Movement between patches, unequal competitors and the ideal free distribution

Models and measures of animal aggregation and dispersal

The dispersal of individuals within an animal population will depend upon local properties intrinsic to the environment that differentiate superior from inferior regions as well as properties of the population. Competing concerns can either draw conspecifics together in aggregation, such as collective defence against predators, or promote dispersal that minimizes local densities, for instance to reduce competition for food. In this paper we consider a range of models of non-independent movement. We include established models, such as the ideal free distribution, but also develop novel models, such as the wheel. We also develop several ways to combine different models to create a flexible model of addressing a variety of dispersal mechanisms. We further devise novel measures of movement coordination and show how to generate a population movement that achieves appropriate values of the measure specified. We find the value of these measures for each of the core models described, as well as discuss their use, and potential limitations, in discerning the underlying movement mechanisms. The movement framework that we develop is both of interest as a stand-alone process to explore movement, but also able to generate a variety of movement patterns that can be embedded into wider evolutionary models where movement is not the only consideration.

Effect of Spatial Dispersion on Evolutionary Stability: A Two-Phenotype and Two-Patch Model

In this paper, we investigate a simple two-phenotype and two-patch model that incorporates both spatial dispersion and density effects in the evolutionary game dynamics. The migration rates from one patch to another are considered to be patch-dependent but independent of individual’s phenotype. Our main goal is to reveal the dynamical properties of the evolutionary game in a heterogeneous patchy environment. By analyzing the equilibria and their stabilities, we find that the dynamical behavior of the evolutionary game dynamics could be very complicated. Numerical analysis shows that the simple model can have twelve equilibria where four of them are stable. This implies that spatial dispersion can significantly complicate the evolutionary game, and the evolutionary outcome in a patchy environment should depend sensitively on the initial state of the patches.

Whether ideal free or not, predatory mites distribute so as to maximize reproduction

Ideal free distribution (IFD) models predict that animals distribute themselves such that no individual can increase its fitness by moving to another patch. Many empirical tests assume that the interference among animals is independent of density and do not quantify the effects of density on fitness traits. Using two species of predatory mites, we measured oviposition as a function of conspecific density. Subsequently, we used these functions to calculate expected distributions on two connected patches. We performed an experimental test of the distributions of mites on two such connected patches, among which one had a food accessibility rate that was twice as high as on the other. For one of the two species, Iphiseius degenerans, the distribution matched the expected distribution. The distribution also coincided with the ratio of food accessibility. The other species, Neoseiulus cucumeris, distributed itself differently than expected. However, the oviposition rates of both species did not differ significantly from the expected oviposition rates based on experiments on single patches. This suggests that the oviposition rate of N. cucumeris was not negatively affected by the observed distribution, despite the fact that N. cucumeris did not match the predicted distributions. Thus, the distribution of one mite species, I. degenerans, was in agreement with IFD theory, whereas for the other mite species, N. cucumeris, unknown factors may have influenced the distribution of the mites. We conclude that density-dependent fitness traits provide essential information for explaining animal distributions.

Generalized movement strategies for constrained consumers: ignoring fitness can be adaptive

Abstract Movements made by real organisms--such as movements involved in dispersal, migration, and habitat selection--are expected to occasionally be suboptimal because of realistic constraints imposed by incomplete information, perceptual limitations, and stochasticity. Previous theory considering such constraints has shown that movements appropriately conditioned on habitat or resource characteristics can balance out suboptimal components of movement and thereby lead organisms to ideal free distributions and fitness maxima, whereas movements conditioned on fitness differentials cannot. These findings suggest a somewhat paradoxical hypothesis: even if organisms have information about their fitness, movement strategies that maximize fitness may be conditioned on something other than fitness per se. We test this hypothesis by investigating the evolutionary stability of generalized, conditional movement strategies that vary in their use of information on fitness versus information on habitat characteristics. We show that when costs of sensory machinery are included, natural selection should favor movement strategies that completely ignore fitness information. Finally, we synthesize previous work by showing how several previous important theoretical results for adaptive movement strategies are united under our one general model.

