The effect of species response form on species distribution model prediction and inference

Ecological theory and current evidence support the validity of various species response curves according to a variety of environmental gradients. Various methods have been developed for building species distribution models but it is not well known how these methods perform under various assumptions about the form of the underlying species response. It is also not well known how spatial correlation in species occurrence affects model performance. These effects were investigated by applying an environmental envelope method (BIOCLIM) and three regression-based methods: logistic regression (LR), generalized additive modelling (GAM), and classification and regression tree (CART) to simulated species occurrence data. Each simulated species was constructed as a sum of responses with varying weights. Three basic species response curves were assumed: Gaussian (bell-shaped), Beta (skew) and linear. The two non-linear responses conform to standard ecological niche theory. All three responses were applied in turn to three simulated environmental variables, each with varying degrees of spatial autocorrelation. GAM produced the most consistent model performance over all forms of simulated species response. BIOCLIM and CART were inclined to underrate the performance of variables with a linear response. BIOCLIM was less sensitive to data density. LR was susceptible to model misspecification. The use of a linear function in LR underestimated the performance of variables with non-linear species response and contributed to increased spatial autocorrelation in model residuals. Omission of important environmental variables with non-linear species response also contributed to increased spatial autocorrelation in model residuals. Adding a spatial autocovariate term to the LR model (autologistic model) reduced the spatial autocorrelation and improved model performance, but did not correct the misidentification of the dominant environmental determinant. This is to be expected since the autologistic approach was designed primarily for prediction and not for inference. Given that various forms of species response to environmental determinants arise commonly in nature: (1) higher order functions should always be tested when applying LR in modelling species distribution; (2) spatial autocorrelation in species distribution model residuals can indicate that environmental determinants with non-linear response are missing from the model; and (3) deficiencies in LR model performance due to model misspecification can be addressed by adding a spatial autocovariate to the model, but care should be taken when interpreting the coefficients of the model parameters.     

Intertype mark correlation function: A new tool for the analysis of species interactions

The spatial pattern of the different species in complex ecosystems reflects the underlying ecological processes. In this paper a second order moment function is proposed and tested to analyse the spatial distribution of a mark, which could be a tree characteristic such as diameter or height, between two different types of points, which could be two different tree species. The proposed function was a conditional density function based on the intertype K_rs(d) function, incorporating as test function the correlation of the marks between pairs composed of points of different types. The results obtained in simulated and real plots prove that the function is capable of revealing the scale at which spatial correlation of the mark between two types of points exists. The proposed function allows the spatial association between individuals of different species at different life stages to be identified. This analysis may reveal information on species ecology and interspecific interactions in forest ecosystems.     

Social organisation of thornbill-dominated mixed-species flocks using social network analysis

Mixed-species associations are a widespread phenomenon, comprising interacting heterospecific individuals which gain predator, foraging or social benefits. Avian flocks have traditionally been classified as monolithic species units, with species-wide functional roles, such as nuclear, active, passive, or follower. It has also been suggested that flocks are mutualistic interactions, where niches of participating species converge. However the species-level perspective has limited previous studies, because both interactions and benefits occur at the level of the individual. Social network analysis provides a set of tools for quantitative assessment of individual participation. We used mark-resighting methods to develop networks of nodes (colour-marked individuals) and edges (their interactions within flocks). We found that variation in flock participation across individuals within species, especially in the buff-rumped thornbill, encompassed virtually the entire range of variation across all individuals in the entire set of species. For example, female, but not male, buff-rumped thornbills had high network betweenness, indicating that they interact with multiple flocks, likely as part of a female-specific dispersal strategy. Finally, we provide new evidence that mixed-species flocking is mutualistic, by quantifying an active shift in individual foraging niches towards those of their individual associates, with implications for trade-off between costs and benefits to individuals derived from participating in mixed-species flocks. This study is, to our knowledge, the first instance of a heterospecific social network built on pairwise interactions.     

