Understanding variability of population abundances is of central concern to theoretical and applied evolutionary ecology, yet quantifying the conceptually simple idea has been substantially problematic. Standard statistical measures of variability are particularly biassed by rare events, zero counts and other 'non-Gaussian' behaviour, which are often inappropriately weighted or excluded from analysis. I conjecture that these problems are primarily a function of calculating variation as deviation from an average abundance, while the average may not be static, nor actually reflect abundance at any point in the time series. Here I describe a simple metric (population variability PV) that quantifies variability as the average percent difference between all combinations of observed abundances. Zero counts can be included if desired. Similar to standard metrics, variability is measured on a proportional scale, facilitating comparative applications. Standard metrics are based on Gaussian distributions, are over-sensitive to rare events and heavy tailed behaviour, and can inappropriately indicate 'more time-more variation' effects (reddened spectrum). Here I demonstrate that, while PV behaves similarly for 'normal' time series, it is independent of deviation from mean abundance for heavy tailed distributions, its robustness to non-Gaussian behaviour resolves artificial reddened spectrum issues, and variability calculated using PV from short time series is substantially more accurate at estimating known long term variability than standard metrics. PV therefore provides common ground for evaluating the variability of populations undergoing different dynamics, and with different statistical distributions of abundance, and can be easily generalized to a variety of contexts and disciplines.

The dynamics of resource patches and species that exploit such patches are of interest to ecologists, conservation biologists, modelers, and mathematicians. Here we consider how social interactions can create unique, evolving patterns in space and time. Whereas simple prey taxis (with consumable prey) promotes spatial uniform distributions, here we show that taxis in producer-scrounger groups can lead to pattern formation. We consider two types of foragers: those that search directly ("producers") and those that exploit other foragers to find food ("scroungers" or exploiters). We show that such groups can sustain fluctuating spatiotemporal patterns, akin to "waves of pursuit." Investigating the relative benefits to the individuals, we observed conditions under which either strategy leads to enhanced success, defined as net food consumption. Foragers that search for food directly have an advantage when food patches are localized. Those that seek aggregations of group mates do better when their ability to track group mates exceeds the foragers' food-sensing acuity. When behavioral switching or reproductive success of the strategies is included, the relative abundance of foragers and exploiters is dynamic over time, in contrast with classic models that predict stable frequencies. Our work shows the importance of considering two-way interactioni.e., how food distribution both influences and is influenced by social foraging and aggregation of predators.pattern formation | foraging strategies | ecological patchiness | chemotaxis | spatial ecology I n this paper, we study the dynamics of social interactions to explore the consequences for spatiotemporal population structure and dynamics. We show that interactions among individuals are key for pattern formation and self-organization when foragers either follow gradients of food or socialize with those that do. Our aim is to demonstrate that social interactions among foragers could have particularly important implications for spatial models of forager-resource dynamics. A comprehensive understanding of the spatial dynamics of social foraging needs to consider the two-way dynamic interaction between forager aggregation and resource patchiness, a problem that remains poorly understood (1, 2).A secondary theme is the discovery of another pattern-forming mechanism. Nature abounds with patterns that the human eye is adept at picking out. Patterns occur in chemical, physical, and biological systems on many scales, from distribution of proteins in a cell, and tissue morphogenesis, to patchy distribution of species in ecology (3-5, 6). There is great interest in finding both universal mechanisms for such patterns (e.g., the balance of repulsion-attraction forces, local activation and long-range inhibition, or motion in an external field; ref. 7), as well as specific examples that have rich pattern-forming features (8).Patterns formed by organisms, and the way they shape their environment, is a rich area with physical (phase transitions), engineering (robotics), sociological (e.g...

