Evolving social influence in large populations

Darwinian studies of collective human behaviour, which deal fluently with change and are grounded in the details of social influence among individuals, have much to offer “social” models from the physical sciences which have elegant statistical regularities. Although Darwinian evolution is often associated with selection and adaptation, “neutral” models of drift are equally relevant. Building on established neutral models, we present a general, yet highly parsimonious, stochastic model, which generates an entire family of real-world, right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponents, and power laws across the whole data. The widely used Barabási and Albert (1999) Science 286: 509-512 “B-A” model of preferential attachment is a special case of this general model. In addition, the model produces the continuous turnover observed empirically within these distributions. Previous preferential attachment models have generated specific distributions with turnover using arbitrary add-on rules, but turnover is an inherent feature of our model. The model also replicates an intriguing new relationship, observed across a range of empirical studies, between the power law exponent and the proportion of data represented in the distribution.     

Incorporation of Recreational Fishing Effort into Design of Marine Protected Areas

Abstract:  Theoretical models of marine protected areas (MPAs) that explore benefits to fisheries or biodiversity conservation often assume a dynamic pool of fishing effort. For instance, effort is homogenously distributed over areas from which subsets of reserves are chosen. I tested this and other model assumptions with a case study of the multiple-use Jervis Bay Marine Park. Prior to zoning of the park I conducted 166 surveys of the park's recreational fisheries, plotting the location of 16,009 anglers. I converted these plots into diagrams of fishing effort and analyzed correlates between fishing and habitat and the effect of two reserve designs—the draft and final zoning plans of the park—on the 15 fisheries observed. Fisheries were strongly correlated with particular habitats and had negatively skewed and often bimodal spatial distribution. The second mode of intensely fished habitat could be 6 SD greater than the fishery's mean allocation of effort by area. In the draft-zoning plan, sanctuary zone (no-take) area and potential subduction of fishing effort were similar. In the final plan, which was altered in response to public comment, the area of sanctuary zone increased, and the impact on fishing effort decreased. In only one case was a fishery's most intensely targeted location closed to fishing. Because of the discriminating manner with which fishers target habitats, if simple percentage targets are used for planning, sanctuary location can be adjusted to avoid existing fishing effort. According to modeled outcomes, the implication of this may be diminished reserve effectiveness. To address this, reserve area should be implicitly linked to subducted fishing effort when promoting or modeling MPAs.     

Species abundance distributions result from body size-energetics relationships

Abundance distributions are a central characteristic of ecosystems. Certain distributions have been derived from theoretical models of community organization, and therefore the fit of data to these distributions has been proposed as a test of these theories. However, it is shown here that the geometric sequence distribution can be derived directly from the empirical relationship between population density and body size, with the assumption of random or uniform body size distributions on a log scale (as holds at local scales). The geometric sequence model provides a good to excellent fit to empirical data. The presence of noise in the relationship between population density and body size creates a curve that begins to approximate a lognormal species abundance distribution as the noise term increases. For continental-scale data in which the body size distribution is not flat, the result of sampling tends again toward the lognormal. Repeat sampling over time smooths out species population fluctuations and damps out the noise, giving a more precise geometric sequence abundance distribution. It is argued that the direct derivation of this distribution from empirical relationships gives it priority over distributions derived from complex theoretical community models.     

Power-law behaviour and parametric models for the size-distribution of forest fires

This paper examines the distribution of areas burned in forest fires. Empirical size distributions, derived from extensive fire records, for six regions in North America are presented. While they show some commonalities, it appears that a simple power-law distribution of sizes, as has been suggested by some authors, is too simple to describe the distributions over their full range. A stochastic model for the spread and extinguishment of fires is used to examine conditions for power-law behaviour and deviations from it. The concept of the extinguishment growth rate ratio (EGRR) is developed. A null model with constant EGRR leads to a power-law distribution, but this does not appear to hold empirically for the data sets examined. Some alternative parametric forms for the size distribution are presented, with a four-parameter ‘competing hazards’ model providing the overall best fit.     

