty shells across spatial scales. We also evaluated the importance of other ecological aspects of conservation relevance such as the size distribution of individuals, and the possible association to seagrass habitats. The population assessment showed no recent mortality and a clear dominance of large adults among empty shells (97.3%) pointing to no disease spread during the study period. At the low spatial scale Nearest Neighbor (NN) analyses evidenced significant clustering (NN Ratios of 0.4–0.8), but in one of the zones NN distances were closer in empty shells than in live individuals, suggesting a former localized outbreak. At the larger spatial scale, MDSCA confirmed clustering patterns up to distances of 115 to 190 m, with higher aggregation of empty shells at the same study zone. The bay also featured low juvenile availability (3.2%), which risks the continuity of the population. No evidence for habitat or conspecific selection could be observed from abundance patterns and variation in NN across study regions. Our research provides a tool for assessing population condition in paralic environments, where salinity conditions tend to slow down disease spread, thus allowing a time gap for undertaking conservation decisions.

Probability-based approach for characterization of microarchitecture and its effect on elastic properties of trabecular bone

Trabecular bone is a random cellular solid with an interconnected network of plate-like and rod-like components. However, the structural randomness and complexity have hindered rigorous mathematical modeling of trabecular bone microarchitecture. Recent advancements in imaging processing techniques have enabled us to define the size, orientation, and spatial location of individual trabecular plates and rods in trabecular bone. Based on the essential information, this study proposed a probability-based approach to define the size, orientation, and spatial distributions of trabecular plates and rods for trabecular bone cubes (N = 547) acquired from six human cadaver proximal femurs. Using two groups of probability-based parameters, it was attempted to capture microarchitectural details, which could not be captured by the existing histomorphometric parameters, but crucial to the elastic properties of trabecular bone. The elastic properties of the trabecular bone cubes in three principal axes were estimated using microCT based finite element (FE) simulations. Based on the results of multivariate multiple regression modeling, the efficacy of the two groups of probability-based parameters in prediction of the elastic properties was verified in comparison with that of the existing histomorphometric parameters (BV/TV, Tb.Th, Tb.Sp, DA, EF.Med, and Conn.D). The results indicated that the regression models trained using the probability-based parameters had a comparable and even better accuracy (rMSE = 0.621 and 0.548) than that of the histomorphometric parameters (rMSE = 0.647). More importantly, the probability-based parameters could provide more insights into some unexplored microarchitectural features, such as individual trabecular size, orientation, and spatial distributions, which are also critical to the elastic properties of trabecular bone.

Genetic and Environmental Effects on Grain Size Uniformity in Winter Wheat

Grain size is an important yield component and also influences flour yield, seed vigor and early plantlet development. It is usually described by the weight (or mass) of thousand grains or average of dimensions of a sample, without paying attention to the variability of individual grains. However, variation in individual grain size is economically important for milling industry, because many small grains are lost during the cleaning process prior to milling and a high proportion of small grains is indicative of a poor flour yield. Also, when grains are sown for a new crop, grain mass variability increases the heterogeneity of germination and leads to non-uniform seedling emergence and crop establishment, often leading to decreased yield. We analyzed using the software ImageJ (http://imagej.nih.gov/ij/) individual grain size distributions of samples 80 to 120 individual grains each, harvested from yield trials at NARDI Fundulea Romania with 13 cultivars grown on four management variants, during two years. Individual grain projected area, as a proxy of grain size, ranged from 8.18 to 29.06 mm2, and for most cultivars minimum values of individual grain projected area were less than half of maximum values. On average over all management variants and years, coefficients of variation (s%) varied from less than 14% in cultivars Bezostaya 1, Glosa and Pajura to more than 15.5% in cultivars Adelina and Litera. ANOVA for the coefficients of variation of grain projection areas showed that the main source of variation was the effect of cultivars, which was significant when tested both against the Error and the interaction Cultivars*Years. The effect of the four studied managements was significant when tested against the Error, but not when tested against the interaction with Years, suggesting that the managements did not have the same effect in the two years of study. The large differences between cultivars found in our study provide opportunities in breeding for higher grain uniformity.

Competition and epibiosis by the sponge Pseudoceratina purpurea (Carter, 1880) on scleractinian corals at a tourism hotspot in the Gulf of Thailand

Competition for space on coral reefs is fierce, however when external natural and anthropogenic drivers disproportionately benefit certain organisms, reefs can quickly be conquered. Sponges in particular, have been shown to be competitive benthic colonisers and incidences of their epibiosis on scleractinian corals in the Indo-Pacific have been growing. Here we document the competitive capacity, frequency, and overgrowth interactions of the sponge Pseudoceratina purpurea on the island of Koh Tao, Gulf of Thailand. A comparison between four chosen sites revealed remarkable variability in the extent of sponge competition with two sites showing high incidences of P. purpurea epibiosis and two others showing low incidences. A total of 303 coral colonies were found to be overgrown by the sponge, with indications that mushroom corals and Pavona spp. may be disproportionally affected compared to other corals. Smaller P. purpurea individuals were found most often to colonise​ rock and larger individuals most often covering mushroom corals. Individual size and spatial distribution of the sponge suggest highly localised factors determine growth of both individuals and populations as a whole. No records of extensive overgrowth of any pseudoceratinid sponge is currently known from elsewhere, making this study a novel baseline for the Gulf of Thailand.

