How do grazers achieve their distribution? A continuum of models from random diffusion to the ideal free distribution using biased random walks

A conceptual model is described for generating distributions of grazing animals, according to their searching behavior, to investigate the mechanisms animals may use to achieve their distributions. The model simulates behaviors ranging from random diffusion, through taxis and cognitively aided navigation (i.e., using memory), to the optimization extreme of the Ideal Free Distribution. These behaviors are generated from simulation of biased diffusion that operates at multiple scales simultaneously, formalizing ideas of multiple-scale foraging behavior. It uses probabilistic bias to represent decisions, allowing multiple search goals to be combined (e.g., foraging and social goals) and the representation of suboptimal behavior. By allowing bias to arise at multiple scales within the environment, each weighted relative to the others, the model can represent different scales of simultaneous decision-making and scale-dependent behavior. The model also allows different constraints to be applied to the animal's ability (e.g., applying food-patch accessibility and information limits). Simulations show that foraging-decision randomness and spatial scale of decision bias have potentially profound effects on both animal intake rate and the distribution of resources in the environment. Spatial variograms show that foraging strategies can differentially change the spatial pattern of resource abundance in the environment to one characteristic of the foraging strategy.</

Beyond the ideal free distribution: More general models of predator distribution

The ideal free distribution model which relates the spatial distribution of mobile consumers to that of their resource is shown to be a limiting case of a more general model which we develop using simple concepts of diffusion. We show how the ideal free distribution model can be derived from a more general model and extended by incorporating simple models of social influences on predator spacing. First, a free distribution model based on patch switching rules, with a power-law interference term, which represents instantaneous biased diffusion is derived. A social bias term is then introduced to represent the effect of predator aggregation on predator fitness, separate from any effects which act through intake rate. The social bias term is expanded to express an optimum spacing for predators and example solutions of the resulting biased diffusion models are shown. The model demonstrates how an empirical interference coefficient, derived from measurements of predator and prey densities, may include factors expressing the impact of social spacing behaviour on fitness. We conclude that empirical values of log predator/log prey ratio may contain information about more than the relationship between consumer and resource densities. Unlike many previous models, the model shown here applies to conditions without continual input. (C) 1997 Academic Press Limited.</p>

Non-competitive phenotypic differences can have a strong effect on ideal free distributions

1. We present a model of the ideal free distribution (IFD) where differences between phenotypes other than those involved in direct competition for resources are considered. We show that these post-acquisitional differences can have a dramatic impact on the predicted distributions of individuals.

2. Specifically, we predict that, when the relative abilities of phenotypes are independent of location, there will be a continuum of mixed evolutionarily stable strategy (ESS) distributions (where all phenotypes are present in all patches).

3, When the relative strengths of the post-acquisitional trait in the two phenotypes differ between patches, however, we predict only a single ESS at equilibrium. Further, this distribution may be fully or partially segregated (with the distribution of at least one phenotype being spatially restricted) but it will never be mixed.

4, Our results for post-acquisitional traits mirror those of Parker (1982) for direct competitive traits. This comparison illustrates that it does not matter whether individual differences are expressed before or after competition for resources, they will still exert considerable influence on the distribution of the individuals concerned.

Drivers of the distribution of fisher effort at Lake Alaotra, Madagascar

Understanding how fishers make decisions is important for improving management of fisheries. There is debate about the extent to which small-scale fishers follow an ideal free distribution (IFD) - distributing their fishing effort efficiently according to resource availability rather than being influenced by social factors or personal preference. Using detailed data from 1800 fisher catches and from semi-structured interviews with over 700 fishers at Lake Alaotra, the largest inland fishery in Madagascar, we show that fishers generally conform to IFD. However, there were differences in catch: effort relationships between fishers using different gear types as well as other revealing deviations from the predictions of IFD. Fishers report routine as the primary determinant of their choice of fishing location, explaining why they do not quickly respond to changes in catch at a site. Understanding the influences on fishers' spatial behaviour will allow better estimates of costs of fishing policies on resource users, and help predict their likely responses. This can inform management strategies to minimise the negative impacts of interventions, increasing local support for and compliance with rules.

