CoFee-L: A Model of Animal Displacement in Large Groups Combining Cohesion Maintenance, Feeding Area Search and Transient Leadership

Simple Summary

In the current context of climate change and forest cover degradation, the dispersal potential of trees is an issue of great importance. This is particularly the case in the tropics, where trees often need animals to disperse their seeds, as this increases the chances of survival of the progeny and allows migration in the face of climate change. An accurate representation of animal movement is therefore necessary to study the colonization potential of trees in new areas. We have conceived an innovative mathematical model describing the individual movement of gregarious animals, integrating several fundamental features of collective behaviors: cohesion maintenance, feeding area search and leadership. The model was applied to simulate the movements of a wild-ranging troop of primates in a nature reserve. As a result, the model allowed us to simulate the movement of the troop, taking into account the movement and individual characteristics of each member, which is important to consider when the group is composed of many individuals. In the future, this model could be used to improve existing zoochoric seed dispersal models and can be coupled with dynamic vegetation models to predict the shifts of trees species distribution under future climate hypotheses.

Abstract

In the tropics, the conservation of tree species is closely linked to that of animals, as a large proportion of trees are zoochoric and therefore rely on the movement of animals to disperse their seeds in order to increase the chances of the survival of progeny and to allow migration in the face of climate change. Research into the prediction of animal movements is therefore critical but has so far focused only on particular features of collective behavior. In contrast, we included the concepts of cohesion maintenance, feeding area search and transient leadership in a single model, CoFee-L, and tested it to simulate the movement of a wild-ranging troop of primates (Macaca leonina). We analyzed and compared observations and simulations with a statistical physics tool (mean squared displacement) and with histograms and χ² (for the step length and turning angle distributions). CoFee-L allowed us to simulate the physical properties of the troop’s center of mass trajectory as well as the step length and angle distributions of the field data. The parametrization of CoFee-L was rather straightforward, as it was sufficient to fix a set of parameters easily observable in the field and then to adjust the values of four parameters that have biological meaning.

Individual Network Topology of Patch Selection Under Influence of Drifting Site Fidelity

Network theory has led to important insight into statistical-mechanical aspects of systems showing scaling complexity. I apply this approach to simulate the behavior of animal space use under the influence of memory and site fidelity. Based on the parsimonious Multi-scaled random walk model (MRW) an emergent property of self-reinforcing returns to a subset of historic locations shows how a network of nodes grows into an increased hierarchical depth of site fidelity. While most locations along a movement path may have a low revisit probability, habitat selection is maturing with respect to utilization of the most visited patches, in particular for patches that emerge during the early phase of node development. Using simulations with default MRW properties, which have been shown to produce space use in close statistical compliance with utilization distributions of many species of mammals, I illustrate how a shifting spatio-temporal mosaic of habitat utilization may be described statistically and given behavioral-ecological interpretation. The proposed method is illustrated with a pilot study using black bear Ursus americanus telemetry fixes. One specific parameter, the Characteristic Scale of Space Use, is here shown to express strong resilience against shifting site fidelity. This robust result may seem counter-intuitive, but is logical under the premise of the MRW model and its relationship to site fidelity, whether stable or shifting spatially over time. Thus, spatial analysis of the dynamics of a gradually drifting site fidelity using simulated scenarios may indirectly cast light on the dynamics of movement behavior as preferred patches are shifting over time. Both aspects of complex space use, network topology and dynamically drifting dispersion of site fidelity, provide in tandem important descriptors of behavioral ecology with relevance to habitat selection.

