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.     

Stochastic gravity models for modeling lake invasions

Freshwater aquatic systems in North America are being invaded by many different species, ranging from fish, mollusks, cladocerans to various bacteria and viruses. These invasions have serious ecological and economic impacts. Human activities such as recreational boating are an important pathway for dispersal. Gravity models are used to quantify the dispersal effect of human activity. Gravity models currently used in ecology are deterministic. This paper proposes the use of stochastic gravity models in ecology, which provides new capabilities both in model building and in potential model applications. These models allow us to use standard statistical inference tools such as maximum likelihood estimation and model selection based on information criteria. To facilitate prediction, we use only those covariates that are easily available from common data sources and can be forecasted in future. This is important for forecasting the spread of invasive species in geographical and temporal domain. The proposed model is portable, that is it can be used for estimating relative boater traffic and hence relative propagule pressure for the lakes not covered by current boater surveys. This makes our results broadly applicable to various invasion prediction and management models.     

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.     

Closed population estimation models and their extensions in Program MARK

Program MARK provides > 65 data types in a common configuration for the estimation of population parameters from mark-encounter data. Encounter information from live captures, live resightings, and dead recoveries can be incorporated to estimate demographic parameters. Available estimates include survival (S or ϕ), rate of population change (λ), transition rates between strata (Ψ), emigration and immigration rates, and population size (N). Although N is the parameter most often desired by biologists, N is one of the most difficult parameters to estimate precisely without bias for a geographically and demographically closed population. The set of closed population estimation models available in Program MARK incorporate time (t) and behavioral (b) variation, and individual heterogeneity (h) in the estimation of capture and recapture probabilities in a likelihood framework. The full range of models from M ₀ (null model with all capture and recapture probabilities equal) to M _tbh are possible, including the ability to include temporal, group, and individual covariates to model capture and recapture probabilities. Both the full likelihood formulation of Otis et al. (1978) and the conditional model formulation of Huggins (1989, 1991) and Alho (1990) are provided in Program MARK, and all of these models are incorporated into the robust design (Kendall et al. 1995, 1997; Kendall and Nichols 1995) and robust-design multistrata (Hestbeck et al. 1991, Brownie et al. 1993) data types. Model selection is performed with AICc (Burnham and Anderson 2002) and model averaging (Burnham and Anderson 2002) is available in Program MARK to provide estimates of N with standard error that reflect model selection uncertainty.     

Wildfire smoke and health impacts: A closer look at fire attributes and their marginal effects

Existing studies on the economic impact of wildfire smoke have focused on single fire events or entire seasons without considering the marginal effect of daily fire progression on downwind communities. Neither approach allows for an examination of the impact of even the most basic fire attributes, such as distance and fuel type, on air quality and health outcomes. Improved knowledge of these effects can provide important guidance for efficient wildfire management strategies. This study aims to bridge this gap using detailed information on 24 large-scale wildfires that sent smoke plumes to the Reno/Sparks area of Northern Nevada over a 4-year period. We relate the daily acreage burned by these fires to daily data on air pollutants and local hospital admissions. Using information on medical expenses, we compute the per-acre health cost of wildfires of different attributes. We find that patient counts can be causally linked to fires as far as 200–300 miles from the impact area. As expected, the marginal impact per acre burned generally diminishes with distance and for fires with lighter fuel loads. Our results also highlight the importance of allowing for temporal lags between fire occurrence and pollutant levels.     

Dynamic environ analysis of compartmental systems: A computational approach

Ecosystems are often modeled as stocks of matter or energy connected by flows. Network environ analysis (NEA) is a set of mathematical methods for using powers of matrices to trace energy and material flows through such models. NEA has revealed several interesting properties of flow–storage networks, including dominance of indirect effects and the tendency for networks to create mutually positive interactions between species. However, the applicability of NEA is greatly limited by the fact that it can only be applied to models at constant steady states. In this paper, we present a new, computationally oriented approach to environ analysis called dynamic environ approximation (DEA). As a test of DEA, we use it to compute compartment throughflow in two implementations of a model of energy flow through an oyster reef ecosystem. We use a newly derived equation to compute model throughflow and compare its output to that of DEA. We find that DEA approximates the exact results given by this equation quite closely – in this particular case, with a mean Euclidean error ranging between 0.0008 and 0.21 – which gives a sense of how closely it reproduces other NEA-related quantities that cannot be exactly computed and discuss how to reduce this error. An application to calculating indirect flows in ecosystems is also discussed and dominance of indirect effects in a nonlinear model is demonstrated.     

Disentangling the effects of heterogeneity, stochastic dynamics and sampling in a community of aquatic insects

A dynamic and heterogeneous species abundance model generating the lognormal species abundance distribution is fitted to time series of species data from an assemblage of stoneflies and mayflies (Plecoptera and Ephemeroptera) of an aquatic insect community collected over a period of 15 years. In each year except one, we analyze 5 parallel samples taken at the same time of the season giving information about the over-dispersion in the sampling relative to the Poisson distribution. Results are derived from a correlation analysis, where the correlation in the bivariate normal distribution of log abundance is used as measurement of similarity between communities. The analysis enables decomposition of the variance of the lognormal species abundance distribution into three components due to heterogeneity among species, stochastic dynamics driven by environmental noise, and over-dispersion in sampling, accounting for 62.9, 30.6 and 6.5% of the total variance, respectively. Corrected for sampling the heterogeneity and stochastic components accordingly account for 67.3 and 32.7% of the among species variance in log abundance. By using this method, it is possible to disentangle the effect of heterogeneity and stochastic dynamics by quantifying these components and correctly remove sampling effects on the observed species abundance distribution.     

