Bayesian hierarchical modelling of size spectra

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

Receiver Mount Design, Transmitter Depth, and Wind Speed Affect Detection Probability of Acoustic Telemetry Transmitters in a Missouri River Tributary

Background One of the most important considerations for acoustic telemetry study designs is det:ection probability between the transmitter and the receiver. Variation in environmental (i.e., wind and flow) and abiotic (i.e., bathymetry) conditions among aquatic systems can lead to differences in detection probability temporally or between systems. In this study we evaluate the effect of distance, receiver mount design, transmitter depth, and wind speed on detection probabilities of two models of acoustic transmitters in a mid-sized river. InnovaSea V16-6H (hereafter V16) and V13-1L (hereafter V13) tags were deployed in the James River, SD at 0.36 m (deep) and 2.29 m (V16 tag) or 1.98 m (V13 tag; shallow) above the benthic surface downstream of InnovaSea VR2W stationary receivers at distances of 100, 200, or 300 m. We used two receiver mount designs that included a fixed position within a PVC pipe on the downstream side of a bridge piling or a metal frame deployed in the middle of the river channel. Tags were deployed for 72 h at each location, and hourly detections were summarized. We evaluated downstream distance, receiver mount design, tag depth, and wind effects on tag detection using Bayesian logistic regression. Results: Detection probability decreased as distance increased for all combinations of tag types and mount designs and varied from nearly 100% at 100 m to less than 10% at 300 m. The V16 transmitter had greater detection probability by the receiver mounted in the pipe than in the midriver frame. For both mounts, the deep V16 transmitter had greater detection probability than the V16 shallow transmitter. Detection probability of the V13 transmitter was similar between receiver mounts or transmitter depths. Wind speed had a negative impact on detection probabilities of both transmitter types and depths, except the deep V16 transmitter. Conclusions: Deploying acoustic receivers in PVC pipes rather than midriver frames provided greater downstream detection probabilities for V16 transmitters under conditions evaluated in this study. In addition, V16 transmitters had greater detection probabilities when positioned deep within the water column rather than near the surface. We also demonstrated that wind speed can have a negative impact on detection probabilities

Loss of Potential Aquatic-Terrestrial Subsidies Along the Missouri River Floodplain

The floodplains of large rivers have been heavily modified due to riparian development and channel modifications, both of which can eliminate shallow off-channel habitats. The importance of these habitats for aquatic organisms like fishes is well studied. However, loss of off-channel habitat also eliminates habitats for the production of emerging aquatic insects, which subsidize riparian consumers in terrestrial food webs. We used field collections of insect emergence, historical mapping, and statistical modeling to estimate the loss of insect emergence due to channel modifications along eight segments of the Missouri River (USA), encompassing 1566 river km, between 1890 and 2012. We estimate annual production of emerging aquatic insects declined by a median of 36,000 kgC (95% CrI: 3000 to 450,000) between 1890 and 2012 (a 34% loss), due to the loss of surface area in backwaters and related off-channel habitats. Under a conservative assumption that riparian birds obtain 24% of their annual energy budget from adult aquatic insects, this amount of insect loss would be enough to subsidize approximately 790,000 riparan woodland birds during the breeding and nesting period (May to August; 95% CrI: 57,000 to 10,000,000). Most of the loss is concentrated in the lower reaches of the Missouri River, which historically had a wide floodplain, a meandering channel, and a high density of off-channel habitats, but which were substantially reduced due to channelization and bank stabilization. Our results indicate that the loss of off-channel habitats in large river floodplains has the potential to substantially affect energy availability for riparian insectivores, further demonstrating the importance of maintaining and restoring these habitats for linked aquatic-terrestrial ecosystems

Severing Ties: Different Responses of Larval and Adult Aquatic Insects to Atrazine and Selenium

Aquatic insects link aquatic and terrestrial ecosystems through their metamorphosis and subsequent transition from water to land. Chemical stressors in freshwater, such as agricultural contaminants, can potentially disrupt insect life cycles and reduce the number of insects emerging as terrestrial adults, thereby damaging or severing this linkage. Atrazine and selenium, though frequently detected in waterways and often co-occurring, have not been previously studied together in controlled experiments. We conducted a six-week mesocosm experiment to measure the responses of larval and emerging aquatic insects to treatments of atrazine (15 μg/L), selenium (10 μg/L), and a direct combination of the two. Peak adult insect abundance was reduced in all treatments by 35% to 45% relative to the control. Further, cumulative adult emergence in the combined treatment was 33% lower than in the control. However, no reductions in primary production were observed with treatments, and consistent reductions in benthic insect abundance relative to the control were not observed until the end of the experiment, when overall abundance was low. Results suggest that adult insects are more sensitive than larval insects to atrazine and selenium and that the impacts of these contaminants are stronger on the terrestrial than the aquatic ecosystem

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 3 years, we constructed 160 individual size distribution relationships (i.e. abundance size spectra). The exponent parameter describing ISD\u27s 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 to theoretical predictions. Our study suggests conservation of individual size distribution 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

