Predator–prey encounter rates in freshwater piscivores: effects of prey density and water transparency

One of the most fundamental components of predator–prey models is encounter rate, modelled as the product of prey density and search efficiency. Encounter rates have, however, rarely been measured in empirical studies. In this study, we used a video system approach to estimate how encounter rates between piscivorous fish that use a sit-and-wait foraging strategy and their prey depend on prey density and environmental factors such as turbidity. We first manipulated prey density in a controlled pool and field enclosure experiments where environmental factors were held constant. In a correlative study of 15 freshwater lakes we then estimated encounter rates in natural habitats and related the results to both prey fish density and environmental factors. We found the expected positive dependence of individual encounter rates on prey density in our pool and enclosure experiments, whereas the relation between school encounter rate and prey density was less clear. In the field survey, encounter rates did not correlate with prey density but instead correlated positively with water transparency. Water transparency decreases with increasing prey density along the productivity gradient and will reduce prey detection distance and thus predator search efficiency. Therefore, visual predator–prey encounter rates do not increase, and may even decrease, with increasing productivity despite increasing prey densities.     

Dynamics of populations with individual variation in dispersal on bounded domains

Most classical models for the movement of organisms assume that all individuals have the same patterns and rates of movement (for example, diffusion with a fixed diffusion coefficient) but there is empirical evidence that movement rates and patterns may vary among different individuals. A simple way to capture variation in dispersal that has been suggested in the ecological literature is to allow individuals to switch between two distinct dispersal modes. We study models for populations whose members can switch between two different nonzero rates of diffusion and whose local population dynamics are subject to density dependence of logistic type. The resulting models are reaction–diffusion systems that can be cooperative at some population densities and competitive at others. We assume that the focal population inhabits a bounded region and study how its overall dynamics depend on the parameters describing switching rates and local population dynamics. (Traveling waves and spread rates have been studied for similar models in the context of biological invasions.) The analytic methods include ideas and results from reaction–diffusion theory, semi-dynamical systems, and bifurcation/continuation theory.     

Unifying population and landscape ecology with spatial capture–recapture

Spatial heterogeneity in the environment induces variation in population demographic rates and dispersal patterns, which result in spatio‐temporal variation in density and gene flow. Unfortunately, applying theory to learn about the role of spatial structure on populations has been hindered by the lack of mechanistic spatial models and inability to make precise observations of population state and structure. Spatial capture–recapture (SCR) represents an individual‐based analytic framework for overcoming this fundamental obstacle that has limited the utility of ecological theory. SCR methods make explicit use of spatial encounter information on individuals in order to model density and other spatial aspects of animal population structure, and they have been widely adopted in the last decade. We review the historical context and emerging developments in SCR models that enable the integration of explicit ecological hypotheses about landscape connectivity, movement, resource selection, and spatial variation in density, directly with individual encounter history data obtained by new technologies (e.g. camera trapping, non‐invasive DNA sampling). We describe ways in which SCR methods stand to advance the study of animal population ecology.     

Aggregations from using inadvertent social information: a form of ideal habitat selection

Social information in breeding site selection has received extensive study; however, few attempts have been made to link this process to pre‐existing models. We examine the importance of social information to three pertinent models of habitat selection that describe breeding aggregations and spatial patterns: 1) the ideal despotic distribution (IDD) which considers conspecific competition and habitat availability, 2) the perceptual constraints model which accounts for patch selection when animals experience a threshold of undetectable difference in quality, and 3) the “neighbourhood model” which predicts concordance between resources and settlers can be disrupted by conspecific attraction when resources are patchy. These models all predict initial settlers will select a high quality patch first. However, their predictions of subsequent settlement behaviour in remaining patches differ: the IDD predicts subsequent settlers will be distributed regularly, the perceptual constraints model predicts a random distribution, and the neighbourhood model predicts clustering from conspecific attraction. We examined which model best described settlement patterns of bobolink Dolichonyx oryzivorus and savannah sparrow Passerculus sandwichensis, in the context of social information. We observed settlement timing, quantified available resources, and determined where they occurred in the highest (local population “core”) and lowest densities (local population “periphery”). We then assessed whether individuals in the periphery settled in greater concordance with resources or conspecific presence. Core territories were clustered strongly on relevant resources, and these territory holders were older than in the periphery. Peripheral territories were likewise clustered but did not always co‐occur with the best available resources, matching the neighbourhood model prediction that social information may not always direct them to the best sites available. This suggests older individuals used their own experience to locate ideal habitat, whereas younger individuals attempted to aggregate on seemingly ideal habitat by using conspecific location; such information asymmetry due to age can be viewed as an “ideal aggregative distribution”.     

