How do animal territories form and change? Lessons from 20 years of mechanistic modelling

Territory formation is ubiquitous throughout the animal kingdom. At the individual level, various behaviours attempt to exclude conspecifics from regions of space. At the population level, animals often segregate into distinct territorial areas. Consequently, it should be possible to derive territorial patterns from the underlying behavioural processes of animal movements and interactions. Such derivations are an important element in the development of an ecological theory that can predict the effects of changing conditions on territorial populations. Here, we review the approaches developed over the past 20 years or so, which go under the umbrella of ‘mechanistic territorial models’. We detail the two main strands to this research: partial differential equations and individual-based approaches, showing what each has offered to our understanding of territoriality and how they can be unified. We explain how they are related to other approaches to studying territories and home ranges, and point towards possible future directions

Ecosystem heterogeneity and diversity mitigate Amazon forest resilience to frequent extreme droughts

© 2018 The Authors. New Phytologist © 2018 New Phytologist Trust The impact of increases in drought frequency on the Amazon forest's composition, structure and functioning remain uncertain. We used a process- and individual-based ecosystem model (ED2) to quantify the forest's vulnerability to increased drought recurrence. We generated meteorologically realistic, drier-than-observed rainfall scenarios for two Amazon forest sites, Paracou (wetter) and Tapajós (drier), to evaluate the impacts of more frequent droughts on forest biomass, structure and composition. The wet site was insensitive to the tested scenarios, whereas at the dry site biomass declined when average rainfall reduction exceeded 15%, due to high mortality of large-sized evergreen trees. Biomass losses persisted when year-long drought recurrence was shorter than 2–7 yr, depending upon soil texture and leaf phenology. From the site-level scenario results, we developed regionally applicable metrics to quantify the Amazon forest's climatological proximity to rainfall regimes likely to cause biomass loss > 20% in 50 yr according to ED2 predictions. Nearly 25% (1.8 million km2) of the Amazon forests could experience frequent droughts and biomass loss if mean annual rainfall or interannual variability changed by 2σ. At least 10% of the high-emission climate projections (CMIP5/RCP8.5 models) predict critically dry regimes over 25% of the Amazon forest area by 2100

Integrating evolution into ecological modelling: accommodating phenotypic changes in agent based models.

PMCID: PMC3733718This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Evolutionary change is a characteristic of living organisms and forms one of the ways in which species adapt to changed conditions. However, most ecological models do not incorporate this ubiquitous phenomenon. We have developed a model that takes a 'phenotypic gambit' approach and focuses on changes in the frequency of phenotypes (which differ in timing of breeding and fecundity) within a population, using, as an example, seasonal breeding. Fitness per phenotype calculated as the individual's contribution to population growth on an annual basis coincide with the population dynamics per phenotype. Simplified model variants were explored to examine whether the complexity included in the model is justified. Outputs from the spatially implicit model underestimated the number of individuals across all phenotypes. When no phenotype transitions are included (i.e. offspring always inherit their parent's phenotype) numbers of all individuals are always underestimated. We conclude that by using a phenotypic gambit approach evolutionary dynamics can be incorporated into individual based models, and that all that is required is an understanding of the probability of offspring inheriting the parental phenotype

Multiscale models for movement in oriented environments and their application to hilltopping in butterflies

Hilltopping butterflies direct their movement in response to topography, facilitating mating encounters via accumulation at summits. In this paper, we take hilltopping as a case study to explore the impact of complex orienteering cues on population dynamics. The modelling employs a standard multiscale framework, in which an individual's movement path is described as a stochastic 'velocity-jump' process and scaling applied to generate a macroscopic model capable of simulating large populations in landscapes. In this manner, the terms and parameters of the macroscopic model directly relate to statistical inputs of the individual-level model (mean speeds, turning rates and turning distributions). Applied to hilltopping in butterflies, we demonstrate how hilltopping acts to aggregate populations at summits, optimising mating for low-density species. However, for abundant populations, hilltopping is not only less effective but also possibly disadvantageous, with hilltopping males recording a lower mating rate than their non-hilltopping competitors. © 2013 Springer Science+Business Media Dordrecht

