Seed dispersal in heterogeneous landscapes: linking field observations with spatially explicit models

Seed dispersal by animals drives persistence and colonization of the majority of fleshy‐fruited plants. Different factors have been identified as important in shaping patterns of seed deposition. These factors include habitat heterogeneity, movement patterns of frugivore species, and their feeding behavior. Most studies, however, have analysed the effect of one factor at the time, either with a modelling approach or from field observations. Here, we combine empirical data with spatially‐explicit models to explore the contribution of habitat availability and patterns of frugivore post‐feeding flight distances to the spatial patterns of seed dispersal. We found that both factors, distance from the mother tree and microhabitat identity, were shaping those patterns. Our results show that seed dispersal is tremendously heterogeneous and complex in space. The observed seed shadow is not the result of a single process but instead an intricate combination of distance and habitat selection. We suggest that the apparent combination of processes results from the simultaneous effects of distinct functional groups of frugivores.     

Understanding foraging behaviour in spatially heterogeneous environments

The role of stochasticity and spatial heterogeneity in foraging systems is investigated. We formulate a spatially explicit model which describes the behaviour of grazing animals in response to local information using simple stochastic rules. In particular the model reflects the biology in that decisions to move to a new location are based on visual assessment of the sward height in a surrounding neighbourhood, whilst the decision to graze the current location is based on the residual sward height and olfactory assessment of local faecal contamination. It is assumed that animals do not interact directly, but do so through modification of, and response to a common environment. Spatial heterogeneity is shown to have significant effects including reducing the equilibrium intake rate and increasing the optimal stocking density, and must therefore be taken into account by resource managers. We demonstrate the relationship between the stochastic spatial model and its non-spatial deterministic counterpart, and in the process derive a moment-closure approximation to the full process, which can be regarded as an intermediate, or pseudo-spatial model. The role of spatial heterogeneity is emphasized, and better understood by comparing the results obtained from each approach. The relative efficiency of random and directed searching behaviour in spatially heterogeneous environments is explored for both clean and contaminated pastures, and the impact of faecal avoidance behaviour assessed.     

Prey-predator models in spatially heterogeneous environments

The effects of environmental heterogeneity on models of prey-predator systems are investigated. Refuge behaviour is found in a continuous gradually varying environment. In this situation we do not necessarily get oscillating population cycles. The stabilizing effect observed depends on environmental variation and is not produced by diffusion alone. Our conclusions are fairly independent of the details of the model.     

Coevolution across landscapes: a spatially explicit model of parasitoid-host coevolution

The geographic mosaic theory of coevolution suggests that population spatial structure may have a strong impact on coevolutionary dynamics. Therefore, coevolution must be studied across geographic scales, not just in single populations. To examine the impact of movement rate on coevolutionary dynamics, we developed a spatially explicit model of host–parasitoid coevolution. We described space as a coupled-map lattice and assumed that resistance (defined as the ability of a host to encapsulate a parasitoid egg) and virulence (defined as the successful parasitization of a host) traits were graded and costly. The model explicitly detailed population and evolutionary dynamics. When holding all parameters constant and varying only the movement rate of the host and parasitoid, profoundly different dynamics were observed. We found that fluctuations in the mean levels of resistance and virulence in the global population were greatest when the movement rate of the host and parasitoid was high. In addition, we found that the variation in resistance and virulence levels among neighboring patches was greatest when the movement rates of the host and parasitoid was low. However, as the distance among patches increased, so did the variation in resistance and virulence levels regardless of movement rate. These generalizations did not hold when spatial patterns in the distribution of resistance and virulence traits, such as spirals, were observed. Finally, we found that the evolution of resistance and virulence caused the abundance of hosts to increase and the abundance of parasitoids to decrease. As a result, the spatial distribution of hosts and parasitoids was influenced.     

Metapopulation models for extinction threshold in spatially correlated landscapes

Simple analytical models assuming homogeneous space have been used to examine the effects of habitat loss and fragmentation on metapopulation size. The models predict an extinction threshold, a critical amount of suitable habitat below which the metapopulation goes deterministically extinct. The consequences of non-random loss of habitat for species with localized dispersal have been studied mainly numerically. In this paper, we present two analytical approaches to the study of habitat loss and its metapopulation dynamic consequences incorporating spatial correlation in both metapopulation dynamics as well as in the pattern of habitat destruction. One approach is based on a measure called metapopulation capacity, given by the dominant eigenvalue of a "landscape" matrix, which encapsulates the effects of landscape structure on population extinctions and colonizations. The other approach is based on pair approximation. These models allow us to examine analytically the effects of spatial structure in habitat loss on the equilibrium metapopulation size and the threshold condition for persistence. In contrast to the pair approximation based approaches, the metapopulation capacity based approach allows us to consider species with long as well as short dispersal range and landscapes with spatial correlation at different scales. The two methods make dissimilar assumptions, but the broad conclusions concerning the consequences of spatial correlation in the landscape structure are the same. Our results show that increasing correlation in the spatial arrangement of the remaining habitat increases patch occupancy, that this increase is more evident for species with short-range than long-range dispersal, and that to be most beneficial for metapopulation size, the range of spatial correlation in landscape structure should be at least a few times greater than the dispersal range of the species.     