Null model analysis of species associations using abundance data

The influence of negative species interactions has dominated much of the literature on community assembly rules. Patterns of negative covariation among species are typically documented through null model analyses of binary presence/absence matrices in which rows designate species, columns designate sites, and the matrix entries indicate the presence (1) or absence (0) of a particular species in a particular site. However, the outcome of species interactions ultimately depends on population-level processes. Therefore, patterns of species segregation and aggregation might be more clearly expressed in abundance matrices, in which the matrix entries indicate the abundance or density of a species in a particular site. We conducted a series of benchmark tests to evaluate the performance of 14 candidate null model algorithms and six covariation metrics that can be used with abundance matrices. We first created a series of random test matrices by sampling a metacommunity from a lognormal species abundance distribution. We also created a series of structured matrices by altering the random matrices to incorporate patterns of pairwise species segregation and aggregation. We next screened each algorithm-index combination with the random and structured matrices to determine which tests had low Type I error rates and good power for detecting segregated and aggregated species distributions. In our benchmark tests, the best-performing null model does not constrain species richness, but assigns individuals to matrix cells proportional to the observed row and column marginal distributions until, for each row and column, total abundances are reached. Using this null model algorithm with a set of four covariance metrics, we tested for patterns of species segregation and aggregation in a collection of 149 empirical abundance matrices and 36 interaction matrices collated from published papers and posted data sets. More than 80% of the matrices were significantly segregated, which reinforces a previous meta-analysis of presence/absence matrices. However, using two of the metrics we detected a significant pattern of aggregation for plants and for the interaction matrices (which include plant-pollinator data sets). These results suggest that abundance matrices, analyzed with an appropriate null model, may be a powerful tool for quantifying patterns of species segregation and aggregation.     

Estimating nonlinear interaction strengths: an observation-based method for species-rich food webs

Efforts to estimate the strength of species interactions in species-rich, reticulate food webs have been hampered by the multitude of direct and indirect interactions such systems exhibit and have been limited by an assumption that pairwise interactions display linear functional forms. Here we present a new method for directly measuring, on a per capita basis, the nonlinear strength of trophic species interactions within such food webs. This is an observation-based method, requiring three pieces of information: (1) species abundances, (2) predator and prey-specific handling times, and (3) data from predator-specific feeding surveys in which the number of individuals observed feeding on each of the predator's prey species has been tallied. The method offers a straightforward way to assess the completeness of one's sampling effort in accurately estimating interaction strengths through the construction of predator-specific prey accumulation curves. The method should be applicable to a variety of systems in which empirical estimates of direct interaction strengths have thus far remained elusive.     

Evolving metacommunities: toward an evolutionary perspective on metacommunities

The metacommunity framework predicts that local coexistence depends on the outcome of local species interactions and regional migration. In analogous fashion, spatial structure among populations can shape species interactions through evolutionary mechanisms. Yet, most metacommunity theories assume that populations do not evolve. Here, we evaluate how evolution shapes local species coexistence and exclusion within the multiscale and multispecies context embodied by the metacommunity framework. In general, coexistence in joint ecological-evolutionary models requires low to intermediate dispersal rates that can promote maintenance of both regional species and genetic diversity. These conditions support a set of key mechanisms that modify patterns of species coexistence including local adaptation, gene storage effects, genetic rescue effects, spatial genetic subsidies, and metacommunity evolution. Multispecies extensions indicate that correlated selection can further alter the outcome of interspecific interactions depending on the magnitude and direction of correlations and shape of fitness trade-offs. We suggest that an evolving metacommunity perspective has the potential to generate novel predictions about community structure and function by incorporating the genetic and species diversity that characterize natural communities. In adopting such a perspective, we seek to facilitate understanding about the interactions between evolutionary and metacommunity dynamics.     

