Incorporating animal behavior into seed dispersal models: implications for seed shadows

Seed dispersal fundamentally influences plant population and community dynamics but is difficult to quantify directly. Consequently, models are frequently used to describe the seed shadow (the seed deposition pattern of a plant population). For vertebrate-dispersed plants, animal behavior is known to influence seed shadows but is poorly integrated in seed dispersal models. Here, we illustrate a modeling approach that incorporates animal behavior and develop a stochastic, spatially explicit simulation model that predicts the seed shadow for a primate-dispersed tree species (Virola calophylla, Myristicaceae) at the forest stand scale. The model was parameterized from field-collected data on fruit production and seed dispersal, behaviors and movement patterns of the key disperser, the spider monkey (Ateles paniscus), densities of dispersed and non-dispersed seeds, and direct estimates of seed dispersal distances. Our model demonstrated that the spatial scale of dispersal for this V. calophylla population was large, as spider monkeys routinely dispersed seeds >100 m, a commonly used threshold for long-distance dispersal. The simulated seed shadow was heterogeneous, with high spatial variance in seed density resulting largely from behaviors and movement patterns of spider monkeys that aggregated seeds (dispersal at their sleeping sites) and that scattered seeds (dispersal during diurnal foraging and resting). The single-distribution dispersal kernels frequently used to model dispersal substantially underestimated this variance and poorly fit the simulated seed-dispersal curve, primarily because of its multimodality, and a mixture distribution always fit the simulated dispersal curve better. Both seed shadow heterogeneity and dispersal curve multimodality arose directly from these different dispersal processes generated by spider monkeys. Compared to models that did not account for disperser behavior, our modeling approach improved prediction of the seed shadow of this V. calophylla population. An important function of seed dispersal models is to use the seed shadows they predict to estimate components of plant demography, particularly seedling population dynamics and distributions. Our model demonstrated that improved seed shadow prediction for animal-dispersed plants can be accomplished by incorporating spatially explicit information on disperser behavior and movements, using scales large enough to capture routine long-distance dispersal, and using dispersal kernels, such as mixture distributions, that account for spatially aggregated dispersal.     

Modelling species distributions with penalised logistic regressions: A comparison with maximum entropy models

An important aspect of species distribution modelling is the choice of the modelling method because a suboptimal method may have poor predictive performance. Previous comparisons have found that novel methods, such as Maxent models, outperform well-established modelling methods, such as the standard logistic regression. These comparisons used training samples with small numbers of occurrences per estimated model parameter, and this limited sample size may have caused poorer predictive performance due to overfitting. Our hypothesis is that Maxent models would outperform a standard logistic regression because Maxent models avoid overfitting by using regularisation techniques and a standard logistic regression does not. Regularisation can be applied to logistic regression models using penalised maximum likelihood estimation. This estimation procedure shrinks the regression coefficients towards zero, causing biased predictions if applied to the training sample but improving the accuracy of new predictions. We used Maxent and logistic regression (standard and penalised) to analyse presence/pseudo-absence data for 13 tree species and evaluated the predictive performance (discrimination) using presence-absence data. The penalised logistic regression outperformed standard logistic regression and equalled the performance of Maxent. The penalised logistic regression may be considered one of the best methods to develop species distribution models trained with presence/pseudo-absence data, as it is comparable to Maxent. Our results encourage further use of the penalised logistic regression for species distribution modelling, especially in those cases in which a complex model must be fitted to a sample with a limited size.     