In vivo measurement of bending stiffness in fracture healing

BACKGROUND: Measurement of the bending stiffness a healing fracture represents a valid variable in the assessment of fracture healing. However, currently available methods typically have high measurement errors, even for mild pin loosening. Furthermore, these methods cannot provide actual values of bending stiffness, which precludes comparisons among individual fractures. Thus, even today, little information is available with regards to the fracture healing pattern with respect to actual values of bending stiffness. Our goals were, therefore: to develop a measurement device that would allow accurate and sensitive measurement of bending stiffness, even in the presence of mild pin loosening; to describe the course of healing in individual fractures; and help to evaluate whether the individual pattern of bending stiffness can be predicted at an early stage of healing. METHODS: A new measurement device has been developed to precisely measure the bending stiffness of the healing fracture by simulating four-point-bending. The system was calibrated on aluminum models and intact tibiae. The influence of pin loosening on measurement error was evaluated. The system was tested at weekly intervals in an animal experiment to determine the actual bending stiffness of the fracture. Transverse fractures were created in the right tibia of twelve sheep, and then stabilized with an external fixator. At ten weeks, bending stiffness of the tibiae were determined in a four-point-bending test device to validate the in-vivo-measurement data. RESULTS: In-vivo bending stiffness can be measured accurately and sensitive, even in the early phase of callus healing. Up to a bending stiffness of 10 Nm/degree, measurement error was below 3.4% for one pin loose, and below 29.3% for four pins loose, respectively. Measurement of stiffness data over time revealed a significant logarithmic increase between the third and seventh weeks, whereby the logarithmic rate of change among sheep was similar, but started from different levels. Comparative measurements showed that early individual changes between the third and fourth weeks can be used as a predictor of bending stiffness at seven weeks (r = 0.928) and at ten weeks (r = 0.710). CONCLUSION: Bending stiffness can be measured precisely, with less error in the case of pin loosening. Prediction of the future healing course of the individual fracture can be assessed by changes from the third to the fourth week, with differences in stiffness levels. Therefore, the initial status of the fracture seems to have a high impact on the individual healing course

Terrestrial vegetation redistribution and carbon balance under climate change

BACKGROUND: Dynamic Global Vegetation Models (DGVMs) compute the terrestrial carbon balance as well as the transient spatial distribution of vegetation. We study two scenarios of moderate and strong climate change (2.9 K and 5.3 K temperature increase over present) to investigate the spatial redistribution of major vegetation types and their carbon balance in the year 2100. RESULTS: The world's land vegetation will be more deciduous than at present, and contain about 125 billion tons of additional carbon. While a recession of the boreal forest is simulated in some areas, along with a general expansion to the north, we do not observe a reported collapse of the central Amazonian rain forest. Rather, a decrease of biomass and a change of vegetation type occurs in its northeastern part. The ability of the terrestrial biosphere to sequester carbon from the atmosphere declines strongly in the second half of the 21(st )century. CONCLUSION: Climate change will cause widespread shifts in the distribution of major vegetation functional types on all continents by the year 2100

Tropical carbon sink accelerated by symbiotic dinitrogen fixation

A major uncertainty in the land carbon cycle is whether symbiotic nitrogen fixation acts to enhance the tropical forest carbon sink. Nitrogen-fixing trees can supply vital quantities of the growth-limiting nutrient nitrogen, but the extent to which the resulting carbon–nitrogen feedback safeguards ecosystem carbon sequestration remains unclear. We combine (i) field observations from 112 plots spanning 300 years of succession in Panamanian tropical forests, and (ii) a new model that resolves nitrogen and light competition at the scale of individual trees. Fixation doubled carbon accumulation in early succession and enhanced total carbon in mature forests by ~10% (~12MgC ha−1) through two mechanisms: (i) a direct fixation effect on tree growth, and (ii) an indirect effect on the successional sequence of non-fixing trees. We estimate that including nitrogen-fixing trees in Neotropical reforestation projects could safeguard the sequestration of 6.7 Gt CO2 over the next 20 years. Our results highlight the connection between functional diversity of plant communities and the critical ecosystem service of carbon sequestration for mitigating climate change