Prey encounters and spatial memory influence use of foraging patches in a marine central place forager

Given the patchiness and long-term predictability of marine resources, memory of high-quality foraging grounds is expected to provide fitness advantages for central place foragers. However, it remains challenging to characterize how marine predators integrate memory with recent prey encounters to adjust fine-scale movement and use of foraging patches. Here, we used two months of movement data from harbour seals (Phoca vitulina) to quantify the repeatability in foraging patches as a proxy for memory. We then integrated these data into analyses of fine-scale movement and underwater behaviour to test how both spatial memory and prey encounter rates influenced the seals' area-restricted search (ARS) behaviour. Specifically, we used one month's GPS data from 29 individuals to build spatial memory maps of searched areas and archived accelerometery data from a subset of five individuals to detect prey catch attempts, a proxy for prey encounters. Individuals were highly consistent in the areas they visited over two consecutive months. Hidden Markov models showed that both spatial memory and prey encounters increased the probability of seals initiating ARS. These results provide evidence that predators use memory to adjust their fine-scale movement, and this ability should be accounted for in movement models.

Memory drives the formation of animal home ranges: Evidence from a reintroduction

Most animals live in home ranges, and memory is thought to be an important process in their formation. However, a general memory-based model for characterising and predicting home range emergence has been lacking. Here, we use a mechanistic movement model to: (1) quantify the role of memory in the movements of a large mammal reintroduced into a novel environment, and (2) predict observed patterns of home range emergence in this experimental setting. We show that an interplay between memory and resource preferences is the primary process influencing the movements of reintroduced roe deer (Capreolus capreolus). Our memory-based model fitted with empirical data successfully predicts the formation of home ranges, as well as emergent properties of movement and spatial revisitation observed in the reintroduced animals. These results provide a mechanistic framework for combining memory-based movements, resource preferences, and the formation of home ranges in nature.

A review of bioenergetic modelling for marine mammal populations

Bioenergetic models describe the processes through which animals acquire energy from resources in the environment and allocate it to different life history functions. They capture some of the fundamental mechanisms regulating individuals, populations and ecosystems and have thus been used in a wide variety of theoretical and applied contexts. Here, I review the development of bioenergetic models for marine mammals and their application to management and conservation. For these long-lived, wide-ranging species, bioenergetic approaches were initially used to assess the energy requirements and prey consumption of individuals and populations. Increasingly, models are developed to describe the dynamics of energy intake and allocation and predict how resulting body reserves, vital rates and population dynamics might change as external conditions vary. The building blocks required to develop such models include estimates of intake rate, maintenance costs, growth patterns, energy storage and the dynamics of gestation and lactation, as well as rules for prioritizing allocation. I describe how these components have been parameterized for marine mammals and highlight critical research gaps. Large variation exists among available analytical approaches, reflecting the large range of life histories, management needs and data availability across studies. Flexibility in modelling strategy has supported tailored applications to specific case studies but has resulted in limited generality. Despite the many empirical and theoretical uncertainties that remain, bioenergetic models can be used to predict individual and population responses to environmental change and other anthropogenic impacts, thus providing powerful tools to inform effective management and conservation.

Exploring the Evolution of Perception: An Agent-Based Approach

Perception is central to the survival of an individual for many reasons, especially as it affects the ability to gather resources. Consequently, costs associated with perception are partially shaped by resource availability. Understanding the interplay of environmental factors (such as the density and distribution of resources) with species-specific factors (such as growth rate, mutation, and metabolic costs) allows the exploration of possible trajectories by which perception may evolve. Here, we used an agent-based foraging model with a context-dependent movement strategy in which each agent switches between undirected and directed movement based on its perception of resources. This switching behavior is central to our goal of exploring how environmental and species-specific factors determine the evolution and maintenance of perception in an ecological system. We observed a non-linear response in the evolved perceptual ranges as a function of parameters in our model. Overall, we identified two groups of parameters, one of which promotes evolution of perception and another group that restricts it. We found that resource density, basal energy cost, perceptual cost and mutation rate were the best predictors of the resultant perceptual range distribution, but detailed exploration indicated that individual parameters affect different parts of the distribution in different ways.