Patch Size and Connectivity Thresholds for Butterfly Habitat Restoration

Abstract:  Recovery of endangered species in highly fragmented habitats often requires habitat restoration. Selection of restoration sites typically involves too many options and too much uncertainty to reach a decision based on existing reserve design methods. The Fender's blue butterfly (  Icaricia icarioides fenderi ) survives in small, isolated patches of remnant prairie in Oregon's Willamette Valley—a habitat for which <0.5% of the original remains. Recovery of this species will require considerable habitat restoration. We investigated the potential of biologically based rules of thumb and more complex models to serve as tools in making land acquisitions. Based on Fender's blue dispersal behavior and demography, we have estimated that restored patches should be <1 km from existing habitat and at least 2 ha. We compared these rules to the results of two modeling approaches: an incidence function model and a spatially explicit simulation of demography and dispersal behavior. Not surprisingly, the simple rules and complex models all conclude that large (>2 ha) connected (<1 km) patches have the highest restoration value. The dispersal model, however, suggests that small, connected patches have more restoration value than large, isolated patches, whereas the incidence function model suggests that size and connectivity are equally important. These differences stem from model assumptions. We used incidence functions to predict long-term, stochastic, steady-state conditions and dispersal simulations to predict short-term (25-year) colonization dynamics. To apply our results in the context of selecting restoration sites on the ground, we recommend selecting nearby sites when short-term colonization dynamics are expected to be an important aspect of a species' biology.     

Null models reveal preferential sampling, spatial autocorrelation and overfitting in habitat suitability modelling

Nowadays, species are driven to extinction at a high rate. To reduce this rate it is important to delineate suitable habitats for these species in such a way that these areas can be suggested as conservation areas. The use of habitat suitability models (HSMs) can be of great importance for the delineation of such areas. In this study MaxEnt, a presence-only modelling technique, is used to develop HSMs for 223 nematode species of the Southern Bight of the North Sea. However, it is essential that these models are beyond discussion and they should be checked for potential errors. In this study we focused on two categories (1) errors which can be attributed to the database such as preferential sampling and spatial autocorrelation and (2) errors induced by the modelling technique such as overfitting, In order to quantify these adverse effects thousands of nulls models were created. The effect of preferential sampling (i.e. some areas where visited more frequenty than others) was investigated by comparing model outcomes based from null models sampling the actual sampling stations and null models sampling the entire mapping area (Raes and ter Steege, 2007). Overfitting is exposed by a fivefold cross-validation and the influence of spatial autocorrelation is assessed by separating test and training sets in space. Our results clearly show that all these effects are present: preferential sampling has a strong effect on the selection of non-random species models. Crossvalidation seems to have less influence on the model selection and spatial autocorrelation is also strongly present. It is clear from this study that predefined thresholds are not readily applicable to all datasets and additional tests are needed in model selection.     

Facilitating climate‐change‐induced range shifts across continental land‐use barriers

Climate changes impose requirements for many species to shift their ranges to remain within environmentally tolerable areas, but near‐continuous regions of intense human land use stretching across continental extents diminish dispersal prospects for many species. We reviewed the impact of habitat loss and fragmentation on species’ abilities to track changing climates and existing plans to facilitate species dispersal in response to climate change through regions of intensive land uses, drawing on examples from North America and elsewhere. We identified an emerging analytical framework that accounts for variation in species' dispersal capacities relative to both the pace of climate change and habitat availability. Habitat loss and fragmentation hinder climate change tracking, particularly for specialists, by impeding both propagule dispersal and population growth. This framework can be used to identify prospective modern‐era climatic refugia, where the pace of climate change has been slower than surrounding areas, that are defined relative to individual species' needs. The framework also underscores the importance of identifying and managing dispersal pathways or corridors through semi‐continental land use barriers that can benefit many species simultaneously. These emerging strategies to facilitate range shifts must account for uncertainties around population adaptation to local environmental conditions. Accounting for uncertainties in climate change and dispersal capabilities among species and expanding biological monitoring programs within an adaptive management paradigm are vital strategies that will improve species' capacities to track rapidly shifting climatic conditions across landscapes dominated by intensive human land use.     

Seed terminal velocity, wind turbulence, and demography drive the spread of an invasive tree in an analytical model