Are there trade-offs between pre- and post-fledging survival in black brent geese?

1. The growth period is an important determinant of fitness later in life through its effects on first-year survival and future reproduction. Choices by adult females about where to rear their offspring strongly affect growth rates and offspring fitness in geese. 2. Individual female black brent (Branta bernicla nigricans) tend to raise their broods in the same areas each year, and these areas are consistently ranked with respect to growth rates of goslings. Therefore, some females consistently rear their broods on areas resulting in lower post-fledging fitness. 3. We explore the potential that growth rates of offspring (and associated fitness consequences) are traded off against other vital rates influencing fitness of either adult females or goslings. Growth of goslings primarily influences fitness after fledging, so one hypothesis is that survival before fledging, which is influenced by predation, is traded off against growth rates and post-fledging survival. 4. We estimated pre-fledging and post-fledging survival for goslings reared on areas used by broods from the Tutakoke River black brent colony. We examined recaptures, recoveries by hunters and resightings of brent marked as goslings with webtags and standard leg rings. These data were analyzed using capture-mark-recapture models in program mark to derive separate estimates of pre- and post-fledging survival for 18 cohorts (1987-2004) of black brent goslings across seven brood rearing areas (BRAs). 5. Estimates of pre-fledging survival probability varied from 0·00 ± 0·00 (mean ± 95% confidence interval) to 0·92 ± 0·1; and estimates of post-fledging survival probability varied from 0·00 ± 0·00 to 1·00 ± 0·08. Substantial variation existed both among BRAs and years but post-fledging survival declined substantially during the study. 6. Pre- and post-fledging survival were positively correlated, exhibiting a quadratic relationship (ß(post-fledging survival)  = 1·00 (±0·47)x-0·83 (±0·480)x(2) , where x = pre-fledging survival). Therefore, we did not find a trade-off between pre- and post-fledging survival in black brent goslings across BRAs, suggesting that factors other than foraging conditions and predation on goslings must influence selection of BRAs.

Process-based approach reveals directional effects of environmental factors on movement between habitats

1. Understanding the effects of environmental factors on animal distributions is a central issue in ecology. However, movement rules inferred from distribution patterns do not reveal the processes through which animal distribution is realized. 2. We investigated individual movement rules using a process-based approach. In experiments, coastal fish larvae (red drum, Sciaenops ocellatus) were matched with an intraspecific competitor of different sizes, and time series of habitat transition of individuals were fitted with a continuous-time Markov chain model to evaluate the effects of the presence of a competitor, behavioural interactions and habitat quality on the likelihoods of habitat transition. 3. The process-based approach revealed that these factors did not simply act as a 'slope' between habitats that makes it easier to go in one direction and more difficult to return. Rather, these factors modify the movement rules differently depending on the directions of the movement. 4. Individuals were less likely to enter a better habitat in the presence of a larger conspecific, more likely to shift to a poorer habitat when they received aggressive behaviour and more likely to stay in a better habitat in the presence of food. However, no effect was found on the transition intensity for moving in the opposite direction. 5. The process-based approach to evaluating movement rules of animals allowed us to see the contrasting directional effects of different factors on the underlying movement rules used by animals, as opposed to pattern-based fitting of observed distributions. Consideration of these rules would improve the existing habitat-choice models.

The ideal free distribution: a review and synthesis of the game-theoretic perspective