From theory to practice in pattern-oriented modelling: identifying and using empirical patterns in predictive models

To robustly predict the effects of disturbance and ecosystem changes on species, it is necessary to produce structurally realistic models with high predictive power and flexibility. To ensure that these models reflect the natural conditions necessary for reliable prediction, models must be informed and tested using relevant empirical observations. Pattern-oriented modelling (POM) offers a systematic framework for employing empirical patterns throughout the modelling process and has been coupled with complex systems modelling, such as in agent-based models (ABMs). However, while the production of ABMs has been rising rapidly, the explicit use of POM has not increased. Challenges with identifying patterns and an absence of specific guidelines on how to implement empirical observations may limit the accessibility of POM and lead to the production of models which lack a systematic consideration of reality. This review serves to provide guidance on how to identify and apply patterns following a POM approach in ABMs (POM-ABMs), specifically addressing: where in the ecological hierarchy can we find patterns; what kinds of patterns are useful; how should simulations and observations be compared; and when in the modelling cycle are patterns used? The guidance and examples provided herein are intended to encourage the application of POM and inspire efficient identification and implementation of patterns for both new and experienced modellers alike. Additionally, by generalising patterns found especially useful for POM-ABM development, these guidelines provide practical help for the identification of data gaps and guide the collection of observations useful for the development and verification of predictive models. Improving the accessibility and explicitness of POM could facilitate the production of robust and structurally realistic models in the ecological community, contributing to the advancement of predictive ecology at large.

Movement and Seasonal Energetics Mediate Vulnerability to Disturbance in Marine Mammal Populations

AbstractIn marine environments, noise from human activities is increasing dramatically, causing animals to alter their behavior and forage less efficiently. These alterations incur energetic costs that can result in reproductive failure and death and may ultimately influence population viability, yet the link between population dynamics and individual energetics is poorly understood. We present an energy budget model for simulating effects of acoustic disturbance on populations. It accounts for environmental variability and individual state, while incorporating realistic animal movements. Using harbor porpoises (Phocoena phocoena) as a case study, we evaluated population consequences of disturbance from seismic surveys and investigated underlying drivers of vulnerability. The framework reproduced empirical estimates of population structure and seasonal variations in energetics. The largest effects predicted for seismic surveys were in late summer and fall and were unrelated to local abundance, but instead were related to lactation costs, water temperature, and body fat. Our results demonstrate that consideration of temporal variation in individual energetics and their link to costs associated with disturbances is imperative when predicting disturbance impacts. These mechanisms are general to animal species, and the framework presented here can be used for gaining new insights into the spatiotemporal variability of animal movements and energetics that control population dynamics.

Deterministic modelling of seed dispersal based on observed behaviours of an endemic primate in Brazil

Plant species models are among the available tools to predict the future of ecosystems threatened by climate change, habitat loss, and degradation. However, they suffer from low to no inclusion of plant dispersal, which is necessary to predict ecosystem evolution. A variety of seed dispersal models have been conceived for anemochorous and zoochorous plant species, but the coupling between vegetation models and seed dispersal processes remains rare. The main challenge in modelling zoochoric dispersal is simulating animal movements in their complex habitat. Recent developments allow straightforward applications of hidden Markov modelling (HMM) to animal movements, which could ease generalizations when modelling zoochoric seed dispersal. We tested the use of HMM to model seed dispersal by an endangered primate in the Brazilian Atlantic forest, to demonstrate its potential simplicity to simulate seed dispersal processes. We also discuss how to adapt it to other species. We collected information on movement, fruit consumption, deposition, and habitat use of Leontopithecus chrysomelas. We analysed daily trajectories using HMM and built a deterministic Model Of Seed Transfer (MOST), which replicated, with good approximation, the primate's movement and seed deposition patterns as observed in the field. Our results suggest that the dispersal behaviour and short daily-trajectories of L. chrysomelas restrict the species' role in large-scale forest regeneration, but contribute to the prevalence of resource tree species locally, and potentially maintaining tree diversity by preventing local extinction. However, it may be possible to accurately simulate dispersal in an area, without necessarily quantifying variables that influence movement, if the movement can be broken down to step-length and turning angles, and parametrised along with the distribution of gut-transit times. For future objectives, coupling MOST with a DVM could be used to test hypotheses on tree species survival in various scenarios, simulating regeneration and growth at regional scales by including data on main dispersal agents over the area of interest, distribution of tree species, and land use data. The principal advantage of the MOST model is its functionality with data available from the literature as the variables are easy to parametrise. We suggest using the coupled model to perform experiments using only available information, but varying the numbers and species of seed dispersers, or modifying land cover or configuration to test for possible thresholds preventing the extinction of selected tree species.