Little is known about the relative importance of mechanistic drivers of plant spread, particularly when long-distance dispersal (LDD) events occur. Most methods to date approach LDD phenomenologically, and all mechanistic models, with one exception, have been implemented through simulation. Furthermore, the few recent mechanistically derived spread models have examined the relative role of different dispersal parameters using simulations, and a formal analytical approach has not yet been implemented. Here we incorporate an analytical mechanistic wind dispersal model (WALD) into a demographic matrix model within an analytical integrodifference equation spread model. We carry out analytical perturbation analysis on the combined model to determine the relative effects of dispersal and demographic traits and wind statistics on the spread of an invasive tree. Models are parameterized using data collected in situ and tested using independent data on historical spread. Predicted spread rates and direction match well the two historical phases of observed spread. Seed terminal velocity has the greatest potential influence on spread rate, and three wind properties (turbulence coefficient, mean horizontal wind speed, and standard deviation of vertical wind speed) are also important. Fecundity has marginal importance for spread rate, but juvenile survival and establishment are consistently important. This coupled empirical/theoretical framework enables prediction of plant spread rate and direction using fundamental dispersal and demographic parameters and identifies the traits and environmental conditions that facilitate spread. The development of an analytical perturbation analysis for a mechanistic spread model will enable multispecies comparative studies to be easily implemented in the future.     

The influence of environmental spatial structure on the life-history traits and diversity of species in a metacommunity

Several models have been proposed to understand how so many species can coexist in ecosystems. Despite evidence showing that natural habitats are often patchy and fragmented, these models rarely take into account environmental spatial structure. In this study we investigated the influence of spatial structure in habitat and disturbance regime upon species’ traits and species’ coexistence in a metacommunity. We used a population-based model to simulate competing species in spatially explicit landscapes. The species traits we focused on were dispersal ability, competitiveness, reproductive investment and survival rate. Communities were characterized by their species richness and by the four life-history traits averaged over all the surviving species. Our results show that spatial structure and disturbance have a strong influence on the equilibrium life-history traits within a metacommunity. In the absence of disturbance, spatially structured landscapes favour species investing more in reproduction, but less in dispersal and survival. However, this influence is strongly dependent on the disturbance rate, pointing to an important interaction between spatial structure and disturbance. This interaction also plays a role in species coexistence. While spatial structure tends to reduce diversity in the absence of disturbance, the tendency is reversed when disturbance occurs. In conclusion, the spatial structure of communities is an important determinant of their diversity and characteristic traits. These traits are likely to influence important ecological properties such as resistance to invasion or response to climate change, which in turn will determine the fate of ecosystems facing the current global ecological crisis.     

Generation time and the maximum growth rate for populations with age-specific fecundities and unknown juvenile survival

In age-classified population models where all parameters are known, the generation time and growth rate are calculated in a straightforward manner. For many populations, some parameters, such as juvenile survival, are difficult to estimate accurately. In a simplified population model where fecundity and survival are constant from the onset of breeding, it is known that generation time may be calculated given only adult survival, age at first reproduction, and the population growth rate. However, the assumption of constant fecundity from the onset of breeding does not hold for many populations. An extended population model allows calculation of generation time with the additional knowledge of the ratio of age-specific fecundities compared to a maximum fecundity rate. When these relative fecundities are unknown, an ad hoc adjustment to the simplified model performs well.When the study population is in an ideal environment, the optimal generation time and maximum growth rate are linked, and both may be approximated knowing only adult survival, age at first reproduction, and the relative fecundities. The maximum growth rate has important conservation implications, and calculating it correctly is therefore important. Improper use of the simplified population model to calculate the maximum growth rate, combined with a simple decision rule, leads to an average overharvest of 36%, and >60% for three of six bird species studied, compared to the full population model. By comparison, using the approximation from the extended or adjusted models results in average overharvests of only 8% (extended model) and 5% (adjusted model), and <50% for all six species (either model).     

Invasive species distribution modeling (iSDM): Are absence data and dispersal constraints needed to predict actual distributions?