A hierarchical model for spatial capture-recapture data

Estimating density is a fundamental objective of many animal population studies. Application of methods for estimating population size from ostensibly closed populations is widespread, but ineffective for estimating absolute density because most populations are subject to short-term movements or so-called temporary emigration. This phenomenon invalidates the resulting estimates because the effective sample area is unknown. A number of methods involving the adjustment of estimates based on heuristic considerations are in widespread use. In this paper, a hierarchical model of spatially indexed capture-recapture data is proposed for sampling based on area searches of spatial sample units subject to uniform sampling intensity. The hierarchical model contains explicit models for the distribution of individuals and their movements, in addition to an observation model that is conditional on the location of individuals during sampling. Bayesian analysis of the hierarchical model is achieved by the use of data augmentation, which allows for a straightforward implementation in the freely available software WinBUGS. We present results of a simulation study that was carried out to evaluate the operating characteristics of the Bayesian estimator under variable densities and movement patterns of individuals. An application of the model is presented for survey data on the flat-tailed horned lizard (Phrynosoma mcallii) in Arizona, USA.     

Modelling the spatial structure of forest stands by multivariate point processes with hierarchical interactions

A stochastic model is applied to describe the spatial structure of a forest stand. We aim at quantifying the strength of the competition process between the trees in terms of interaction within and between different size classes of trees using multivariate Gibbs point processes with hierarchical interactions introduced in [Högmander, H., Särkkä, A., 1999. Multitype spatial point patterns with hierarchical interactions. Biometrics 55, 1051–1058]. The new model overcomes the main limitation of the traditional use of the Gibbs models allowing to describe systems with non-symmetric interactions between different objects. When analyzing interactions between neighbouring trees it is natural to assume that the size of a tree determines its hierarchical level: the largest trees are not influenced by any other trees than the trees in the same size class, while trees in the other size classes are influenced by the other trees in the same class as well as by all larger trees. In this paper, we describe a wide range of Gibbs models with both hierarchical and non-hierarchical interactions as well as a simulation algorithm and a parameter estimation procedure for the hierarchical models. We apply the hierarchical interaction model to the analysis of forest data consisting of locations and diameters of tree stems.     

A simulation model for Japanese sardine (Sardinops melanostictus) migrations in the western North Pacific

A two-dimensional individual-based model coupled with fish bioenergetics was developed to simulate migration and growth of Japanese sardine (Sardinops melanostictus) in the western North Pacific. In the model, fish movement is controlled by feeding and spawning migrations with passive transport by simulated ocean current. Feeding migration was assumed to be governed by search for local optimal habitats, which is estimated by the spatial distribution of net growth rate of a sardine bioenergetics model. The forage density is one of the most important factors which determines the geographical distributions of Japanese sardine during their feeding migrations. Spawning migration was modeled by an artificial neural network (ANN) with an input layer composed of five neurons that receive environmental information (surface temperature, temperature change experienced, current speed, day length and distance from land). Once the weight of the ANN was determined, the fish movement was solved by combining with the feeding migration model. To obtain the weights of the ANN, three experiments were conducted in which (1) the ANN was trained with back propagation (BP) method with optimum training data, (2) genetic algorithm (GA) was used to adjust the weights and (3) the weights of the ANN were decided by the GA with BP, respectively. BP is a supervised learning technique for training ANNs. GA is a search technique used in computing to find approximate solutions, such as optimization of parameters. Condition factor of sardine in the model is used as a factor of optimization in the GA works. The methods using only BP or GA did not work to search the appropriate weights in the ANN for spawning migration. In the third method, which is a combined approach of GA with BP, the model reproduced the most realistic spawning migration of Japanese sardine. The changes in temperature and day length are important factors for the orientation cues of Japanese sardine according to the sensitivity analysis of the weights of the ANN.     

Modelling the distribution of plant species using the autologistic regression model

For modeling the distribution of plant species in terms of climate covariates, we consider an autologistic regression model for spatial binary data on a regularly spaced lattice. This model belongs to the class of autologistic models introduced by Besag (1974). Three estimation methods, the coding method, maximum pseudolikelihood method and Markov chain Monte Carlo method are studied and comparedvia simulation and real data examples. As examples, we use the proposed methodology to model the distributions of two plant species in the state of Florida.     