Agent-based model approach to optimal foraging in heterogeneous landscapes: effects of patch clumpiness

Optimal foraging theory concerns animal behavior in landscapes where food is concentrated in patches. The efficiency of foraging is an effect of both the animal behavior and the geometry of the landscape; furthermore, the landscape is itself affected by the foraging of animals. We investigated the effect of landscape heterogeneity on the efficiency of an optimal forager. The particular aspect of heterogeneity we considered was "clumpiness"– the degree to which food resource patches are clustered together. The starting point for our study was the framework of the Mean Value Theorem (MVT) by Charnov. Since MVT is not spatially explicit, and thus not apt to investigate effects of clumpiness, we built an agent-based (or individual-based) model for animal movement in discrete landscapes extending the MVT. We also constructed a model for generating landscapes where the clumpiness of patches can be easily controlled, or "tuned", by an input parameter. We evaluated the agent based model by comparing the results with what the MTV would give, i.e. if the spatial effects were removed. The MVT matched the simulations best on landscapes with random patch configuration and high food recovery rates. As for our main question about the effects of clumpiness, we found that, when landscapes were highly productive (rapid food replenishment), foraging efficiency was greatest in clumped landscapes. In less productive landscapes, however, foraging efficiency was lowest in landscapes with a clumped patch distribution.     

Range limits in spatially explicit models of quantitative traits

In an influential paper, Kirkpatrick and Barton (Am Nat 150:1–23 1997) presented a system of diffusive partial differential equations modeling the joint evolution of population density and the mean of a quantitative trait when the trait optimum varies over a continuous spatial domain. We present a stability theorem for steady states of a simplified version of the system, originally studied in Kirkpatrick and Barton (Am Nat 150:1–23 1997). We also present a derivation of the system.     

Using mixture models to characterize disease-related traits

We consider 12 event-related potentials and one electroencephalogram measure as disease-related traits to compare alcohol-dependent individuals (cases) to unaffected individuals (controls). We use two approaches: 1) two-way analysis of variance (with sex and alcohol dependency as the factors), and 2) likelihood ratio tests comparing sex adjusted values of cases to controls assuming that within each group the trait has a 2 (or 3) component normal mixture distribution. In the second approach, we test the null hypothesis that the parameters of the mixtures are equal for the cases and controls. Based on the two-way analysis of variance, we find 1) males have significantly (p < 0.05) lower mean response values than females for 7 of these traits. 2) Alcohol-dependent cases have significantly lower mean response than controls for 3 traits. The mixture analysis of sex-adjusted values of 1 of these traits, the event-related potential obtained at the parietal midline channel (ttth4), found the appearance of a 3-component normal mixture in cases and controls. The mixtures differed in that the cases had significantly lower mean values than controls and significantly different mixing proportions in 2 of the 3 components. Implications of this study are: 1) Sex needs to be taken into account when studying risk factors for alcohol dependency to prevent finding a spurious association between alcohol dependency and the risk factor. 2) Mixture analysis indicates that for the event-related potential "ttth4", the difference observed reflects strong evidence of heterogeneity of response in both the cases and controls.     

Spatial coherence and the persistence of high diversity in spatially heterogeneous landscapes

Our planet hosts a variety of highly diverse ecosystems. The persistence of high diversity is generally attributed to factors such as the structure of interactions among species and the dispersal of species in metacommunities. Here, we show that large contiguous landscapes—that are characterized by high dispersal—facilitate high species richness due to the spatial heterogeneity in interspecies interactions. We base our analysis on metacommunities under high dispersal where species densities become equal across habitats (spatially coherent). We find that the spatially coherent metacommunity can be represented by an effective species interaction‐web that has a significantly lower complexity than the constituent habitats. Our framework also explains how spatial heterogeneity eliminates differences in the effective interaction‐web, providing a basis for deviations from the area‐heterogeneity tradeoff. These results highlight the often‐overlooked case of high dispersal where spatial coherence provides a novel mechanism for supporting high diversity in large heterogeneous landscapes.     