Species distribution models (SDMs) based on statistical relationships between occurrence data and underlying environmental conditions are increasingly used to predict spatial patterns of biological invasions and prioritize locations for early detection and control of invasion outbreaks. However, invasive species distribution models (iSDMs) face special challenges because (i) they typically violate SDM's assumption that the organism is in equilibrium with its environment, and (ii) species absence data are often unavailable or believed to be too difficult to interpret. This often leads researchers to generate pseudo-absences for model training or utilize presence-only methods, and to confuse the distinction between predictions of potential vs. actual distribution. We examined the hypothesis that true-absence data, when accompanied by dispersal constraints, improve prediction accuracy and ecological understanding of iSDMs that aim to predict the actual distribution of biological invasions. We evaluated the impact of presence-only, true-absence and pseudo-absence data on model accuracy using an extensive dataset on the distribution of the invasive forest pathogen Phytophthora ramorum in California. Two traditional presence/absence models (generalized linear model and classification trees) and two alternative presence-only models (ecological niche factor analysis and maximum entropy) were developed based on 890 field plots of pathogen occurrence and several climatic, topographic, host vegetation and dispersal variables. The effects of all three possible types of occurrence data on model performance were evaluated with receiver operating characteristic (ROC) and omission/commission error rates. Results show that prediction of actual distribution was less accurate when we ignored true-absences and dispersal constraints. Presence-only models and models without dispersal information tended to over-predict the actual range of invasions. Models based on pseudo-absence data exhibited similar accuracies as presence-only models but produced spatially less feasible predictions. We suggest that true-absence data are a critical ingredient not only for accurate calibration but also for ecologically meaningful assessment of iSDMs that focus on predictions of actual distributions.     

Managing plant population spread: prediction and analysis using a simple model

Models can be used to direct the management of population spread for the control of invasives or to encourage species of conservation value. Analytical models are attractive because of their theoretical basis and limited data requirements, but there is concern that their simplicity may limit their practical utility. We address the applied use of simple models in a study of a declining annual herb, Rhinanthus minor. We parameterized a population-spread model using field data on demography and dispersal for four management systems: grazed only (GR), hay-cut once (H1), hay-cut twice (H2), and hay-cut with autumn grazing (HG). Within a replicated experiment we measured spread rates of introduced R. minor populations over eight years. The modeled and measured spread rates were very similar in terms of both patterns of management effects and absolute values, so that in both cases HG > H2, H1 > GR. The treatments affected both dispersal and demography (establishment and survival) and so we used decomposition approaches to analyze the major causes of differences in population spread. Increased dispersal under hay-cutting was more important than demographic changes and accounted for approximately 70% of the differences in spread rate between the hay-cut and grazed-only treatments. Furthermore, management effects on the tail of the dispersal curve were by far the most critical in governing spread. This study suggests that simple models can be used to inform practical conservation management, and we demonstrate straightforward uses of our model to predict the impacts of different management strategies. While simple models can give accurate projections, we emphasize that they must be parameterized with high-quality data gathered at the appropriate spatial scale.     

Multiple socioecological factors influence timing of natal dispersal in kangaroo rats

Natal dispersal is an important event in the life history of many species. Timing of natal dispersal can influence survivorship and subsequent reproductive success. A variety of individual proximal factors determine if and when offspring disperse from the natal territory by influencing the costs of dispersing and the benefits of delaying dispersal. I examined the influence of multiple factors on dispersal age in the banner-tailed kangaroo rat (Dipodomys spectabilis), a solitary species lacking extreme sex-biased dispersal. I used an information theoretic approach to compare Cox proportional hazards regression models of dispersal age for 121 offspring over a 3-year period consisting of low and high population densities. The top-ranked models indicated that dispersal age was influenced by a combination of socioecological factors related to resource competition, environmental conditions, kin competition, and a lesser extent sex. Circumstances that likely reduced the probability of successful dispersal such as intense resource competition at high population density and being born earlier in the breeding season when environmental conditions were poor lead to longer delays in natal dispersal. Offspring in larger litters also dispersed earlier possibly to avoid competition with kin. Sex was weakly supported in top models but may only influence dispersal age at high population densities. These results suggest that the proximal factors that trigger dispersal are influenced by a combination of multiple effects related to the costs of dispersing and the benefits of remaining at home, even in species that do not form long-term social groups or have extreme sex-biased dispersal.     

Consequences of ignoring dispersal variation in network models for landscape connectivity

Habitat loss and fragmentation can negatively influence population persistence and biodiversity, but the effects can be mitigated if species successfully disperse between isolated habitat patches. Network models are the primary tool for quantifying landscape connectivity, yet in practice, an overly simplistic view of species dispersal is applied. These models often ignore individual variation in dispersal ability under the assumption that all individuals move the same fixed distance with equal probability. We developed a modeling approach to address this problem. We incorporated dispersal kernels into network models to determine how individual variation in dispersal alters understanding of landscape-level connectivity and implemented our approach on a fragmented grassland landscape in Minnesota. Ignoring dispersal variation consistently overestimated a population's robustness to local extinctions and underestimated its robustness to local habitat loss. Furthermore, a simplified view of dispersal underestimated the amount of habitat substructure for small populations but overestimated habitat substructure for large populations. Our results demonstrate that considering biologically realistic dispersal alters understanding of landscape connectivity in ecological theory and conservation practice.     