Effects of perceptual and movement ranges on joint predator–prey distributions

We developed a spatially‐explicit individual‐based model to study how limited perceptual and movement ranges affect spatial predator–prey interactions. Earlier models of ‘predator–prey space games’ were often developed by modifying ideal free distribution models, which are spatially‐implicit and also assume that individuals are omniscient, although some more recent models have relaxed these assumptions. We found that under some conditions, the spatially‐explicit model generated similar predictions to previous models. However, the model showed that limited range in a spatially‐explicit context generated different predictions when 1) predator density and range are both small, and 2) when the predator movement range varied while the prey range was small. The model suggests that the differences were the result of 1) movement range changing the value of information sources and thus changing the behavior of individual predators and prey and 2) movement range limiting the ability of individuals to exploit the environment.     

The Dispersal System of a Butterfly: A Test of Source-Sink Theory Suggests the Intermediate-Scale Hypothesis

Theory predicts source-sink dynamics can occur in species with the ideal preemptive distribution but not with the ideal free distribution. Source-sink dynamics can also occur in species with passive dispersal, in which a fixed fraction of the population disperses each generation. However, in nature, dispersal often approximates random diffusion rather than ideal choices or fixed probabilities. Here, I ask which dispersal system occurred in a butterfly (Euphydryas editha) known to have source-sink dynamics. The study used 13 experimental sites, where vacant and occupied habitat patches were juxtaposed. I estimated movement during the flight season and tested hypotheses about the type of dispersal system. Ideal free and ideal preemptive models were rejected because per capita movement rates were density independent. Passive dispersal was rejected because per capita rates were related to patch area and habitat preference. The diffusion model best explained the data because it predicted both the area relationship and an odd feature of the habitat preference: immigration was not higher in preferred habitat; rather, emigration was lower. The diffusion model implied that source-sink dynamics were driven by diffusion from areas of high to low population density. Existing source-sink theory assumes fine-scale patchiness, in which animals have perfect knowledge and ease of mobility. The results from the butterfly suggest that source-sink dynamics arise at coarser spatial scales, where diffusion models apply.     

A Model of Spatial Epidemic Spread When Individuals Move Within Overlapping Home Ranges

One of the central goals of mathematical epidemiology is to predict disease transmission patterns in populations. Two models are commonly used to predict spatial spread of a disease. The first is the distributed-contacts model, often described by a contact distribution among stationary individuals. The second is the distributed-infectives model, often described by the diffusion of infected individuals. However, neither approach is ideal when individuals move within home ranges. This paper presents a unified modeling hypothesis, called the restricted-movement model. We use this model to predict spatial spread in settings where infected individuals move within overlapping home ranges. Using mathematical and computational approaches, we show that our restricted-movement model has three limits: the distributed-contacts model, the distributed-infectives model, and a third, less studied advective distributed-infectives limit. We also calculate approximate upper bounds for the rates of an epidemic's spatial spread. Guidelines are suggested for determining which limit is most appropriate for a specific disease.     

Population assessment without individual identification using camera-traps: A comparison of four methods

The use of camera traps to estimate population size when animals are not individually recognizable is gaining traction in the ecological literature, because of its applicability in population conservation and management.We estimated population size of synthetic animals with four camera trap sampling-based statistical models that do not rely on individual recognition. Using a realistic model of animal movement to generate synthetic data, we compared the random encounter model, the random encounter and staying time model, the association model and the time-to-event-model and we investigated the impact of violation of assumptions on the population size estimates.While under ideal conditions these models provide reliable population estimates, when synthetic animal movements were characterised by differences in speed (due to diverse behaviours such as locomotion, grazing and resting) none of the model provided both unbiased and precise density estimates. The random encounter model and the time-to-event-model provided precise results but tended to overestimate population size, while the random encounter and staying time model was less precise and tended to underestimate population size. Lastly, the association model was unable to provide precise results. We found that each tested model was very sensitive to the method used to estimate the range of the field-of-view of camera traps. Density estimates from both random encounter model and time-to-event-model were also very sensitive to biases in the estimate of animals’ speed. We provide guidelines on how to use these statistical models to get population size estimates that could be useful to wildlife managers and practitioners.     