Individual size distributions across North American streams vary with local temperature.

Parameters describing the negative relationship between abundance and body size within ecological communities provide a summary of many important biological processes. While it is considered to be one of the few consistent patterns in ecology, spatiotemporal variation of this relationship across continental scale temperature gradients is unknown. Using a database of stream communities collected across North America (18-68°N latitude, -4 to 25°C mean annual air temperature) over 3years, we constructed 160 individual size distribution (ISD) relationships (i.e. abundance size spectra). The exponent parameter describing ISD's decreased (became steeper) with increasing mean annual temperature, with median slopes varying by ~0.2 units across the 29°C temperature gradient. In addition, total community biomass increased with increasing temperatures, contrary with theoretical predictions. Our study suggests conservation of ISD relationships in streams across broad natural environmental gradients. This supports the emerging use of size-spectra deviations as indicators of fundamental changes to the structure and function of ecological communities.

Numerical model of the spatio-temporal dynamics in a water strider group

The water strider group demonstrates a very complex dynamics consisting of competition for the food items, territoriality and aggression to the conspecific individuals, escaping from the predators, etc. The situation is even more complex due to the presence of different instars, which in most water strider species live in the same habitat and occupy the same niche. The presented swarm model of water striders demonstrates the realistic population dynamics. For the swarm formation in the model, attraction and repulsion forces were used. Animal motion in the model takes into account inertia and kinetic energy dissipation effects. The model includes three different rates related to the growth of individuals: food appearance rate, food assimilation rate, and stored energy loss rate. The results of our modeling show that the size distribution of individuals seems to be an adequate measure for population status, and it has a characteristic shape for different model parameter combinations. Distribution of the distances between nearest neighbors is other important measure of the population density and its dynamics. Parameters of the model can be tuned in such a way, that the shape of both distributions in a steady phase coincides with that shape observed in a natural population, which helps to understand the factors leading to particular momentary distribution of both parameters (size and distance) in the population. From this point of view, the model can predict how both distributions can further develop from certain state depending on particular combination of factors.

Mechanisms underlying lack of functional compensation by insect grazers after tadpole declines in a Neotropical stream

AbstractResilience of ecosystems to the sudden decline of large‐bodied species is dependent on characteristics of surviving guild members. However, that response may also be mediated by local habitat conditions. Here, we examine the mechanisms behind the observed lack of functional compensation in the algal‐grazing guild by insect grazers following the decline of tadpole grazers in a forested Panamanian stream. We examined: (1) shifts to the individual size distribution of insect grazers between pre‐ and post‐tadpole declines in pool and riffle habitats; (2) tadpole and insect preferences for small‐, medium‐, and large‐sized diatoms; and (3) a causal explanation for why insects did not functionally compensate for tadpole declines. The size distribution of insect grazers following tadpole declines differed between habitats, becoming uniform in pools and more right skewed toward a smaller size class in riffles. In both habitats, tadpoles selectively consumed medium‐sized diatoms but avoided the largest‐sized diatoms. In contrast, grazing insects selectively consumed small‐sized diatoms, but switched to medium‐sized diatoms after tadpole declines. Tadpole declines led to the loss of the strongest interactions between consumers and diatoms. Smaller‐bodied grazing insects could not duplicate these interactions, even with a shift in resource use, providing an explanation for the lack of functional compensation. Furthermore, tadpole declines led to different community structures in each habitat indicating that local habitat conditions mediated the response of surviving guild members. This suggests that the sudden decline of a large‐bodied species does not lead to a singular outcome for the surviving community.

Quantitative assessment of microstructural changes of hydrated cement blends due to leaching and carbonation, based on statistical analysis of image data

The evolution of the microstructure in corrosive environments plays a key role for the performance and durability of cementitious materials, however, appropriate methods to quantitatively describe microstructural alterations are limited. Here, statistical analysis of microscopic data is used to describe changes in porosity, continuous and individual pore size distributions of reactive cement phases during leaching and carbonation of hydrated cement blends. Therefore, BSE images obtained from (un)damaged areas of the cement blends were segmented using image processing techniques, followed by geometrical characterization and quantitative evaluation of the microstructural response(s). It is shown that the dissolution of portlandite generates a high meso- and macro-porosity (> 100-4000 nm pores), whereas precipitation of C-(A)-S-H and Ca-carbonate polymorphs leads to a densification of the microstructure, i.e., reducing the fine meso- and micro-porosity (< 500 nm pores). Cement blends made with hydraulically active SCMs and chemically poorly reactive carbonate fillers performed better than pure (OPC-based) cement paste.