Movement patterns of large juvenile loggerhead turtles in the Mediterranean Sea: Ontogenetic space use in a small ocean basin

Mechanisms that determine how, where, and when ontogenetic habitat shifts occur are mostly unknown in wild populations. Differences in size and environmental characteristics of ontogenetic habitats can lead to differences in movement patterns, behavior, habitat use, and spatial distributions across individuals of the same species. Knowledge of juvenile loggerhead turtles' dispersal, movements, and habitat use is largely unknown, especially in the Mediterranean Sea. Satellite relay data loggers were used to monitor movements, diving behavior, and water temperature of eleven large juvenile loggerhead turtles (Caretta caretta) deliberately caught in an oceanic habitat in the Mediterranean Sea. Hidden Markov models were used over 4,430 spatial locations to quantify the different activities performed by each individual: transit, low-, and high-intensity diving. Model results were then analyzed in relation to water temperature, bathymetry, and distance to the coast. The hidden Markov model differentiated between bouts of area-restricted search as low- and high-intensity diving, and transit movements. The turtles foraged in deep oceanic waters within 60 km from the coast as well as above 140 km from the coast. They used an average area of 194,802 km2, where most individuals used the deepest part of the Southern Tyrrhenian Sea with the highest seamounts, while only two switched to neritic foraging showing plasticity in foraging strategies among turtles of similar age classes. The foraging distribution of large juvenile loggerhead turtles, including some which were of the minimum size of adults, in the Tyrrhenian Sea is mainly concentrated in a relatively small oceanic area with predictable mesoscale oceanographic features, despite the proximity of suitable neritic foraging habitats. Our study highlights the importance of collecting high-resolution data about species distribution and behavior across different spatio-temporal scales and life stages for implementing conservation and dynamic ocean management actions.

Northern pigtailed macaques rely on old growth plantations to offset low fruit availability in a degraded forest fragment

Space-use and foraging strategies are important facets to consider in regard to the ecology and conservation of primates. For this study, we documented movement, ranging, and foraging patterns of northern pigtailed macaques (Macaca leonina) for 14 months in a degraded habitat with old growth Acacia and Eucalyptus plantations at the Sakaerat Biosphere Reserve in northeastern Thailand. We used hidden Markov models and characteristic hull polygons to analyze these patterns in regard to fruit availability. Macaques' home range (HR) was 599 ha and spanned through a natural dry-evergreen forest (DEF), and plantation forest. Our results showed that active foraging increased with higher fruit availability in DEF. Macaques changed to a less continuous behavioral state during periods of lower fruit availability in DEF, repeatedly moving from foraging to transiting behavior, while extending their HR further into plantation forest and surrounding edge areas. Concomitantly, macaques shifted their diet from fleshy to dry fruit such as the introduced Acacia species. Our results showed that the diet and movement ecology adaptations of northern pigtailed macaques were largely dependent on availability of native fruits, and reflected a "high-cost, high-yield" foraging strategy when fresh food was scarce and dry fruit was available in plantation forest. Conversely, wild-feeding northern pigtailed macaque populations inhabiting pristine habitat approached a "low-cost, low-yield" foraging strategy. Our results outline the effects of habitat degradation on foraging strategies and show how a flexible species can cope with its nutritional requirements.