Characteristic spatial and temporal scales unify models of animal movement

Animal movements have been modeled with diffusion at large scales and with more detailed movement models at smaller scales. We argue that the biologically relevant behavior of a wide class of movement models can be efficiently summarized with two parameters: the characteristic temporal and spatial scales of movement. We define these scales so that they describe movement behavior both at short scales (through the velocity autocorrelation function) and at long scales (through the diffusion coefficient). We derive these scales for two types of commonly used movement models: the discrete-step correlated random walk, with either constant or random step intervals, and the continuous-time correlated velocity model. For a given set of characteristic scales, the models produce very similar trajectories and encounter rates between moving searchers and stationary targets. Thus, we argue that characteristic scales provide a unifying currency that can be used to parameterize a wide range of ecological phenomena related to movement.     

Individual‐based ecology of coastal birds

Conservation objectives for non‐breeding coastal birds (shorebirds and wildfowl) are determined from their population size at coastal sites. To advise coastal managers, models must predict quantitatively the effects of environmental change on population size or the demographic rates (mortality and reproduction) that determine it. As habitat association models and depletion models are not able to do this, we developed an approach that has produced such predictions thereby enabling policy makers to make evidence‐based decisions. Our conceptual framework is individual‐based ecology, in which populations are viewed as having properties (e.g. size) that arise from the traits (e.g. behaviour, physiology) and interactions of their constituent individuals. The link between individuals and populations is made through individual‐based models (IBMs) that follow the fitness‐maximising decisions of individuals and predict population‐level consequences (e.g. mortality rate) from the fates of these individuals. Our first IBM was for oystercatchers Haematopus ostralegus and accurately predicted their density‐dependent mortality. Subsequently, IBMs were developed for several shorebird and wildfowl species at several European sites, and were shown to predict accurately overwinter mortality, and the foraging behaviour from which predictions are derived. They have been used to predict the effect on survival in coastal birds of sea level rise, habitat loss, wind farm development, shellfishing and human disturbance. This review emphasises the wider applicability of the approach, and identifies other systems to which it could be applied. We view the IBM approach as a very useful contribution to the general problem of how to advance ecology to the point where we can routinely make meaningful predictions of how populations respond to environmental change.     

Phenotypic plasticity and optimal timing of metamorphosis under uncertain time constraints

Life-history theory suggests that optimal timing of metamorphosis should depend on growth conditions and time constraints under which individuals develop. Current models cannot make reliable predictions for species in ephemeral habitats where individuals often face an increasing mortality risk over time because these models assume time-invariant mortality rates (i.e., daily mortality rates remain constant) and fixed seasons. We examined the plasticity of growth, development, and body mass at metamorphosis in tadpoles of the tree-hole breeding frog Phrynobatrachus guineensis in relation to an unpredictable time constraint in the field and in controlled experiments along a fixed density and food gradient. Mean mass and age at metamorphosis of sibships were positively correlated with per capita food level. Based on our results, we developed a simple model of the optimal timing of metamorphosis under time-dependent mortality rates showing that development rates are not only adjusted to growth conditions but also to time-variant mortality rates. The increasing mortality rate represents a time constraint that favors a reduced larval period, but because it is based on probabilities of survival it allows a trade-off between development time and mass. We extend this model to different types of time constraints and show that it can predict the range of documented reaction norms. Differences between species in␣the correlation of age and mass at metamorphosis may have evolved due to differences in their time-variant mortality rates.     