Area-based assessment of extinction risk

Underpinning the International Union for Conservation of Nature (IUCN) Red List is the assessment of extinction risk as determined by the size and degree of loss of populations. The IUCN system lists a species as Critically Endangered, Endangered, or Vulnerable if its population size declines 80%, 50%, or 30% within a given time frame. However, effective implementation of the system faces substantial challenges and uncertainty because geographic scale data on population size and long-term dynamics are scarce. I develop a model to quantify extinction risk using a measure based on a species' distribution, a much more readily obtained quantity. The model calculates the loss of the area of occupancy that is equivalent to the loss of a given proportion of a population. It is a very simple yet general model that has no free parameters and is independent of scale. The model predicted well the distributions of 302 tree species at a local scale and the distributions of 348 species of North American land birds. This area-based model provides a solution to the long-standing problem for IUCN assessments of lack of data on population sizes, and thus it will contribute to facilitating the quantification of extinction risk worldwide.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

Modelling landscape effects on density-contact rate relationships of deer in eastern Alberta: Implications for chronic wasting disease

Managing wildlife diseases requires an understanding of disease transmission, which may be strongly affected by host population density and landscape features. Transmission models are typically fit from time-series disease prevalence data and modelled based on how the contact rate among hosts is affected by density, which is often assumed to be a linear (density-dependent transmission) or constant (frequency-dependent transmission) relationship. However, long-term time-series data is unavailable for emerging diseases, and this approach cannot account for independent effects of landscape. We developed a mechanistic model based on ecological data to empirically derive the contact rate-density relationship in white-tailed and mule deer in an enzootic region of chronic wasting disease (CWD) in Alberta, Canada and to determine whether it was affected by landscape. Using data collected from aerial surveys and GPS-telemetry, we developed empirical relationships predicting deer group size, home range size, and habitat selection to iteratively simulate deer distributions across a range of densities and landscapes. We calculated a relative measure of total per-capita contact rate, which is proportional to the number of other deer contacted per individual per unit time, for each distribution as the sum of pairwise contact rates between a target deer and all other individuals. Each pairwise contact rate was estimated from an empirical relationship developed from GPS-telemetry data predicting pairwise contact rates as a function of home range overlap and landscape structure. Total per-capita contact rates increased as a saturating function of density, supporting a transmission model intermediate between density- and frequency-dependent transmission. This pattern resulted from group sizes that reached an asymptote with increasing deer density, although this relationship was mediated by tree and shrub coverage in the landscape, such that in heavily wooded areas, the contact rate saturated at much lower densities. These results suggest that CWD management based on herd reductions, which require a density-dependent contact rate to be effective, may have variable effects on disease across a single management region. The novel mechanistic approach we employed for estimating effects of density and landscape on transmission is a powerful complement to typical data-fitting approaches for modelling disease transmission.     

Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals

A surprisingly diverse variety of foragers have previously been concluded to exhibit movement patterns known as Lévy flights, a special type of random walk. These foragers range in size from microzooplankton in experiments to fishermen in the Pacific Ocean and the North Sea. The Lévy flight conclusion implies that all the foragers have similar scale-free movement patterns that can be described by a single dimensionless parameter, the exponent micro of a power-law (Pareto) distribution. However, the previous conclusions have been made using methods that have since been shown to be problematic: inaccurate techniques were used to estimate micro, and the power-law distribution was usually assumed to hold without testing any alternative hypotheses. Therefore, I address the open question of whether the previous data still support the Lévy flight hypothesis, and thus determine whether Lévy flights really are so ubiquitous in ecology. I present a comprehensive reanalysis of 17 data sets from seven previous studies for which Lévy flight behavior had been concluded, covering marine, terrestrial, and experimental systems from four continents. I use the modern likelihood and Akaike weights approach to test whether simple alternative models are more supported by the data than Lévy flights. The previously estimated values of the power-law exponent micro do not match those calculated here using the accurate likelihood approach, and almost all of them lie outside of the likelihood-based 95% confidence intervals. Furthermore, the original power-law Lévy flight model is overwhelmingly rejected for 16 out of the 17 data sets when tested against three other simple models. For one data set, the data are consistent with coming from a bounded power-law distribution (a truncated Lévy flight). For three other data sets, an exponential distribution corresponding to a simple Poisson process is suitable. Thus, Lévy flight movement patterns are not the common phenomena that was once thought, and are not suitable for use as ecosystem indicators for fisheries management, as has been proposed.     

An energy-centric theory of agglomeration

This paper sets out a simple spatial model of energy exploitation to ask how the location and productivity of energy resources affects the distribution of economic activity across geographic space. By combining elements from energy economics and economic geography we link the productivity of energy resources to the incentives for economic activity to agglomerate. We find a novel scaling law links the productivity of energy resources to population sizes, while rivers and roads effectively magnify productivity. We show how our theory's predictions concerning a single core, aggregate to predictions over regional landscapes and city size distributions at the country level.     