Territory surveillance and prey management: Wolves keep track of space and time

Identifying behavioral mechanisms that underlie observed movement patterns is difficult when animals employ sophisticated cognitive‐based strategies. Such strategies may arise when timing of return visits is important, for instance to allow for resource renewal or territorial patrolling. We fitted spatially explicit random‐walk models to GPS movement data of six wolves (Canis lupus; Linnaeus, 1758) from Alberta, Canada to investigate the importance of the following: (1) territorial surveillance likely related to renewal of scent marks along territorial edges, to reduce intraspecific risk among packs, and (2) delay in return to recently hunted areas, which may be related to anti‐predator responses of prey under varying prey densities. The movement models incorporated the spatiotemporal variable “time since last visit,” which acts as a wolf's memory index of its travel history and is integrated into the movement decision along with its position in relation to territory boundaries and information on local prey densities. We used a model selection framework to test hypotheses about the combined importance of these variables in wolf movement strategies. Time‐dependent movement for territory surveillance was supported by all wolf movement tracks. Wolves generally avoided territory edges, but this avoidance was reduced as time since last visit increased. Time‐dependent prey management was weak except in one wolf. This wolf selected locations with longer time since last visit and lower prey density, which led to a longer delay in revisiting high prey density sites. Our study shows that we can use spatially explicit random walks to identify behavioral strategies that merge environmental information and explicit spatiotemporal information on past movements (i.e., “when” and “where”) to make movement decisions. The approach allows us to better understand cognition‐based movement in relation to dynamic environments and resources.

Breeding success of a marine central place forager in the context of climate change: A modeling approach

In response to climate warming, a southward shift in productive frontal systems serving as the main foraging sites for many top predator species is likely to occur in Subantarctic areas. Central place foragers, such as seabirds and pinnipeds, are thus likely to cope with an increase in the distance between foraging locations and their land-based breeding colonies. Understanding how central place foragers should modify their foraging behavior in response to changes in prey accessibility appears crucial. A spatially explicit individual-based simulation model (Marine Central Place Forager Simulator (MarCPFS)), including bio-energetic components, was built to evaluate effects of possible changes in prey resources accessibility on individual performances and breeding success. The study was calibrated on a particular example: the Antarctic fur seal (Arctocephalus gazella), which alternates between oceanic areas in which females feed and the land-based colony in which they suckle their young over a 120 days rearing period. Our model shows the importance of the distance covered to feed and prey aggregation which appeared to be key factors to which animals are highly sensitive. Memorization and learning abilities also appear to be essential breeding success traits. Females were found to be most successful for intermediate levels of prey aggregation and short distance to the resource, resulting in optimal female body length. Increased distance to resources due to climate warming should hinder pups’ growth and survival while female body length should increase.

A stochastic movement simulator improves estimates of landscape connectivity

Conservation actions often focus on restoration or creation of natural areas designed to facilitate the movements of organisms among populations. To be efficient, these actions need to be based on reliable estimates or predictions of landscape connectivity. While circuit theory and least-cost paths (LCPs) are increasingly being used to estimate connectivity, these methods also have proven limitations. We compared their performance in predicting genetic connectivity with that of an alternative approach based on a simple, individual-based "stochastic movement simulator" (SMS). SMS predicts dispersal of organisms using the same landscape representation as LCPs and circuit theory-based estimates (i.e., a cost surface), while relaxing key LCP assumptions, namely individual omniscience of the landscape (by incorporating perceptual range) and the optimality of individual movements (by including stochasticity in simulated movements). The performance of the three estimators was assessed by the degree to which they correlated with genetic estimates of connectivity in two species with contrasting movement abilities (Cabanis's Greenbul, an Afrotropical forest bird species, and natterjack toad, an amphibian restricted to European sandy and heathland areas). For both species, the correlation between dispersal model and genetic data was substantially higher when SMS was used. Importantly, the results also demonstrate that the improvement gained by using SMS is robust both to variation in spatial resolution of the landscape and to uncertainty in the perceptual range model parameter. Integration of this individual-based approach with other developing methods in the field of connectivity research, such as graph theory, can yield rapid progress towards more robust connectivity indices and more effective recommendations for land management.