Designating Seasonality Using Rate of Movement

ABSTRACT Traditionally, seasons for animals have been designated based on single external variables such as climate or plant phenology, rather than an animal's response to the dynamic environments within which it lives. By interpreting a rate of movement function of cumulative movement through time we established a method that distinguishes transitions between behaviors limited by winter habitat conditions from those present during summer. Identification of these time periods provides temporal definition to subsequent home-range analyses and use-availability comparisons. We used location data from 32 Global Positioning System-collared female moose (Alces alces) to demonstrate the method. We used model selection (Akaike's Information Criterion) to differentiate between candidate rate of movement response curves. Of 32 moose, 29 clearly conformed to an annual movement pattern described by a logistic curve, with increased rates of movement in summer compared to winter. Conversely, 3 aberrant individuals did not alter their movement rate through the year and were best fit with a linear response curve. The seasonal rate of movement model we developed suggests an average summer period of 122 days (median = 119 days, range = 96–173 days) for moose in northwestern Ontario, Canada. The rate of movement model we applied to individuals indicated 1 May as the median date for the winter-summer transition (range = 2 Apr–24 May), and the median transition from summer to winter was 25 August (range = 1 Aug–23 Oct). Wide variation in timing and duration of summer and winter seasons among individuals demonstrates potential failure of the single external variable approach to capture the suite of factors potentially influencing animal behaviors. By plotting cumulative distance moved throughout the year, we elucidated individual variation in response to known and unknown variables that affect animal movement. Accounting for variability among individuals in designation of biologically significant temporal boundaries is critical to delineation of seasonally important habitats for conservation and sustainability of healthy wildlife populations.     

Ideal free distributions when individuals differ in competitive ability: phenotype-limited ideal free models

A series of prospective models is developed to investigate ideal free distributions in populations where individuals differ in competitive ability. The models are of three types. In the continuous-input models, there is continuous arrival of food or mates into each habitat patch, and competitors scramble to obtain as large a share as possible. In the interference models, the prey density in a particular patch stays constant but the presence of competitors slows down the rate at which prey are captured. In the kleptoparasitism model, individuals have food or females stolen from them by competitors higher in the dominance hierarchy, and in turn steal items from subordinates. A general result of the continuous-input and interference models is that the population of competitors can be truncated between patches so that the individuals with the highest competitive ability occur in the best patches, or in the patches where competitive differences are greatest. Individuals of lowest competitive ability occur in the poorest patches or where competitive differences are least, and intermediate phenotypes are ranked between these two extremes. Thus the ideal free prediction that all individuals will achieve equal fitness will not apply. However, in continuous-input cases where competitive differences between phenotypes remain constant across patches, this solution is only neutrally stable, and forms only one element of a set of equilibrium distributions. The fact that many empirical studies of continuous-input have found approximately equal mean fitness across patches may relate to this finding. Most interference studies contradict the simple ideal free solution by having different mean intake rates across patches; this may relate to the predicted positive correlation of competitive ability with patch quality. The kleptoparasitism model usually generated continuous cycling of individuals between habitat patches, though some correlation could be found between competitive ability and patch quality.     

Optimal diet selection,frequency dependence and prey renewal

This paper extends existing models of frequency-dependent diet selection by considering the optimal diet selection of a predator feeding upon prey populations which can be depleted but are also capable of renewal (e.g. immigration, growth, or reproduction). This model and existing models which include prey depletion, predict partial-preference and a generic diet preference for the commonest prey types (apostatic selection). Unlike previous diet selection models, it is found that the optimal diet selection of an individual predator can be to favour the rarest prey type (anti-apostatic selection) when encounter rates are high, even if the individual prey do not differ in their nutritional value. Studies have demonstrated that predators generally show apostatic selection, even when all prey have the same nutritional value. Anti-apostatic selection has also been observed when prey are crowded, and therefore at high density, consistent with the idea of high encounter rates. This anti-apostatic diet selection has previously been proposed as evidence for the use of prey search images by a predator, or variation in individual prey preference. In this paper it is suggested that prey renewal is a further factor, often confounded in experiments, which could favour anti-apostatic selection.     