An evaluation of environmental factors affecting species distributions

Many different models can be built to explain the distributions of species. Often there is no single model that is clearly better than the alternatives, and this leads to uncertainty over which environmental factors are limiting species’ distributions. We investigated the support for different environmental factors by determining the drop in model performance when selected predictors were excluded from the model building process. We used a paired t-test over 37 plant species so that an environmental factor was only deemed significant if it consistently improved the results for multiple species. Geology and winter minimum temperatures were found to be the environmental factors with the most support, with a significant drop in model performance when either of these factors was excluded. However, there was less support for summer maximum temperature, as other environmental factors could combine to produce similar model performance. Our method of evaluating environmental factors using multiple species will not be capable of detecting predictors that are only important for one or two species, but it is difficult to distinguish these from spurious correlations. The strength of the method is that it increases inference for factors that consistently affect the distributions of many species. We discourage the assessment of models against predefined benchmarks, such as an area under the curve (AUC) of more than 0.7, as many alternative models for the same species produce similar results. Therefore, the benchmarks do not provide any indication of how the performance of the selected model compares to alternative models, and they provide weak inference to accept any selected model.     

Disentangling the drivers of reduced long-distance seed dispersal by birds in an experimentally fragmented landscape

Seed dispersal is a crucial component of plant population dynamics. Human landscape modifications, such as habitat destruction and fragmentation, can alter the abundance of fruiting plants and animal dispersers, foraging rates, vector movement, and the composition of the disperser community, all of which can singly or in concert affect seed dispersal. Here, we quantify and tease apart the effects of landscape configuration, namely, fragmentation of primary forest and the composition of the surrounding forest matrix, on individual components of seed dispersal of Heliconia acuminata, an Amazonian understory herb. First we identified the effects of landscape configuration on the abundance of fruiting plants and six bird disperser species. Although highly variable in space and time, densities of fruiting plants were similar in continuous forest and fragments. However, the two largest-bodied avian dispersers were less common or absent in small fragments. Second, we determined whether fragmentation affected foraging rates. Fruit removal rates were similar and very high across the landscape, suggesting that Heliconia fruits are a key resource for small frugivores in this landscape. Third, we used radiotelemetry and statistical models to quantify how landscape configuration influences vector movement patterns. Bird dispersers flew farther and faster, and perched longer in primary relative to secondary forests. One species also altered its movement direction in response to habitat boundaries between primary and secondary forests. Finally, we parameterized a simulation model linking data on fruit density and disperser abundance and behavior with empirical estimates of seed retention times to generate seed dispersal patterns in two hypothetical landscapes. Despite clear changes in bird movement in response to landscape configuration, our simulations demonstrate that these differences had negligible effects on dispersal distances. However, small fragments had reduced densities of Turdus albicollis, the largest-bodied disperser and the only one to both regurgitate and defecate seeds. This change in Turdus abundance acted together with lower numbers of fruiting plants in small fragments to decrease the probability of long-distance dispersal events from small patches. These findings emphasize the importance of foraging style for seed dispersal and highlight the primacy of habitat size relative to spatial configuration in preserving biotic interactions.     

Measuring impacts on species with models and metrics of varying ecological and computational complexity