Different modes of resource variation provide a critical test of ideal free distribution models

Ideal free distribution (IFD) models are perhaps the group of mathematical models of behavior that have been the most widely and successfully applied by empiricists. These models can be applied to nearly any situation in which consumers compete—by any mechanism—for resources that are patchily distributed in their environment. Although IFD models have come to be broadly accepted, experiments that simultaneously test more than a single prediction are rare. Instead, investigators normally either test (1) for a relationship between the distribution of consumers and the distribution of resources or (2) whether average fitnesses are equal across resource patches. We conducted experiments with pea aphids (Acyrthosiphon pisum Harris) feeding on two patches of fava beans (Vicia faba L.) to fully independently parameterize an IFD model with interference competition and then test quantitative predictions about aphid spatial distributions and the payoffs of patch choice. We found a precise fit between aphids’ predicted and observed reproductive successes. Furthermore, by varying patch “quality” in two ways, we were able to show that aphid distributions vary with the mode of resource variation in the predicted manner: aphids (1) matched resources when patches varied in size but not quality and (2) overmatched the good patch when patches varied in quality but not size (predicted as a consequence of weak interference). The close correspondence between quantitative predictions of the model with observed behaviors suggests that IFD theory is a framework with more explanatory power than is generally appreciated.     

A general bioeconomic simulation model for annual-crop marine fisheries

A generalized bioeconomic simulation model of annual-crop marine fisheries is described and its use in marine fisheries management is demonstrated. The biological submodel represents the recruitment of new organisms into the fishery, the movement of organisms from one fishing area to another and from one depth to another, the growth of organisms and the mortality of organisms resulting both from natural causes and from fishing. The economic submodel represents the fishing effort exerted on each resource species, the monetary costs of fishing, the value of the harvest and the rent (or excess profits) to the fishery.Basic dynamics of the model results from changes in the number of organisms in the fishery over time, which can be summarized as a set of difference equations of the general form ΔN/Δt = R + I ? E ? M ? F where ΔN/Δt is the net change in number of organisms in the fishery over time, R is recruitment, I is immigration, E is emigration, M is natural mortality and F is fishing mortality. R is a driving variable, whereas I, E, M and F are functions of the state of the system at any given point in time. The model can be run in a deterministic or stochastic mode. Values for parameters affecting rates of recruitment, movement, growth, natural mortality and fishing mortality can be selected from uniform, triangular or normal distributions.Use of the model within a fisheries-management framework is demonstrated by evaluating several management alternatives for the pink shrimp (Penaeus duorarum) fishery on the Tortugas grounds in the Gulf of Mexico. Steps involved in use of the model, including parameterization, validation, sensitivity analysis and stochastic simulations of management policies, are explained.     

Using fisher-contributed secondary fins to fill critical shark-fisheries data gaps

Developing-world shark fisheries are typically not assessed or actively managed for sustainability; one fundamental obstacle is the lack of species and size-composition catch data. We tested and implemented a new and potentially widely applicable approach for collecting these data: mandatory submission of low-value secondary fins (anal fins) from landed sharks by fishers and use of the fins to reconstruct catch species and size. Visual and low-cost genetic identification were used to determine species composition, and linear regression was applied to total length and anal fin base length for catch-size reconstruction. We tested the feasibility of this approach in Belize, first in a local proof-of-concept study and then scaling it up to the national level for the 2017–2018 shark-fishing season (1,786 fins analyzed). Sixteen species occurred in this fishery. The most common were the Caribbean reef (Carcharhinus perezi), blacktip (C. limbatus), sharpnose (Atlantic [Rhizoprionodon terraenovae] and Caribbean [R. porosus] considered as a group), and bonnethead (Sphyrna cf. tiburo). Sharpnose and bonnethead sharks were landed primarily above size at maturity, whereas Caribbean reef and blacktip sharks were primarily landed below size at maturity. Our approach proved effective in obtaining critical data for managing the shark fishery, and we suggest the tools developed as part of this program could be exported to other nations in this region and applied almost immediately if there were means to communicate with fishers and incentivize them to provide anal fins. Outside the tropical Western Atlantic, we recommend further investigation of the feasibility of sampling of secondary fins, including considerations of time, effort, and cost of species identification from these fins, what secondary fin type to use, and the means with which to communicate with fishers and incentivize participation. This program could be a model for collecting urgently needed data for developing-world shark fisheries globally. Article impact statement: Shark fins collected from fishers yield data critical to shark fisheries management in developing nations.     