The Ideal Free Distribution (IFD), introduced by Fretwell and Lucas in [Fretwell, D.S., Lucas, H.L., 1970. On territorial behavior and other factors influencing habitat distribution in birds. Acta Biotheoretica 19, 16-32] to predict how a single species will distribute itself among several patches, is often cited as an example of an evolutionarily stable strategy (ESS). By defining the strategies and payoffs for habitat selection, this article puts the IFD concept in a more general game-theoretic setting of the "habitat selection game". Within this game-theoretic framework, the article focuses on recent progress in the following directions: (1) studying evolutionarily stable dispersal rates and corresponding dispersal dynamics; (2) extending the concept when population numbers are not fixed but undergo population dynamics; (3) generalizing the IFD to multiple species. For a single species, the article briefly reviews existing results. It also develops a new perspective for Parker's matching principle, showing that this can be viewed as the IFD of the habitat selection game that models consumer behavior in several resource patches and analyzing complications involved when the model includes resource dynamics as well. For two species, the article first demonstrates that the connection between IFD and ESS is now more delicate by pointing out pitfalls that arise when applying several existing game-theoretic approaches to these habitat selection games. However, by providing a new detailed analysis of dispersal dynamics for predator-prey or competitive interactions in two habitats, it also pinpoints one approach that shows much promise in this general setting, the so-called "two-species ESS". The consequences of this concept are shown to be related to recent studies of population dynamics combined with individual dispersal and are explored for more species or more patches.

Stochastic models of kleptoparasitism

In this paper, we consider a model of kleptoparasitism amongst a small group of individuals, where the state of the population is described by the distribution of its individuals over three specific types of behaviour (handling, searching for or fighting over, food). The model used is based upon earlier work which considered an equivalent deterministic model relating to large, effectively infinite, populations. We find explicit equations for the probability of the population being in each state. For any reasonably sized population, the number of possible states, and hence the number of equations, is large. These equations are used to find a set of equations for the means, variances, covariances and higher moments for the number of individuals performing each type of behaviour. Given the fixed population size, there are five moments of order one or two (two means, two variances and a covariance). A normal approximation is used to find a set of equations for these five principal moments. The results of our model are then analysed numerically, with the exact solutions, the normal approximation and the deterministic infinite population model compared. It is found that the original deterministic models approximate the stochastic model well in most situations, but that the normal approximations are better, proving to be good approximations to the exact distribution, which can greatly reduce computing time.

The role of behavioral dynamics in determining the patch distributions of interacting species

The effect of the behavioral dynamics of movement on the population dynamics of interacting species in multipatch systems is studied. The behavioral dynamics of habitat choice used in a range of previous models are reviewed. There is very limited empirical evidence for distinguishing between these different models, but they differ in important ways, and many lack properties that would guarantee stability of an ideal free distribution in a single-species system. The importance of finding out more about movement dynamics in multispecies systems is shown by an analysis of the effect of movement rules on the dynamics of a particular two-species-two-patch model of competition, where the population dynamical equilibrium in the absence of movement is often not a behavioral equilibrium in the presence of adaptive movement. The population dynamics of this system are explored for several different movement rules and different parameter values, producing a variety of outcomes. Other systems of interacting species that may lack a dynamically stable distribution among patches are discussed, and it is argued that such systems are not rare. The sensitivity of community properties to individual movement behavior in this and earlier studies argues that there is a great need for empirical investigation to determine the applicability of different models of the behavioral dynamics of habitat selection.

Putting competition strategies into ideal free distribution models: habitat selection as a tug of war

When resources are patchily distributed in an environment, behavioral ecologists frequently turn to ideal free distribution (IFD) models to predict the spatial distribution of organisms. In these models, predictions about distributions depend upon two key factors: the quality of habitat patches and the nature of competition between consumers. Surprisingly, however, no IFD models have explored the possibility that consumers modulate their competitive efforts in an evolutionarily stable manner. Instead, previous models assume that resource acquisition ability and competition are fixed within species or within phenotypes. We explored the consequences of adaptive modulation of competitive effort by incorporating tug-of-war theory into payoff equations from the two main classes of IFD models (continuous input (CI) and interference). In the models we develop, individuals can increase their share of the resources available in a patch, but do so at the costs of increased resource expenditures and increased negative interactions with conspecifics. We show how such models can provide new hypotheses to explain what are thought to be deviations from IFDs (e.g., the frequent observation of fewer animals than predicted in "good" patches of habitat). We also detail straightforward predictions made uniquely by the models we develop, and we outline experimental tests that will distinguish among alternatives.