Few ecotoxicological studies exist for rare earth elements (REEs), particularly field-based studies on their bioaccumulation and food web dynamics. REE mining has led to significant environmental impacts in several countries (China, Brazil, U.S.), yet little is known about the fate and transport of these contaminants of emerging concern. Northern ecosystems are potentially vulnerable to REE enrichment from prospective mining projects at high latitudes. To understand how REEs behave in remote northern food webs, we measured REE concentrations and carbon and nitrogen stable isotope ratios (∂N, ∂C) in biota from marine, freshwater, and terrestrial ecosystems of the eastern Canadian Arctic (N = 339). Wildlife harvesting and tissue sampling was partly conducted by local hunters through a community-based monitoring project. Results show that REEs generally follow a coherent bioaccumulation pattern for sample tissues, with some anomalies for redox-sensitive elements (Ce, Eu). Highest REE concentrations were found at low trophic levels, especially in vegetation and aquatic invertebrates. Terrestrial herbivores, ringed seal, and fish had low total REE levels in muscle tissue (∑REE for 15 elements <0.1 nmol g), yet accumulation was an order of magnitude higher in liver tissues. Age- and length-dependent REE accumulation also suggest that REE uptake is faster than elimination for some species. Overall, REE bioaccumulation patterns appear to be species- and tissue-specific, with limited potential for biomagnification. This study provides novel data on the behaviour of REEs in ecosystems and will be useful for environmental impact assessment of REE enrichment in northern regions.

A variety of ecological, physiological and environmental factors influence the energy budgets of diving animals. For common eiders Somateria mollissima sedentaria wintering in sea ice habitats in the Canadian Arctic, time and energy costs of diving increase exponentially with tidal current speed. Here we use literature estimates of diving energetics and underwater dive data to quantitatively model net energy gain per dive cycle as a function of current speed. The model indicates a strong non-linear decrease in the profitability of diving with increasing currents, predicting that net energy gain per dive cycle will reach zero and become unprofitable at 1.21 m s -1 (at 11.3 m depth using baseline parameters from our study). As currents increase travel time, foraging time at the bottom decreases non-linearly, reaching a point where intake is inadequate to balance increasing diving and surface swimming costs. Sensitivity analysis indicates that this threshold is robust over a range of energy expenditure rates and is influenced most by energy intake rate, emphasising the importance of ecological factors such as prey abundance and quality. Eiders stop foraging and rest on the ice well below this threshold in weaker current regimes (~0.8 m s -1 ), at about the point when profitability begins to decelerate. Behavioural time series of diving under constraints of strong tidal current regimes indicate that these eiders do occasionally dive in currents up to ~1.2 m s -1 , providing support for the energetic model. Eiders did not dive in faster currents, which could also be influenced by a physiological limit to swimming speed. We conclude that ocean currents can cause a non-linear decrease in net energy balance and are therefore an important and understudied consideration for diving animals. Many functional aspects of diving (e.g. locomotor costs or convective heat loss) have non-linear characteristics; these diminishing returns can be expected to play an important role in the dynamics of behavioural routines and the ability of organisms to respond to environmental variation.

SUMMARY Swim speed during diving has important energetic consequences. Not only do costs increase as drag rises non-linearly with increasing speed, but speed also affects travel time to foraging patches and therefore time and energy budgets over the entire dive cycle. However, diving behaviour has rarely been considered in relation to current velocity. Strong tidal currents around the Belcher Islands, Nunavut, Canada, produce polynyas, persistent areas of open water in the sea ice which are important habitats for wildlife wintering in Hudson Bay. Some populations of common eiders Somateria mollissima sedentaria remain in polynyas through the winter where they dive to forage on benthic invertebrates. Strong tidal currents keep polynyas from freezing, but current velocity can exceed 1.5 m s–1 and could influence time and energy costs of diving and foraging. Polynyas therefore provide naturally occurring flume tanks allowing investigation of diving strategies of free ranging birds in relation to current velocity. We used a custom designed sub-sea ice camera to non-invasively investigate over 150 dives to a depth of 11.3 m by a population of approximately 100 common eiders at Ulutsatuq polynya during February and March of 2002 and 2003. Current speed during recorded dives ranged from 0 to 1 m s–1. As currents increased, vertical descent speed of eiders decreased, while descent duration and the number of wing strokes and foot strokes during descent to the bottom increased. However, nearly simultaneous strokes of wings and feet, and swim speed relative to the moving water, were maintained within a narrow range(2.28±0.23 Hz; 1.25±0.14 m s–1, respectively). This close regulation of swim speed over a range in current speed of 1.0 m s–1 might correspond to efficient muscle contraction rates,and probably reduces work rates by avoiding rapidly increasing drag at greater speeds; however, it also increases travel time to benthic foraging patches. Despite regulation of average swim speed, high instantaneous speeds during oscillatory stroking can increase dive costs due to drag. While most diving birds have been considered either foot or wing propelled, eider ducks used both wing and foot propulsion during descent. Our observations indicate that the power phase of foot strokes coincides with the transition between upstroke and downstroke of the wings, when drag is greatest. Coordinated timing between foot and wing propulsion could therefore serve to maintain a steadier speed during descent and decrease the costs of diving. Despite tight regulation of stroke and swim speed patterns, descent duration and total number of foot and wing strokes during descent increase non-linearly with increasing current velocity, suggesting an increase in energetic costs of diving.