Spatial Patterns in Fish Assemblages across the National Ecological Observation Network (NEON): The First Six Years

The National Ecological Observation Network (NEON) is a thirty-year, open-source, continental-scale ecological observation platform. The objective of the NEON project is to provide data to facilitate the understanding and forecasting of the ecological impacts of anthropogenic change at a continental scale. Fish are sentinel taxa in freshwater systems, and the NEON has been sampling and collecting fish assemblage data at wadable stream sites for six years. One to two NEON wadable stream sites are located in sixteen domains from Alaska to Puerto Rico. The goal of site selection was that sites represent local conditions but with the intention that site data be analyzed at a continental observatory level. Site selection did not include fish assemblage criteria. Without using fish assemblage criteria, anomalies in fish assemblages at the site level may skew the expected spatial patterns of North American stream fish assemblages, thereby hindering change detection in subsequent years. However, if NEON stream sites are representative of the current spatial distributions of North American stream fish assemblages, we could expect to find the most diverse sites in Atlantic drainages and the most depauperate sites in Pacific drainages. Therefore, we calculated the alpha and regional (beta) diversities of wadable stream sites to highlight spatial patterns. As expected, NEON sites followed predictable spatial diversity patterns, which could facilitate future change detection and attribution to changes in environmental drivers, if any

Correction: Monahan et al. Spatial Patterns in Fish Assemblages across the National Ecological Observation Network (NEON): The First Six Years. <i>Fishes</i> 2023, <i>8</i>, 552

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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 ((Formula presented.)) of the power law. A common application of size spectra studies is to detect anthropogenic pressures. Many methods have been proposed for estimating (Formula presented.) 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 (Formula presented.) compared to procedures that directly estimate (Formula presented.) using maximum likelihood estimation (MLE). While it is clear that MLE produces less biased estimates of site-specific λ\u27s, 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 (Formula presented.), and (2) recapture parameters in a linear regression measuring the change in (Formula presented.) 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 (Formula presented.). This bias carried over to the regressions, which were more accurate when (Formula presented.) 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 (Formula presented.) and its relative variation across environmental gradients using MLE over the more common methods of binning

Loss of Potential Aquatic-Terrestrial Subsidies Along the Missouri River Floodplain

The floodplains of large rivers have been heavily modified due to riparian development and channel modifications, both of which can eliminate shallow off-channel habitats. The importance of these habitats for aquatic organisms like fishes is well studied. However, loss of off-channel habitat also eliminates habitats for the production of emerging aquatic insects, which subsidize riparian consumers in terrestrial food webs. We used field collections of insect emergence, historical mapping, and statistical modeling to estimate the loss of insect emergence due to channel modifications along eight segments of the Missouri River (USA), encompassing 1566 river km, between 1890 and 2012. We estimate annual production of emerging aquatic insects declined by a median of 36,000 kgC (95% CrI: 3000 to 450,000) between 1890 and 2012 (a 34% loss), due to the loss of surface area in backwaters and related off-channel habitats. Under a conservative assumption that riparian birds obtain 24% of their annual energy budget from adult aquatic insects, this amount of insect loss would be enough to subsidize approximately 790,000 riparan woodland birds during the breeding and nesting period (May to August; 95% CrI: 57,000 to 10,000,000). Most of the loss is concentrated in the lower reaches of the Missouri River, which historically had a wide floodplain, a meandering channel, and a high density of off-channel habitats, but which were substantially reduced due to channelization and bank stabilization. Our results indicate that the loss of off-channel habitats in large river floodplains has the potential to substantially affect energy availability for riparian insectivores, further demonstrating the importance of maintaining and restoring these habitats for linked aquatic-terrestrial ecosystems

Temperature, resources and predation interact to shape phytoplankton size–abundance relationships at a continental scale

Aim: Communities contain more individuals of small species and fewer individuals of large species. According to the ‘metabolic theory of ecology’, the relationship of log mean abundance with log mean body size across communities should exhibit a slope of −3/4 that is invariant across environmental conditions. Here, we investigate whether this slope is indeed invariant or changes systematically across gradients in temperature, resource availability and predation pressure. Location 1048 lakes across the USA. Time Period 2012. Major Taxa Studied Phytoplankton. Results We found that the size–abundance relationship across all sampled phytoplankton communities was significantly lower than −3/4 and near −1 overall. More importantly, we found strong evidence that the environment affects the slope: it varies between −0.33 and −0.93 across interacting gradients of temperature, resource (phosphorus) supply and zooplankton predation pressure. Therefore, phytoplankton communities have orders of magnitude more small or large cells depending on environmental conditions across geographical locations. Conclusion Our results emphasise the importance of the environmental factors' effect on macroecological patterns that arise through physiological and ecological processes. An investigation of the mechanisms underlying the link between individual energetics constrain and macroecological patterns would allow to predict how global warming and changes in nutrients will alter large‐scale ecological patterns in the future.</p