Assisted species migration and hybridization to conserve cold-adapted plants under climate change

Temperature rise due to climate change is putting many arctic and alpine plants at risk of extinction because their ability to react is outpaced by the speed of climate change. We considered assisted species migration (ASM) and hybridization as methods to conserve cold-adapted species (or the genes thereof) and to minimize the potential perturbation of ecosystems due to climate change. Assisted species migration is the deliberate movement of individuals from their current location to where the species’ ecological requirements will be matched under climate projections. Hybridization refers to crossbreeding of closely related species, where for arctic and alpine plants, 1 parent is the threatened cold-adapted and the other its reproductively compatible, warm-adapted sibling. Traditionally, hybridization is viewed as negative and leading to a loss of biodiversity, even though hybridization has increased biodiversity over geological times. Furthermore, the incorporation of warm-adapted genes into a hybrid may be the only means for the persistence of increasingly more maladapted, cold-adapted species. If approached with thorough consideration of fitness-related parameters of the source population and acknowledgement of the important role hybridization has played in shaping current biodiversity, ASM and hybridization could help save partial or whole genomes of key cold-adapted species at risk due to climate change with minimal negative effects on ecosystem functioning.     

The effect of positive interactions on community structure in a multi-species metacommunity model along an environmental gradient

Positive interactions are widely recognized as playing a major role in the organization of community structure and diversity. As such, recent theoretical and empirical works have revealed the significant contribution of positive interactions in shaping species’ geographical distributions, particularly in harsh abiotic conditions. In this report, we explore the joint influence of local dispersal and an environmental gradient on the spatial distribution, structure and function of communities containing positive interactions. While most previous theoretical efforts were limited to modelling the dynamics of single pairs of associated species being mutualist or competitor, here we employ a spatially explicit multi-species metacommunity model covering a rich range of interspecific interactions (mutualism, competition and exploitation) along an environmental gradient. We find that mutualistic interactions dominate in communities with low diversity characterized by limited species dispersal and poor habitat quality. On the other hand, the fraction of mutualistic interactions decreases at the expense of exploitation and competition with the increase in diversity caused by higher dispersal and/or habitat quality. Our multi-species model exemplifies the ubiquitous presence of mutualistic interactions and the role of mutualistic species as facilitators for the further establishment of species during ecosystem assembly. We therefore argue that mutualism is an essential component driving the origination of complex and diverse communities.     

Cross-validation of species distribution models: removing spatial sorting bias and calibration with a null model

Species distribution models are usually evaluated with cross-validation. In this procedure evaluation statistics are computed from model predictions for sites of presence and absence that were not used to train (fit) the model. Using data for 226 species, from six regions, and two species distribution modeling algorithms (Bioclim and MaxEnt), I show that this procedure is highly sensitive to "spatial sorting bias": the difference between the geographic distance from testing-presence to training-presence sites and the geographic distance from testing-absence (or testing-background) to training-presence sites. I propose the use of pairwise distance sampling to remove this bias, and the use of a null model that only considers the geographic distance to training sites to calibrate cross-validation results for remaining bias. Model evaluation results (AUC) were strongly inflated: the null model performed better than MaxEnt for 45% and better than Bioclim for 67% of the species. Spatial sorting bias and area under the receiver-operator curve (AUC) values increased when using partitioned presence data and random-absence data instead of independently obtained presence-absence testing data from systematic surveys. Pairwise distance sampling removed spatial sorting bias, yielding null models with an AUC close to 0.5, such that AUC was the same as null model calibrated AUC (cAUC). This adjustment strongly decreased AUC values and changed the ranking among species. Cross-validation results for different species are only comparable after removal of spatial sorting bias and/or calibration with an appropriate null model.     