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Real quantities can undergo such a wide variety of dynamics that the mean is often a meaningless reference point for measuring variability. Despite their widespread application, techniques like the Coefficient of Variation are not truly proportional and exhibit pathological properties. The non-parametric measure Proportional Variability (PV) [1] resolves these issues and provides a robust way to summarize and compare variation in quantities exhibiting diverse dynamical behaviour. Instead of being based on deviation from an average value, variation is simply quantified by comparing the numbers to each other, requiring no assumptions about central tendency or underlying statistical distributions. While PV has been introduced before and has already been applied in various contexts to population dynamics, here we present a deeper analysis of this new measure, derive analytical expressions for the PV of several general distributions and present new comparisons with the Coefficient of Variation, demonstrating cases in which PV is the more favorable measure. We show that PV provides an easily interpretable approach for measuring and comparing variation that can be generally applied throughout the sciences, from contexts ranging from stock market stability to climate variation.

The Hudson Bay system is undergoing climate-driven changes in sea ice and freshwater inflow and has seen an increase in winter river inflow since the 1960s due in part to flow regulation for hydropower production. Southeast Hudson Bay and adjacent James Bay are at the forefront of these changes, with more than 1-month shortening of the season of sea ice cover as defined using satellite data, increases in winter inflow from the regulated La Grande River complex, and changes in coastal ice and polynya behavior described by Belcher Islands' Inuit. In summer, there is a fresh coastal domain in southeast Hudson Bay fueled by river runoff and sea ice melt. To investigate winter oceanographic conditions and potential interactions between runoff and ice melt or brine in southeast Hudson Bay, we initiated the first winter study of the shallow waters surrounding the Belchers, collecting conductivity-temperature-depth (CTD) profiles and conductivity-temperature (CT) time series using under-ice moorings, and collecting water samples and ice cores during four campaigns between January 2014 and March 2015. Tandem measurements of salinity and δ 18 O were made for the water and ice samples to discriminate between freshwater sources (river runoff and sea ice melt). We find that southeast Hudson Bay, and particularly the nearshore domain southeast of the Belchers, is distinguished in winter by the presence of river water and strong surface stratification, which runs counter to expectations for a system in which local freshwater remains frozen on land until spring freshet (May-June) and sea ice growth is adding brine to surface waters. The amount of river water around the Belcher Islands increased significantly from fall through to late winter according to δ 18 O records of ice. The accumulation of river water in surface waters during the winter is directly associated with an accumulation of brine, which considerably exceeds the capacity of local ice formation to produce brine. We therefore infer that brine is advected into the study area together with river water, and that interplay between these properties establishes and maintains the level of surface stratification throughout winter. With reference to a NEMO ocean model simulation of winter circulation in the study area, we propose a conceptual model in which winter river inflow into James Bay drives the northward transport of both river water and brine captured near the surface, with reductions in brine-driven deep convection in the area's flaw leads. While past changes in winter oceanographic conditions and sea ice cannot be reconstructed from the few available scientific data, the presence of significant runoff in winter in southeast Hudson Bay implies heightened sensitivity to delayed freeze-up under a warmer climate, which will have the effect of reducing brine early in the winter, also promoting increased stratification and river plume transport.