Migration Dynamics for the Ideal Free Distribution

This article verifies that the ideal free distribution (IFD) is evolutionarily stable, provided the payoff in each patch decreases with an increasing number of individuals. General frequency-dependent models of migratory dynamics that differ in the degree of animal omniscience are then developed. These models do not exclude migration at the IFD where balanced dispersal emerges. It is shown that the population distribution converges to the IFD even when animals are nonideal (i.e., they do not know the quality of all patches). In particular, the IFD emerges when animals never migrate from patches with a higher payoff to patches with a lower payoff and when some animals always migrate to the best patch. It is shown that some random migration does not necessarily lead to undermatching, provided migration occurs at the IFD. The effect of population dynamics on the IFD (and vice versa) is analyzed. Without any migration, it is shown that population dynamics alone drive the population distribution to the IFD. If animal migration tends (for each fixed population size) to the IFD, then the combined migration-population dynamics evolve to the population IFD independent of the two timescales (i.e., behavioral vs. population).

Emergent Properties of Conspecific Attraction in Fragmented Landscapes

Attraction to conspecifics may have wide-ranging implications for habitat selection and metapopulation theory, yet little is known about the process of attraction and its effects relative to other habitat selection strategies. Using individual-based simulations, I investigated the emergent properties of conspecific attraction during habitat selection on survival, fecundity, short-term fitness (survival x fecundity), and distributions in fragmented landscapes. I simulated conspecific attraction during searching and settlement decisions and compared attraction with random, habitat-based (searching for the presence of habitat), and habitat quality sampling strategies (searching for and settling in high-quality habitat). Conspecific attraction during searching or settlement decisions had different consequences for animals: attraction while searching increased survival by decreasing time spent in nonsuitable habitat, whereas attraction during settlement increased fecundity by aggregating animals in high-quality habitats. Habitat-based sampling did not improve fitness over attraction, but directly sampling habitat quality resulted in the highest short-term fitness among strategies. These results suggest that attraction can improve fitness when animals cannot directly assess habitat quality. Interestingly, conspecific attraction influenced distributions by generating patch size effects and weak edge effects, highlighting that attraction is one potential, yet previously unappreciated, mechanism to explain the widespread patterns of animal sensitivity to habitat fragmentation.

Ecological mechanisms favouring behavioural diversification in the absence of morphological diversification: a theoretical examination using brook charr (Salvelinus fontinalis)

1. Behavioural diversification is thought to be an important initial step in the origin of resource polymorphisms. We developed a model for young brook charr (Salvelinus fontinalis Mitchill) to examine four mechanisms that could generate a U-shaped relationship between growth rate (fitness) and the proportion of time spent moving that would favour alternative foraging tactics in the absence of obvious differences in body size and shape. 2. Recently emerged brook charr of similar size and shape inhabit still-water pools along the sides of streams. Some individuals tend to sit and wait for crustacean prey at the pool substrate near the bank, while others tend to search actively for insect prey at the pool surface away from the bank. 3. The ecological mechanisms modelled were (i) the relationship between the rate of prey capture and the proportion of time spent moving is curvilinear, such that net rate of energy gain is maximized at two different levels of activity; (ii) switching between foraging locations and, hence, tactics involves lost opportunity and travel costs; (iii) switching between prey types and, hence, tactics involves a learning cost; and (iv) foraging success is status-dependent with individuals switching between tactics having a lower status than those specializing at a tactic. 4. Singly, no mechanism predicted the U-shaped relationship between growth rate and the proportion of time spent moving. Together, a U-shaped relationship was obtained, indicating that the behavioural diversification and diversifying selection observed in the field may be a consequence of multiple, subtle mechanisms.