Coexistence of intraguild predators and prey in resource-rich environments

The prevalence of intraguild predation (IGP) in productive environments has long puzzled ecologists. Theory predicts the exclusion of intraguild prey from such environments, but data consistently defy this expectation. This suggests that coexistence mechanisms at high resource productivity may differ from those at lower productivity. Here I present a mathematical model that investigates multiple coexistence mechanisms. I incorporate two biological features widely observed in IGP communities: intraspecific interference via cannibalism or superparasitism, and temporal refuges arising from differential sensitivities to abiotic variation. I develop predictions based on three aspects of the IG prey-IG predator interaction: mutual invasibility, transient dynamics, and long-term abundances. These predictions specify the conditions under which coexistence mechanisms reinforce vs. deter one another: when a competition-IGP trade-off allows coexistence at intermediate productivity a temporal refuge for the intraguild prey always allows coexistence at high productivity, but intraspecific interference does so only at a net fitness cost to the intraguild predator. Intraspecific interference that benefits the intraguild predator not only reduces tradeoff-mediated coexistence at intermediate productivity, but also undermines the refuge's coexistence-enhancing effect at high productivity. Different mechanism combinations yield characteristic signatures in time series data during transient dynamics. By judicious measurement of parameters and examining time series for critical signatures, one can elucidate the mechanisms that allow IGP to prevail in resource-rich environments.     

On interacting bee/mite populations: a stochastic model with analysis using cumulant truncation

Parasitism by the Varroa mite has had recent drastic impact on both managed and feral bee colonies. This paper proposes a stochastic population dynamics model for interacting African bee colony and Varroa mite populations. Cumulant truncation procedures are used to obtain approximate transient cumulant functions, unconstrained by the usual assumption of bivariate Normality, for an assumed large-scale model. The apparent size of the variance and skewness functions suggest the importance of the proposed truncation procedure which retains some higher-order cumulants, but determining the accuracy of the approximations is problematical. A smaller-scale bee/Varroa mite model is hence proposed and investigated. The accuracy for the means is exceptional, for the second-order cumulants is moderate, and for some third-order cumulants is poor. Notwithstanding the poor accuracy of a skewness approximation, the saddlepoint approximations for the marginal transient population size distributions are excellent. The cumulant truncation methodology is very general, and research is continuing in its application to this new class of host-parasite models.     

Female grouping best predicts lekking in blackbuck (Antilope cervicapra)

The study of intraspecific variation can provide insights into the evolution and maintenance of behavior. To evaluate the relative importance of ecological, demographic and social conditions thought to favor lekking, I studied variation in mating behavior among and within populations of the blackbuck, Antilope cervicapra, an Indian antelope. Rather than viewing lekking as a discrete mating strategy, I took a continuous approach and treated lekking as a question of the clustering of mating territories, with leks representing one extreme in a range of territory distributions. I surveyed nine blackbuck populations, which differed in population density and in habitat conditions. For each population, I described the mating system in terms of the clustering of mating territories, and measured various factors suggested to favor lekking. I found that large-scale, among-population variation in territory clustering was most strongly related to female group size. Territory clustering was not related to population density. Female group size, in turn, was best explained by habitat structure. Interestingly, these among-population patterns were repeated at a finer spatial scale within one intensively studied population. These findings suggest that territorial males respond to local patterns in female distribution (represented by group size) when making decisions regarding territory location. Finally, although female distribution may explain territory clustering at the population level and more locally within a population, other selective factors (e.g., female preference, male competition, male harassment) are likely to shape the clustering and size of territories at even finer scales.Electronic Supplementary Material Supplementary material is available in the online version of this article at .Communicated by T. Czeschlik     

Probability law of concentration in plumes dispersing in an urban area

The relationships between various normalized higher-order concentration moments in plumes dispersing in a built-up (urban) environment have been investigated using a large concentration data set obtained in a boundary-layer water channel. This data set consists of measurements of plume dispersion in a number of idealized obstacle arrays (e.g., cubical and non-cubical obstacles in aligned and staggered arrangements with uniform, random and alternating heights). A remarkably robust feature of all the concentration data was the observed collapse of the third- and fourth-order normalized concentration moments on the second-order normalized concentration moment. The data are shown to collapse to a series of universal curves (independent of the geometry of the obstacle array) and these curves were found to be identical to those observed previously for open-terrain plumes. The results imply that the probability law of concentration in a plume dispersing in either a built-up environment or open terrain has a universal form that can be specified by at most two independent parameters. The universal functions representing the relationships between the normalized concentration moments were found to be well modeled (approximated) using a two-parameter clipped-gamma probability law for the concentration. Finally, the clipped-gamma distribution was found to be in very good conformance with the measured probability distribution of concentration for plumes dispersing in a built-up environment.     