Ensemble ecosystem modeling for predicting ecosystem response to predator reintroduction

Introducing a new or extirpated species to an ecosystem is risky, and managers need quantitative methods that can predict the consequences for the recipient ecosystem. Proponents of keystone predator reintroductions commonly argue that the presence of the predator will restore ecosystem function, but this has not always been the case, and mathematical modeling has an important role to play in predicting how reintroductions will likely play out. We devised an ensemble modeling method that integrates species interaction networks and dynamic community simulations and used it to describe the range of plausible consequences of 2 keystone‐predator reintroductions: wolves (Canis lupus) to Yellowstone National Park and dingoes (Canis dingo) to a national park in Australia. Although previous methods for predicting ecosystem responses to such interventions focused on predicting changes around a given equilibrium, we used Lotka–Volterra equations to predict changing abundances through time. We applied our method to interaction networks for wolves in Yellowstone National Park and for dingoes in Australia. Our model replicated the observed dynamics in Yellowstone National Park and produced a larger range of potential outcomes for the dingo network. However, we also found that changes in small vertebrates or invertebrates gave a good indication about the potential future state of the system. Our method allowed us to predict when the systems were far from equilibrium. Our results showed that the method can also be used to predict which species may increase or decrease following a reintroduction and can identify species that are important to monitor (i.e., species whose changes in abundance give extra insight into broad changes in the system). Ensemble ecosystem modeling can also be applied to assess the ecosystem‐wide implications of other types of interventions including assisted migration, biocontrol, and invasive species eradication.     

Predicting the variation in detection function in line transect sampling through random parameter model

A method for calibrating (localizing) detection function models in line transect sampling is proposed. The method is based on a random parameter model which supplies localized predictions of detection function parameters utilizing a few sample data points from the concerned location(s). The method has the clear advantage of being able to provide density estimates based on very few observations from a location which would be impossible through traditional methods. The method is successfully illustrated using census data on sambar (Cervus unicolor) from a set of wildlife sanctuaries in Kerala, India. The need for further research in this direction is indicated.     

Consumptive and nonconsumptive effects of predators on metacommunities of competing prey

Although predators affect prey both via consumption and by changing prey migration behavior, the interplay between these two effects is rarely incorporated into spatial models of predator-prey dynamics and competition among prey. We develop a model where generalist predators have consumptive effects (i.e., altering the likelihood of local prey extinction) as well as nonconsumptive effects (altering the likelihood of colonization) on spatially separated prey populations (metapopulations). We then extend this model to explore the effects of predators on competition among prey. We find that generalist predators can promote persistence of prey metapopulations by promoting prey colonization, but predators can also hasten system-wide extinction by either increasing local extinction or reducing prey migration. By altering rates of prey migration, predators in one location can exert remote control over prey dynamics in another location via predator-mediated changes in prey flux. Thus, the effect of predators may extend well beyond the proportion of patches they visit. In the context of prey metacommunities, predator-mediated shifts in prey migration and mortality can shift the competition-colonization trade-off among competing prey, leading to changes in the prey community as well as changes in the susceptibility of prey species to habitat loss. Consequently, native prey communities may be susceptible to invasion not only by exotic prey species that experience reduced amounts of mortality from resident predators, but also by exotic prey species that exhibit strong dispersal in response to generalist native predators. Ultimately, our work suggests that the consumptive and nonconsumptive effects of generalist predators may have strong, yet potentially cryptic, effects on competing prey capable of mediating coexistence, fostering invasion, and interacting with anthropogenic habitat alteration.     

Analysis of neighborhood dynamics of forest ecosystems using likelihood methods and modeling.