Approaches to assess the impacts of landscape disturbance scenarios on species range from metrics based on patterns of occurrence or habitat to comprehensive models that explicitly include ecological processes. The choice of metrics and models affects how impacts are interpreted and conservation decisions. We explored the impacts of 3 realistic disturbance scenarios on 4 species with different ecological and taxonomic traits. We used progressively more complex models and metrics to evaluate relative impact and rank of scenarios on the species. Models ranged from species distribution models that relied on implicit assumptions about environmental factors and species presence to highly parameterized spatially explicit population models that explicitly included ecological processes and stochasticity. Metrics performed consistently in ranking different scenarios in order of severity primarily when variation in impact was driven by habitat amount. However, they differed in rank for cases where dispersal dynamics were critical in influencing metapopulation persistence. Impacts of scenarios on species with low dispersal ability were better characterized using models that explicitly captured these processes. Metapopulation capacity provided rank orders that most consistently correlated with those from highly parameterized and data-rich models and incorporated information about dispersal with little additional computational and data cost. Our results highlight the importance of explicitly considering species’ ecology, spatial configuration of habitat, and disturbance when choosing indicators of species persistence. We suggest using hybrid approaches that are a mixture of simple and complex models to improve multispecies assessments.     

Importance of species traits for species distribution in fragmented landscapes

Knowledge of the relationship between species traits and species distribution in fragmented landscapes is important for understanding current distribution patterns and as background information for predictive models of the effect of future landscape changes. The existing studies on the topic suffer from several drawbacks. First, they usually consider only traits related to dispersal ability and not growth. Furthermore, they do not apply phylogenetic corrections, and we thus do not know how considerations of phylogenetic relationships can alter the conclusions. Finally, they usually apply only one technique to calculate habitat isolation, and we do not know how other isolation measures would change the results. We studied the issues using 30 species forming congeneric pairs occurring in fragmented dry grasslands. We measured traits related to dispersal, survival, and growth in the species and recorded distribution of the species in 215 grassland fragments. We show many strong relationships between species traits related to both dispersal and growth and species distribution in the landscape, such as the positive relationship between habitat occupancy and anemochory and negative relationships between habitat occupancy and seed dormancy. The directions of these relationships, however, often change after application of phylogenetic correction. For example, more isolated habitats host species with smaller seeds. After phylogenetic correction, however, they turn out to host species with larger seeds. The conclusions also partly change depending on how we calculate habitat isolation. Specifically, habitat isolation calculated from occupied habitats only has the highest predictive power. This indicates slow dynamics of the species. All the results support the expectation that species traits have a high potential to explain patterns of species distribution in the landscape and that they can be used to build predictive models of species distribution. The specific conclusions are, however, dependent on the technique used, and we should carefully consider this when comparing among different studies. Since different techniques answer slightly different questions, we should attempt to use analyses both with and without phylogenetic correction and explore different isolation measures whenever possible and compare the results.     

The effects of plant distribution and frugivore density on the scale and shape of dispersal kernels

For many plant species, seed dispersal is one of the most important spatial demographic processes. We used a diffusion approximation and a spatially explicit simulation model to explore the mechanisms generating seed dispersal kernels for plants dispersed by frugivores. The simulation model combined simple movement and foraging rules with seed gut passage time, plant distribution, and fruit production. A simulation experiment using plant spatial aggregation and frugivore density as factors showed that seed dispersal scale was largely determined by the degree of plant aggregation, whereas kernel shape was mostly dominated by frugivore density. Kernel shapes ranged from fat tailed to thin tailed, but most shapes were between an exponential and that of the solution of a diffusion equation. The proportion of dispersal kernels with fat tails was highest for landscapes with clumped plant distributions and increased with increasing number of dispersers. The diffusion model provides a basis for models including more behavioral details but can also be used to approximate dispersal kernels once a diffusion rate is estimated from animal movement data. Our results suggest that important characteristics of dispersal kernels will depend on the spatial pattern of plant distribution and on disperser density when frugivores mediate seed dispersal.     

Aphid population response to agricultural landscape change: A spatially explicit,individual-based model

A spatially explicit individual-based simulation model has been developed to represent aphid population dynamics in agricultural landscapes. The application of the model to Rhopalosiphum padi (L.) population dynamics is detailed, including an outline of the construction of the model, its parameterisation and validation. Over time, the aphids interact with the landscape and with one another. The landscape is modified by varying a simple pesticide regime, and the multi-scale spatial and temporal implications for a population of aphids is analysed. The results show that a spatial modelling approach that considers the effects on the individual of landscape properties and factors such as wind speed and wind direction provides novel insight into aphid population dynamics both spatially and temporally. This forms the basis for the development of further simulation models that can be used to analyse how changes in landscape structure impact upon important species distributions and population dynamics.