The effects of spatially heterogeneous prey distributions on detection patterns in foraging seabirds

Many attempts to relate animal foraging patterns to landscape heterogeneity are focused on the analysis of foragers movements. Resource detection patterns in space and time are not commonly studied, yet they are tightly coupled to landscape properties and add relevant information on foraging behavior. By exploring simple foraging models in unpredictable environments we show that the distribution of intervals between detected prey (detection statistics) is mostly determined by the spatial structure of the prey field and essentially distinct from predator displacement statistics. Detections are expected to be Poissonian in uniform random environments for markedly different foraging movements (e.g. Lévy and ballistic). This prediction is supported by data on the time intervals between diving events on short-range foraging seabirds such as the thick-billed murre (Uria lomvia). However, Poissonian detection statistics is not observed in long-range seabirds such as the wandering albatross (Diomedea exulans) due to the fractal nature of the prey field, covering a wide range of spatial scales. For this scenario, models of fractal prey fields induce non-Poissonian patterns of detection in good agreement with two albatross data sets. We find that the specific shape of the distribution of time intervals between prey detection is mainly driven by meso and submeso-scale landscape structures and depends little on the forager strategy or behavioral responses.     

Estimating range expansion of wildlife in heterogeneous landscapes: A spatially explicit state‐space matrix model coupled with an improved numerical integration technique

Dispersal as well as population growth is a key demographic process that determines population dynamics. However, determining the effects of environmental covariates on dispersal from spatial‐temporal abundance proxy data is challenging owing to the complexity of model specification for directional dispersal permeability and the extremely high computational loads for numerical integration. In this paper, we present a case study estimating how environmental covariates affect the dispersal of Japanese sika deer by developing a spatially explicit state‐space matrix model coupled with an improved numerical integration technique (Markov chain Monte Carlo with particle filters). In particular, we explored the environmental drivers of inhomogeneous range expansion, characteristic of animals with short dispersal. Our model framework successfully reproduced the complex population dynamics of sika deer, including rapid changes in densely populated areas and distribution fronts within a decade. Furthermore, our results revealed that the inhomogeneous range expansion of sika deer seemed to be primarily caused by the dispersal process (i.e., movement barriers in fragmented forests) rather than population growth. Our state‐space matrix model enables the inference of population dynamics for a broad range of organisms, even those with low dispersal ability, in heterogeneous landscapes, and could address many pressing issues in conservation biology and ecosystem management.     

Predicting continental-scale patterns of bird species richness with spatially explicit models

The causes of global variation in species richness have been debated for nearly two centuries with no clear resolution in sight. Competing hypotheses have typically been evaluated with correlative models that do not explicitly incorporate the mechanisms responsible for biotic diversity gradients. Here, we employ a fundamentally different approach that uses spatially explicit Monte Carlo models of the placement of cohesive geographical ranges in an environmentally heterogeneous landscape. These models predict species richness of endemic South American birds (2248 species) measured at a continental scale. We demonstrate that the principal single-factor and composite (species-energy, water-energy and temperature-kinetics) models proposed thus far fail to predict (r(2) < or =.05) the richness of species with small to moderately large geographical ranges (first three range-size quartiles). These species constitute the bulk of the avifauna and are primary targets for conservation. Climate-driven models performed reasonably well only for species with the largest geographical ranges (fourth quartile) when range cohesion was enforced. Our analyses suggest that present models inadequately explain the extraordinary diversity of avian species in the montane tropics, the most species-rich region on Earth. Our findings imply that correlative climatic models substantially underestimate the importance of historical factors and small-scale niche-driven assembly processes in shaping contemporary species-richness patterns.     

Using simplified watershed hydrology to define spatially explicit ‘zones of influence’

Riparian areas represent dynamic spatial gradients characterized by a varying degree of terrestrial–aquatic interaction. Many studies have considered riparian zones to be discrete watershed sub-portions (e.g., 100-m riparian buffers), whereas I introduce ‘zones of influence’ that are subsets of the riparian zone. The purpose of this study is to introduce the concept of hydrologically defined influence zones using a simple hydrologic model to delimit land-cover. I describe a method for identifying zones of influence using watershed hydrologic patterns to delimit zones along a near-stream continuum between a downstream point (e.g., sample reach) and the watershed boundary. Using hydrologic modeling equations and GIS, travel time was calculated for every 30 × 30-m cell in 10 watersheds providing spatially explicit estimates of watershed hydrology and enabling us to calculate the travel time required for rainfall in any watershed cell to reach the watershed terminus. Shorter-duration travel times (i.e., 30–60 min) described smaller areas than longer-duration travel times (i.e., 210–300 min). This method is an alternative method to delimit near stream areas when quantifying watershed influence. Handling editor: K. Martens     

A spatially explicit method for evaluating accuracy of species distribution models