Advances in computing power in the past 20 years have led to a proliferation of spatially explicit, individual-based models of population and ecosystem dynamics. In forest ecosystems, the individual-based models encapsulate an emerging theory of "neighborhood" dynamics, in which fine-scale spatial interactions regulate the demography of component tree species. The spatial distribution of component species, in turn, regulates spatial variation in a whole host of community and ecosystem properties, with subsequent feedbacks on component species. The development of these models has been facilitated by development of new methods of analysis of field data, in which critical demographic rates and ecosystem processes are analyzed in terms of the spatial distributions of neighboring trees and physical environmental factors. The analyses are based on likelihood methods and information theory, and they allow a tight linkage between the models and explicit parameterization of the models from field data. Maximum likelihood methods have a long history of use for point and interval estimation in statistics. In contrast, likelihood principles have only more gradually emerged in ecology as the foundation for an alternative to traditional hypothesis testing. The alternative framework stresses the process of identifying and selecting among competing models, or in the simplest case, among competing point estimates of a parameter of a model. There are four general steps involved in a likelihood analysis: (1) model specification, (2) parameter estimation using maximum likelihood methods, (3) model comparison, and (4) model evaluation. Our goal in this paper is to review recent developments in the use of likelihood methods and modeling for the analysis of neighborhood processes in forest ecosystems. We will focus on a single class of processes, seed dispersal and seedling dispersion, because recent papers provide compelling evidence of the potential power of the approach, and illustrate some of the statistical challenges in applying the methods.     

Spatiotemporal dynamics in variable population interactions with density-dependent interaction coefficients

In this article, I present a two-patch metapopulation model with locally explicit dynamics to study the effect of spatial heterogeneity and dispersal upon population interactions with variable or conditional outcomes. These are interactions that may be either detrimental or beneficial for each species depending on the balance of the density-dependent costs and benefits involved. The local dynamics respond to density-dependent α-interaction functions that may change sign, thus yielding a diversity of possible local outcomes for the association in terms of type of interaction and in the number of stable solutions. The spatiotemporal model predicts that the fragmentation of space and dispersal between patches may cause further variation in these outcomes. First, the demographic performance of a species in the association is enhanced if migrations cause a proportional increase of individuals of its own species; being so, a victim may become a mutualist or an exploiter, an excluded species may invade, and a good competitor may overcome its own carrying capacity: the ‘enhancement effect of dispersal’; a sort of rescue effect in source-sink dynamics. The underlying mechanisms involve an interplay between density-dependent effects of dispersal per se and the relative local and global average α-interaction functions, which involve costs and benefits at both the local and regional level that may either counteract or reinforce each other; thus, localities and/or populations may change dynamically their sink or source role in the spatial dynamics. A significant insight arises herewith: in the context of variable or conditional interactions the concept of the role of a species does not make strict sense; it becomes a spatiotemporal dynamic quality. Second, regardless of which species disperses, bifurcation of equilibria may occur in those patches that receive the migrating individuals, and annihilation of equilibria in those from where migration leaves; thus, the number of equilibria increases or decreases accordingly.     

Females go where the food is: does the socio-ecological model explain variation in social organisation of solitary foragers?

The socio-ecological model (SEM) links ecological factors with characteristics of social systems and allows predictions about the relationships between resource distribution, type of competition and social organisation. It has been mainly applied to group-living species but ought to explain variation in social organisation of solitary species as well. The aim of this study was to test basic predictions of the SEM in two solitary primates, which differ in two characteristics of female association patterns: (1) spatial ranging and (2) sleeping associations. Beginning in August 2002, we regularly (re-)captured and marked individuals of sympatric populations of Madame Berthe's and grey mouse lemurs (Microcebus berthae, Microcebus murinus) in Kirindy Forest (Madagascar). We recorded data on spatial patterns, feeding and social behaviour by means of direct observation of radio-collared females. The major food sources of M. berthae occurred in small dispersed patches leading to strong within-group scramble competition and over-dispersed females with a low potential for female associations. In contrast, M. murinus additionally used patchily distributed, high-quality (large) resources facilitating within-group contest competition. The combined influence of less strong within-group scramble and contest as well as between-group contest over non-food resources allowed females of this species to cluster in space. Additionally, we experimentally manipulated the spatial distribution of food sources and found that females adjusted their spatial patterns to food resource distribution. Thus, our results support basic predictions of the SEM and demonstrated that it can also explain variation in social organisation of solitary foragers.