Memory Effects on Movement Behavior in Animal Foraging

An individual’s choices are shaped by its experience, a fundamental property of behavior important to understanding complex processes. Learning and memory are observed across many taxa and can drive behaviors, including foraging behavior. To explore the conditions under which memory provides an advantage, we present a continuous-space, continuous-time model of animal movement that incorporates learning and memory. Using simulation models, we evaluate the benefit memory provides across several types of landscapes with variable-quality resources and compare the memory model within a nested hierarchy of simpler models (behavioral switching and random walk). We find that memory almost always leads to improved foraging success, but that this effect is most marked in landscapes containing sparse, contiguous patches of high-value resources that regenerate relatively fast and are located in an otherwise devoid landscape. In these cases, there is a large payoff for finding a resource patch, due to size, value, or locational difficulty. While memory-informed search is difficult to differentiate from other factors using solely movement data, our results suggest that disproportionate spatial use of higher value areas, higher consumption rates, and consumption variability all point to memory influencing the movement direction of animals in certain ecosystems.

Patch-use dynamics by a large herbivore

BACKGROUND

An adaption of the optimal foraging theory suggests that herbivores deplete, depart, and finally return to foraging patches leaving time for regrowth [van Moorter et al., Oikos 118:641-652, 2009]. Inter-patch movement and memory of patches then produce a periodic pattern of use that may define the bounds of a home range. The objective of this work was to evaluate the underlying movements within home ranges of elk (Cervus elaphus) according to the predictions of this theory. Using a spatial temporal permutation scan statistic to identify foraging patches from GPS relocations of cow elk, we evaluated return patterns to foraging patches during the 2012 growing season. Subsequently, we used negative binomial regression to assess environmental characteristics that affect the frequency of returns, and thereby characterize the most successful patches.

RESULTS

We found that elk return to known patches regularly over a season, on average after 15.4 (±5.4 SD) days. Patches in less-rugged terrain, farther from roads and with high productivity were returned to most often when controlling for the time each patch was known to each elk.

CONCLUSIONS

Instead of diffusion processes often used to describe animal movement, our research demonstrates that elk make directed return movements to valuable foraging sites and, as support for Van Moorter et al.'s [Oikos 118:641-652, 2009] model, we submit that these movements could be an integral part of home-range development in wild ungulates.

Solvable random-walk model with memory and its relations with Markovian models of anomalous diffusion

Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only the mean-square displacement (MSD) but also the propagator can be obtained exactly in the asymptotic limit. The model consists of a random walker on a lattice, which, at a constant rate, stochastically relocates at a site occupied at some earlier time. This time in the past is chosen randomly according to a memory kernel, whose temporal decay can be varied via an exponent parameter. In the weakly non-Markovian regime, memory reduces the diffusion coefficient from the bare value. When the mean backward jump in time diverges, the diffusion coefficient vanishes and a transition to an anomalous subdiffusive regime occurs. Paradoxically, at the transition, the process is an anticorrelated Lévy flight. Although in the subdiffusive regime the model exhibits some features of the continuous time random walk with infinite mean waiting time, it belongs to another universality class. If memory is very long-ranged, a second transition takes place to a regime characterized by a logarithmic growth of the MSD with time. In this case the process is asymptotically Gaussian and effectively described as a scaled Brownian motion with a diffusion coefficient decaying as 1/t.

Random walks with preferential relocations to places visited in the past and their application to biology

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available for these processes. Here we solve exactly a model with long range memory where a random walker intermittently revisits previously visited sites according to a reinforced rule. The emergence of frequently visited locations generates very slow diffusion, logarithmic in time, whereas the walker probability density tends to a Gaussian. This scaling form does not emerge from the central limit theorem but from an unusual balance between random and long-range memory steps. In single trajectories, occupation patterns are heterogeneous and have a scale-free structure. The model exhibits good agreement with data of free-ranging capuchin monkeys.