Understanding Demographic and Behavioral Mechanisms that Guide Responses of Neotropical Migratory Birds to Urbanization: a Simulation Approach

Although studies often report that densities of many forest birds are negatively related to urbanization, the mechanisms guiding this pattern are poorly understood. Our objective was to use a population simulation to examine the relative influence of six demographic and behavioral processes on patterns of avian abundance in urbanizing landscapes. We constructed an individual-based population simulation model representing the annual cycle of a Neotropical migratory songbird. Each simulation was performed under two landscape scenarios. The first scenario had similar proportions of high- and low-quality habitat across the urban to rural gradient. Under the first scenario, avian density was negatively related to urbanization only when rural habitats were perceived to be of higher quality than they actually were. The second landscape scenario had declining proportions of high-quality habitat as urbanization increased. Under the second scenario, each mechanism generated a negative relationship between density and urbanization. The strongest effect on density resulted when birds preferentially selected habitats in landscapes from which they fledged or were constrained from dispersing. The next strongest patterns occurred when birds directly evaluated habitat quality and accurately selected the highest-quality available territories. When birds selected habitats based on the presence of conspecifics, the density–urbanization relationship was only one-third the strength of other habitat selection mechanisms and only occurred under certain levels of population survival. Although differences in adult or nest survival in the face of random habitat selection still elicited reduced densities in urban landscapes, the relationships between urbanization and density were weaker than those produced by the conspecific attraction mechanism. Results from our study identify key predictions and areas for future research, including assessing habitat quality in urban and rural areas in order to determine if habitats in urban areas are underutilized.

Sample size determination in combinatorial chemistry.

Combinatorial chemistry is gaining wide appeal as a technique for generating molecular diversity. Among the many combinatorial protocols, the split/recombine method is quite popular and particularly efficient at generating large libraries of compounds. In this process, polymer beads are equally divided into a series of pools and each pool is treated with a unique fragment; then the beads are recombined, mixed to uniformity, and redivided equally into a new series of pools for the subsequent couplings. The deviation from the ideal equimolar distribution of the final products is assessed by a special overall relative error, which is shown to be related to the Pearson statistic. Although the split/recombine sampling scheme is quite different from those used in analysis of categorical data, the Pearson statistic is shown to still follow a chi2 distribution. This result allows us to derive the required number of beads such that, with 99% confidence, the overall relative error is controlled to be less than a pregiven tolerable limit L1. In this paper, we also discuss another criterion, which determines the required number of beads so that, with 99% confidence, all individual relative errors are controlled to be less than a pregiven tolerable limit L2 (0 < L2 < 1).

Habitat selection and population regulation in temporally fluctuating environments

Understanding and predicting the distribution of organisms in heterogeneous environments lies at the heart of ecology, and the theory of density-dependent habitat selection (DDHS) provides ecologists with an inferential framework linking evolution and population dynamics. Current theory does not allow for temporal variation in habitat quality, a serious limitation when confronted with real ecological systems. We develop both a stochastic equivalent of the ideal free distribution to study how spatial patterns of habitat use depend on the magnitude and spatial correlation of environmental stochasticity and also a stochastic habitat selection rule. The emerging patterns are confronted with deterministic predictions based on isodar analysis, an established empirical approach to the analysis of habitat selection patterns. Our simulations highlight some consistent patterns of habitat use, indicating that it is possible to make inferences about the habitat selection process based on observed patterns of habitat use. However, isodar analysis gives results that are contingent on the magnitude and spatial correlation of environmental stochasticity. Hence, DDHS is better revealed by a measure of habitat selectivity than by empirical isodars. The detection of DDHS is but a small component of isodar theory, which remains an important conceptual framework for linking evolutionary strategies in behavior and population dynamics.