Retention Time Variability as a Mechanism for Animal Mediated Long-Distance Dispersal

Long-distance dispersal (LDD) events, although rare for most plant species, can strongly influence population and community dynamics. Animals function as a key biotic vector of seeds and thus, a mechanistic and quantitative understanding of how individual animal behaviors scale to dispersal patterns at different spatial scales is a question of critical importance from both basic and applied perspectives. Using a diffusion-theory based analytical approach for a wide range of animal movement and seed transportation patterns, we show that the scale (a measure of local dispersal) of the seed dispersal kernel increases with the organisms' rate of movement and mean seed retention time. We reveal that variations in seed retention time is a key determinant of various measures of LDD such as kurtosis (or shape) of the kernel, thinkness of tails and the absolute number of seeds falling beyond a threshold distance. Using empirical data sets of frugivores, we illustrate the importance of variability in retention times for predicting the key disperser species that influence LDD. Our study makes testable predictions linking animal movement behaviors and gut retention times to dispersal patterns and, more generally, highlights the potential importance of animal behavioral variability for the LDD of seeds

Crown Plasticity and Competition for Canopy Space: A New Spatially Implicit Model Parameterized for 250 North American Tree Species

BACKGROUND: Canopy structure, which can be defined as the sum of the sizes, shapes and relative placements of the tree crowns in a forest stand, is central to all aspects of forest ecology. But there is no accepted method for deriving canopy structure from the sizes, species and biomechanical properties of the individual trees in a stand. Any such method must capture the fact that trees are highly plastic in their growth, forming tessellating crown shapes that fill all or most of the canopy space. METHODOLOGY/PRINCIPAL FINDINGS: We introduce a new, simple and rapidly-implemented model--the Ideal Tree Distribution, ITD--with tree form (height allometry and crown shape), growth plasticity, and space-filling, at its core. The ITD predicts the canopy status (in or out of canopy), crown depth, and total and exposed crown area of the trees in a stand, given their species, sizes and potential crown shapes. We use maximum likelihood methods, in conjunction with data from over 100,000 trees taken from forests across the coterminous US, to estimate ITD model parameters for 250 North American tree species. With only two free parameters per species--one aggregate parameter to describe crown shape, and one parameter to set the so-called depth bias--the model captures between-species patterns in average canopy status, crown radius, and crown depth, and within-species means of these metrics vs stem diameter. The model also predicts much of the variation in these metrics for a tree of a given species and size, resulting solely from deterministic responses to variation in stand structure. CONCLUSIONS/SIGNIFICANCE: This new model, with parameters for US tree species, opens up new possibilities for understanding and modeling forest dynamics at local and regional scales, and may provide a new way to interpret remote sensing data of forest canopies, including LIDAR and aerial photography

Animal Interactions and the Emergence of Territoriality

Inferring the role of interactions in territorial animals relies upon accurate recordings of the behaviour of neighbouring individuals. Such accurate recordings are rarely available from field studies. As a result, quantification of the interaction mechanisms has often relied upon theoretical approaches, which hitherto have been limited to comparisons of macroscopic population-level predictions from un-tested interaction models. Here we present a quantitative framework that possesses a microscopic testable hypothesis on the mechanism of conspecific avoidance mediated by olfactory signals in the form of scent marks. We find that the key parameters controlling territoriality are two: the average territory size, i.e. the inverse of the population density, and the time span during which animal scent marks remain active. Since permanent monitoring of a territorial border is not possible, scent marks need to function in the temporary absence of the resident. As chemical signals carried by the scent only last a finite amount of time, each animal needs to revisit territorial boundaries frequently and refresh its own scent marks in order to deter possible intruders. The size of the territory an animal can maintain is thus proportional to the time necessary for an animal to move between its own territorial boundaries. By using an agent-based model to take into account the possible spatio-temporal movement trajectories of individual animals, we show that the emerging territories are the result of a form of collective animal movement where, different to shoaling, flocking or herding, interactions are highly heterogeneous in space and time. The applicability of our hypothesis has been tested with a prototypical territorial animal, the red fox (Vulpes vulpes)