A stochastic model of the distribution of unequal competitors between resource patches

We present a stochastic model of individuals' movements between two patches of resources. The population is made up of two types of individual with differing competitive abilities, and two types of movements occur, with individuals moving either to increase their intake rate or at random. Several previous models have used simulations to evaluate the likely distribution of individuals. We instead derive equations for the equilibrium distribution of the population, which can be solved numerically. This avoids the need to choose an initial distribution for the population, and enables us to obtain the probability with which rare events occur. This may not be possible when simulations are used, since a rare event may not occur at all. We find that when random movements are rare, an increase in the rate of random movements out of a patch can increase the number of individuals on that patch. We consider an approximation to the model with rare random movements, which provides an explanation for this phenomenon.

Movements and distribution of northern bottlenose whales, Hyperoodon ampullatus, on the Scotian Slope and in adjacent waters

A small, apparently isolated, and endangered population of ~130 northern bottlenose whales (Hyperoodon ampullatus Forster, 1770) is found on the Scotian Slope south of Nova Scotia, Canada. Virtually all previous information on these animals had come from the Gully, a large submarine canyon where the northern bottlenose whales can be reliably found. A ship survey along the 1000 m depth contour in 2001 showed northern bottlenose whales only in the Gully, Shortland canyon (50 km east of the Gully), and Haldimand canyon (100 km east of the Gully). Studies in 2002 reconfirmed the presence of the whales in these other canyons, although densities were about 50% lower than in the Gully. Photo-identifications showed that individuals moved between the Gully and Shortland and Haldimand canyons over periods from days to years, with mean stays in any canyon of about 22 days. However, the population was not fully mixed: at least some individuals had preferences for particular canyons. The sex ratios were similar in all canyons, but males had higher rates of movement between canyons. These results are consistent with the expectations of optimal foraging theory, when the primary resource for females, deep-water squid of the genus Gonatus Gray, 1849, is more temporally stable than the primary resource for males, which is assumed to be receptive females. Haldimand and Shortland canyons are clearly important habitat for this species, and should receive appropriate protection.

Integrating the roles of information and competitive ability on the spatial distribution of social foragers

Understanding and predicting the spatial distribution of social foragers among patchily distributed resources is a problem that has been addressed with numerous approaches over the 30 yr since the ideal free distribution (IFD) was first introduced. The two main approaches involve perceptual constraints and unequal competitors. Here we present a model of social foragers choosing among resource patches. Each forager makes a probabilistic choice on the basis of the information acquired through past foraging experiences. Food acquisition is determined by the forager's competitive ability. This model predicts that perceptual constraints have a greater influence on the spatial distribution of foragers than unequal competitive abilities but that competitive ability plays an important role in determining an individual's information state and behavior. Better competitors have access to more information; consequently, we find that competitive abilities and perceptual constraints are integrated through the social environment occupied by individual foragers. Relative competitive abilities influence the forager's information state, and the ability to use information determines the resulting spatial distribution.

Influence of food abundance on individual behaviour strategy and growth rate in juvenile brown trout (Salmo trutta)

We studied the benefit of being territorial as an effect of food abundance by measuring the proportions of individuals that displayed a territorial, floating (individuals occasionally displayed territorial behaviour), or nonterritorial (shoaling) behaviour strategy, and individual growth rates. Also, swimming activity was monitored as an indicator of emigration. Replicate groups of 12 juvenile brown trout (Salmo trutta) were released into an artificial stream channel, fed according to one of four food regimes for 10 days, and allocated to one of three behaviour categories. There was no significant relationship between food abundance and the number of territorial individuals. Instead, the proportions of individuals that displayed the alternative behaviour strategies, i.e., floating and nonterritorial, changed with food abundance. At the lowest food level, more individuals displayed nonterritorial than floating behaviour, but these two strategies were equally represented at the highest food level. The difference in growth rates with respect to behaviour category was highest at intermediate food levels. At the highest and lowest food levels, nonterritorial fish and floaters grew nearly as fast or as poorly, respectively, as the territorial individuals. Swimming activity between the two sections of the stream tank was greatest at the lowest food level, and there was a general tendency (not significant) for the floaters to exhibit the greatest activity.