Implications of Urbanization for Artisanal Parrotfish Fisheries in the Western Solomon Islands

Abstract: Increasing migration into urbanized centers in the Solomon Islands poses a great threat to adjacent coral reef fisheries because of negative effects on the fisheries and because it further erodes customary management systems. Parrotfish fisheries are of particular importance because the feeding habits of parrotfish (scrape and excavate coral) are thought to be critical to the resilience of coral reefs and to maintaining coral reef health within marine protected areas. We investigated the ecological impact of localized subsistence and artisanal fishing pressure on parrotfish fisheries in Gizo Town, Western Solomon Islands, by analyzing the density and size distribution of parrotfish with an underwater visual census (UVC), recall diary (i.e., interviews with fishers), and creel surveys to independently assess changes in abundance and catch‐per‐unit‐effort (CPUE) over 2 years. We then compared parrotfish data from Gizo Town with equivalent data from sites open to and closed to fishing in Kida and Nusa Hope villages, which have different customary management regimes. Results indicated a gradient of customary management effectiveness. Parrotfish abundance was greater in customary management areas closed to fishing, especially with regard to larger fish sizes, than in areas open to fishing. The decline in parrotfish abundance from 2004 to 2005 in Gizo was roughly the same magnitude as the difference in abundance decline between inside and outside customary management marine reserves. Our results highlight how weak forms of customary management can result in the rapid decline of vulnerable fisheries around urbanized regions, and we present examples in which working customary management systems (Kinda and Nusa Hope) can positively affect the conservation of parrotfish—and reef fisheries in general—in the highly biodiverse Coral Triangle region.     

Twenty years of changes in spatial association and community structure among desert perennials

I present results from analyses of 20 years of spatiotemporal dynamics in a desert perennial community. Plants were identified and mapped in a 1-ha permanent plot in Joshua Tree National Park (California, USA) in 1984. Plant size, mortality, and new seedlings were censused every five years through 2004. Two species, Ambrosia dumosa and Tetracoccus hallii, were dominant based on their relative abundance and ubiquitous distributions. Spatial analysis for distance indices (SADIE) identified regions of significantly high (patches) or low (gaps) densities. I used SADIE to test for (1) transience in the distribution of patches and gaps within species over time and (2) changes in juvenile-adult associations with conspecific adults and adults of the two dominant species over time. Plant performance was quantified in patches and gaps to determine plant responsiveness to local spatial associations. Species identity was found to influence associations between juveniles and adults. Juveniles of all species showed significant positive spatial associations with the dominant A. dumosa but not with T. hallii. The broad distribution of A. dumosa may increase the spatial extent of non-dominant species that are facilitated by this dominant. The spatial location of patches and gaps was generally consistent over time for adults but not juveniles. Observed variability in the locations of juvenile patches and gaps suggested that suitable locations for establishment were broad relative to occupied regions of the habitat, and that conditions for seed germination were independent of conditions for seedling survival. A dramatic change in spatial distributions and associations within and between species occurred after a major drought that influenced data from the final census. Positive associations between juveniles and adults of all species were found independent of previous associations and most species distributions contracted to areas that were previously characterized by low density. By linking performance to spatial distribution, results from this study offer a spatial context for plant-plant interactions within and among species. Community composition could be influenced both by individual species tolerances of abiotic conditions and by the competitive or facilitative interactions individuals exert over neighbors.     

A mathematical model for type II profile of concentration distribution in turbulent flows

This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.     

Combining heat-transfer and energy budget models to predict thermal stress in Mediterranean intertidal mussels

Recent studies have emphasised that organisms can experience physiological stress well within their geographic range limits. Developing methods for mechanistically predicting the presence, absence and physiological performance of organisms is therefore important because of the ongoing effects of climate change. In this study, we merged a biophysical–ecological (BE) model that estimates the aquatic (high tide) and aerial (low tide) body temperatures of Mytilus galloprovincialis with a Dynamic Energy Budget (DEB) model to predict growth, reproduction and mortality of this Mediterranean mussel in both intertidal and subtidal environments. Using weather and chlorophyll-a data from three Mediterranean sites along the Italian coasts, we show that predictions of sublethal and lethal (acute) stress can potentially explain the observed distribution (both presence and absence) of mussels in the intertidal and subtidal zones, and the maximum size of animals in the subtidal zones. Importantly, our results suggest that different mechanisms limit the intertidal distribution of mussels, and that these mechanisms do not follow a simple latitudinal gradient. At the northernmost site (Palermo), M. galloprovincialis appears to be excluded from the intertidal zone due to persistent exposure to lethal aerial temperatures, whereas at the southernmost sites (Porto Empedocle and Lampedusa) sublethal stress is the most important driver of mussel intertidal distribution. Our predictions provide a set of hypotheses for future work on the role of climate change in limiting intertidal distribution of mussels in the Mediterranean.