Competition for females on leks when male competitive abilities differ: empirical test of a model

Leks are mating arenas visited by females seeking copulationsand can be thought of as patches differing in female encounterrate. Recently, the ideal free distribution model of unequalcompetitors with interference has been applied to explain maledistributions between leks. This model predicts that the malesof highest competitive ability should be present on the lekswith the highest female encounter rates and should be most successful.I tested the predictions from the model with empirical datafrom the ruff, Philomachus pugnax. Contrary to the predictionsfrom the model, low-ranking males preferentially visited theleks with highest female encounter rates, where the degree ofmale aggression was greatest Furthermore, there was no generalrelationship between female encounter rate and male success,and the empirical data again refute the predictions from themodel. The results illustrate the problem of using male per-capitasuccess when predicting individual behavior. Several more generalproblems with applying the ideal free distribution of unequalcompetitors model to competition for mates are also discussed.     

Evidence of a link between demographic rates and species habitat suitability from post release movements in a reinforced bird population

Despite the increasing use of species distribution models for predicting current or future animal distribution, only a few studies have linked the gradient of habitat suitability (HS) to demographic parameters. While such approaches can improve the reliability of models, they can help to better predict the response of species to changes in HS over space and time, as induced by ongoing global change. Here, we tested whether the spatial variation in HS along the individual movement path is related to survival, using extensive tracking data collected from captive‐bred individuals translocated to reinforce the wild populations of houbara bustard. We first modelled and mapped the HS from presence data of wild individuals using niche models in a consensus framework. We further analysed survival of released individuals using capture–recapture modelling and its links to HS, as the trend in suitability from the release sites along movements. We found that the survival of released individuals was related to changes in HS along their movements. For instance, individuals which moved to sites of lower HS than their release sites have lower survival probabilities than the others, independently of the HS of the release sites and daily movement rate. Our results provide an empirical support of the relationship between HS and survival, a major fitness component.     

Spatial capture–recapture models allowing Markovian transience or dispersal

Spatial capture–recapture (SCR) models are a relatively recent development in quantitative ecology, and they are becoming widely used to model density in studies of animal populations using camera traps, DNA sampling and other methods which produce spatially explicit individual encounter information. One of the core assumptions of SCR models is that individuals possess home ranges that are spatially stationary during the sampling period. For many species, this assumption is unlikely to be met and, even for species that are typically territorial, individuals may disperse or exhibit transience at some life stages. In this paper we first conduct a simulation study to evaluate the robustness of estimators of density under ordinary SCR models when dispersal or transience is present in the population. Then, using both simulated and real data, we demonstrate that such models can easily be described in the BUGS language providing a practical framework for their analysis, which allows us to evaluate movement dynamics of species using capture–recapture data. We find that while estimators of density are extremely robust, even to pathological levels of movement (e.g., complete transience), the estimator of the spatial scale parameter of the encounter probability model is confounded with the dispersal/transience scale parameter. Thus, use of ordinary SCR models to make inferences about density is feasible, but interpretation of SCR model parameters in relation to movement should be avoided. Instead, when movement dynamics are of interest, such dynamics should be parameterized explicitly in the model.     

Dynamical modeling of collective behavior from pigeon flight data: flock cohesion and dispersion

Several models of flocking have been promoted based on simulations with qualitatively naturalistic behavior. In this paper we provide the first direct application of computational modeling methods to infer flocking behavior from experimental field data. We show that this approach is able to infer general rules for interaction, or lack of interaction, among members of a flock or, more generally, any community. Using experimental field measurements of homing pigeons in flight we demonstrate the existence of a basic distance dependent attraction/repulsion relationship and show that this rule is sufficient to explain collective behavior observed in nature. Positional data of individuals over time are used as input data to a computational algorithm capable of building complex nonlinear functions that can represent the system behavior. Topological nearest neighbor interactions are considered to characterize the components within this model. The efficacy of this method is demonstrated with simulated noisy data generated from the classical (two dimensional) Vicsek model. When applied to experimental data from homing pigeon flights we show that the more complex three dimensional models are capable of simulating trajectories, as well as exhibiting realistic collective dynamics. The simulations of the reconstructed models are used to extract properties of the collective behavior in pigeons, and how it is affected by changing the initial conditions of the system. Our results demonstrate that this approach may be applied to construct models capable of simulating trajectories and collective dynamics using experimental field measurements of herd movement. From these models, the behavior of the individual agents (animals) may be inferred.