Fish population dynamics in a seasonally varying wetland

Small fishes in seasonally flooded environments such as the Everglades are capable of spreading into newly flooded areas and building up substantial biomass. Passive drift cannot account for the rapidity of observed population expansions. To test the ‘reaction–diffusion’ mechanism for spread of the fish, we estimated their diffusion coefficient and applied a reaction–diffusion model. This mechanism was also too weak to account for the spatial dynamics. Two other hypotheses were tested through modeling. The first—the ‘refuge mechanism’—hypothesizes that small remnant populations of small fishes survive the dry season in small permanent bodies of water (refugia), sites where the water level is otherwise below the surface. The second mechanism, which we call the ‘dynamic ideal free distribution mechanism’ is that consumption by the fish creates a prey density gradient and that fish taxis along this gradient can lead to rapid population expansion in space. We examined the two alternatives and concluded that although refugia may play an important role in recolonization by the fish population during reflooding, only the second, taxis in the direction of the flooding front, seems capable of matching empirical observations. This study has important implications for management of wetlands, as fish biomass is an essential support of higher trophic levels.

Patch selection behaviour in the presence of environmental constraints

Habitat selection behaviour is the primary way in which organisms are able to regulate encounters with their biotic and abiotic environment. An individual chooses an area that best meets their current needs, particularly regarding safety and the presence of high-quality food. Several physical aspects of the environment can make it difficult for individuals to assess the relative habitat quality of the areas available, thus leading to suboptimal habitat selection. In this thesis, I investigated the way in which two aquatic habitat constraints - obstacles to movement between patches and turbidity - affected the ability of fish to make optimal patch choices, using threespine stickleback Gasterosteus aculeatus as a model species. Laboratory experiments showed that when movement between patches was hindered by increasingly challenging obstacles, groups of stickleback did not move as freely between the patches, and thus had greater deviations from the predictions of the Ideal Free Distribution (IFD). I also demonstrated that, unlike other species, stickleback do not use turbid environments to avoid predator detection. A trend was seen towards avoidance of a turbid food patch regardless of risk level, although this was not statistically significant. As expected, the stickleback avoided feeding in the presence of a predator regardless of water clarity. Overall, I found that both turbidity and movement constraints can have significant impacts on patch use and distribution in the threespine stickleback. Both turbidity and ease of transit will impact the distribution of ecologically important species like the threespine stickleback, and therefore should be taken into account when studying habitat selection in the wild.

Residence Time Distribution Models Derived from Non-Ideal Laminar Velocity Profiles in Tubes

The theoretical E-curve for the laminar flow of non-Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks-in-series models of residence time distribution (RTD). In this work, four RTD models derived from non-ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.

On the breakdown of the most probable distribution for mayer clusters

We present an analysis of the breakdown of the most probable approximation to the Mayer cluster size distribution for clusters of size comparable to the size of the system. This failure is illustrated by considering an ideal Bose gas for which exact volume dependent reducible cluster integrals are available.

Activities and their relation to cation distribution in NiAl2O4 MgAl2O4 spinel solid solutions

The activity of NiAl2O4 in NiAl2O4MgAl2O4 solid solutions has been measured by using a solid oxide galvanic cell of the type, Pt, Ni + NiAl2O4 + Al2O3(α)/CaOZrO2/Ni + NixMg1−xAl2O4 + Al2O3(α). Pt, in the temperature range 750–1150°C. The activities in the spinel solid solutions show negative deviations from Raoult's law. The cation distribution in the solid solutions has been calculated using site preference energies independent of composition for Ni2+, Mg2+, and Al3+ ions obtained from crystal field theory and measured cation disorder in pure NiAl2O4 and MgAl2O4, and assumi g ideal mixing of cations on the tetrahedral and octahedral positions. The calculated values correctly predict the decrease in the fraction, α, of Ni2+ ions on tetrahedral sites for 1>x>0.25, observed by Porta et al. [J. Solid State Chem.11, 135 (1974)] but do not support their tentative evidence for an increase in α for x < 0.25. The measured excess free energy of mixing can be completely accounted for by using either the calculated or the measured cation distributions. This suggests that the Madelung energy is approximately a linear function of composition in the solid solutions. The composition of NiOMgO solid solutions in equilibrium with NiAl2O4MgAl2O4 solid solutions has been calculated from the results and information available in literature.