Aim Models predicting the spatial distribution of animals are increasingly used in wildlife management and conservation planning. There is growing recognition that common methods of evaluating species distribution model (SDM) accuracy, as a global overall value of predictive ability, could be enhanced by spatially evaluating the model thereby identifying local areas of relative predictive strength and weakness. Current methods of spatial SDM model assessment focus on applying local measures of spatial autocorrelation to SDM residuals, which require quantitative model outputs. However, SDM outputs are often probabilistic (relative probability of species occurrence) or categorical (species present or absent). The goal of this paper was to develop a new method, using a conditional randomization technique, which can be applied to directly spatially evaluate probabilistic and categorical SDMs. Location Eastern slopes, Rocky Mountains, Alberta, Canada. Methods We used predictions from seasonal grizzly bear (Ursus arctos) resource selection functions (RSF) models to demonstrate our spatial evaluation technique. Local test statistics computed from bear telemetry locations were used to identify areas where bears were located more frequently than predicted. We evaluated the spatial pattern of model inaccuracies using a measure of spatial autocorrelation, local Moran’s I. Results We found the model to have non‐stationary patterns in accuracy, with clusters of inaccuracies located in central habitat areas. Model inaccuracies varied seasonally, with the summer model performing the best and the least error in areas with high RSF values. The landscape characteristics associated with model inaccuracies were examined, and possible factors contributing to RSF error were identified. Main conclusions The presented method complements existing spatial approaches to model error assessment as it can be used with probabilistic and categorical model output, which is typical for SDMs. We recommend that SDM accuracy assessments be done spatially and resulting accuracy maps included in model metadata.     

Coupled map lattice approximations for spatially explicit individual-based models of ecology

Spatially explicit individual-based models are widely used in ecology but they are often difficult to treat analytically. Despite their intractability they often exhibit clear temporal and spatial patterning. We demonstrate how a spatially explicit individual-based model of scramble competition with local dispersal can be approximated by a stochastic coupled map lattice. The approximation disentangles the deterministic and stochastic element of local interaction and dispersal. We are thus able to understand the individual-based model through a simplified set of equations. In particular, we demonstrate that demographic noise leads to increased stability in the dynamics of locally dispersing single-species populations. The coupled map lattice approximation has general application to a range of spatially explicit individual-based models. It provides a new alternative to current approximation techniques, such as the method of moments and reaction-diffusion approximation, that captures both stochastic effects and large-scale patterning arising in individual-based models.     

Adversarial interspecies relationships facilitate population suppression by gene drive in spatially explicit models

Suppression gene drives bias their inheritance to spread through a population, potentially eliminating it when they reach high frequency. CRISPR homing suppression drives have already seen success in the laboratory, but several models predict that success may be elusive in population with realistic spatial structure due to extinction-recolonization cycles. Here, we extend our continuous space framework to include two competing species or predator–prey pairs. We find that in both general and mosquito-specific models, competing species or predators can facilitate drive-based suppression, albeit at the cost of an increased rate of drive loss outcomes. These results are robust in mosquito models with seasonal fluctuations. Our study illustrates the difficulty of predicting outcomes in complex ecosystems. However, our results are promising for the prospects of less powerful suppression gene drives to successfully eliminate target mosquito and other pest populations.     

Honeybee foraging in differentially structured landscapes

Honeybees communicate the distance and location of resource patches by bee dances, but this spatial information has rarely been used to study their foraging ecology. We analysed, for the first time to the best of the authors' knowledge, foraging distances and dance activities of honeybees in relation to landscape structure, season and colony using a replicated experimental approach on a landscape scale. We compared three structurally simple landscapes characterized by a high proportion of arable land and large patches, with three complex landscapes with a high proportion of semi-natural perennial habitats and low mean patch size. Four observation hives were placed in the centre of the landscapes and switched at regular intervals between the six landscapes from the beginning of May to the end of July. A total of 1137 bee dances were observed and decoded. Overall mean foraging distance was 1526.1 +/- 37.2 m, the median 1181.5 m and range 62.1-10037.1 m. Mean foraging distances of all bees and foraging distances of nectar-collecting bees did not significantly differ between simple and complex landscapes, but varied between month and colonies. Foraging distances of pollen-collecting bees were significantly larger in simple (1743 +/- 95.6 m) than in complex landscapes (1543.4 +/- 71 m) and highest in June when resources were scarce. Dancing activity, i.e. the number of observed bee dances per unit time, was significantly higher in complex than in simple landscapes, presumably because of larger spatial and temporal variability of resource patches in complex landscapes. The results facilitate an understanding of how human landscape modification may change the evolutionary significance of bee dances and ecological interactions, such as pollination and competition between honeybees and other bee species.