Enchytraeid population dynamics: Resource limitation and size-dependent mortality

Enchytraeids are regarded as keystone soil organisms in forest ecosystems. Their abundance and biomass fluctuate widely. Predicting the consequences of anthropogenic disturbances requires an understanding of the mechanisms underlying enchytraeid population dynamics. Here I develop a simple model, which predicts that the type of dynamics is controlled by resource input rate. If fungal resource input is a discrete event once a year, an exponential growth phase is followed by starvation and sharp decline of enchytraeid abundance. Model simulations with three different forcing functions were compared to field data. Initial parameter values were obtained from various independent sources, and parameters were estimated by minimizing the residual sum of squares. The best fitting model with resource addition once a year explained 39% of the variation in enchytraeid biomass over an 8-year study period. Further, variation in rainfall explained 59% of the variation in R² of the exponential phase models, which is also an index of the stability of population size-structure. The results emphasize the importance of resource limitation for enchytraeid population dynamics and support the hypothesis that the mortality during the decline phase is size-dependent.     

An inverse model for the analysis of the Venice lagoon food web

A steady-state model of the Venice lagoon food web was constructed, based on a comprehensive set of data, which were collected in the years 2001-2005. Energy flows were estimated by means of an inverse methodology of constrained optimization based on the Minimum Norm criterion, i.e. on the minimization of both the sum of squares of the residuals and of the sum of squares of energy flows. The solution was constrained by a set inequalities, which were derived from general eco-physiological knowledge and site specific data on energy flows. The trophic network was represented by thirty-two nodes, including single-species compartments for the species of high economical or ecological relevance. Mass balance equations were weighted, in order to obtain meaningful results in presence of large differences, up to 5 orders of magnitude, among biomasses. A perturbation technique was applied, with the purpose of reducing the risk of finding solutions heavily affected by the set of constraints and of obtaining a more robust representation of the energy flows. The main patterns of energy flow are consistent with those obtained in previous attempts at modelling the Venice lagoon food web. Micro- and macro-phytobenthos account for the largest fraction of the primary production. Energy is then transferred towards higher trophic levels by means of two main pathways: the recycling of dead biomass through the detritus compartment and the direct consumption by grazers. The first pathway is the most important and accounts for approximately two/thirds of the energy transferred to the second trophic level.     

Demographic Limitations of the Ability of Habitat Restoration to Rescue Declining Populations

Abstract:  Habitat restoration is often recommended in conservation without first evaluating whether populations are in fact habitat limited and thus whether declining populations can be stabilized or recovered through habitat restoration. We used a spatially structured demographic model coupled with a dynamic neutral landscape model to evaluate whether habitat restoration could rescue populations of several generic migratory songbirds that differed in their sensitivity to habitat fragmentation (i.e., severity of edge effects on nesting success). Simulating a best-case scenario, landscapes were instantly restored to 100% habitat before, at, or after habitat loss exceeded the species' vulnerability threshold. The vulnerability threshold is a measure of extinction risk, in which the change in population growth rate ( δλ ) scaled to the rate of habitat loss ( δh ) falls below −1% ( δλ/δh ≤ −0.01). Habitat restoration was most effective for species with low-to-moderate edge sensitivities and in landscapes that had not previously experienced extensive fragmentation. To stabilize populations of species that were highly edge sensitive or any species in heavily fragmented landscapes, restoration needed to be initiated long before the vulnerability threshold was reached. In practice, habitat restoration is generally not initiated until a population is at risk of extinction, but our model results demonstrate that some populations cannot be recovered at this point through habitat restoration alone. At this stage, habitat loss and fragmentation have seriously eroded the species' demographic potential such that halting population declines is limited more by demographic factors than the amount of available habitat. Evidence that populations decline in response to habitat loss is thus not sufficient to conclude that habitat restoration will be sufficient to rescue declining populations.     

Modelling heterogeneity in the recoveries of marked animal populations with covariates of individual animals, groups of animals or recovery time

A general framework is developed for modelling rates of survival and recovery of marked animal populations in terms of auxiliary information collected at the time of marking. The framework may be used to estimate differences in survival or recovery among individual animals, groups of animals, and recovery times. Analyses of the recoveries of tagged fish and banded bird populations are used to illustrate the specification and selection of various models.     

HOMINIDS: An agent-based spatial simulation model to evaluate behavioral patterns of early Pleistocene hominids

The HOMINIDS ABM is a new Agent Based Model that simulates the actions of two species of proto-human agents defined by a few, simple parameters. These proto-human agents attempt to subsist by foraging and nesting on dynamic, spatially explicit landscapes. The landscapes are described with a number of parameters based on empirical field data collected in habitats in East Africa. The results of three separate scenarios with 1 year model runs repeated 30 times each, for a total of 90 simulations, are presented and discussed to illustrate both the capacity and flexibility of our ABM modeling environment. The simulations show that the model food preferences and anatomy ascribed to Australopithecus boisei resulted in different expressions of foraging behaviors and subsistence strategies in two distinct ecological settings, and that adding tubers to the diet significantly increases the chances of the hominid agents meeting their daily caloric requirements year-round. In addition, this paper provides links to the open-source implementation code, along with the user documentation, design document, java API, and all datasets required to replicate the simulations.     

Super-individuals a simple solution for modelling large populations on an individual basis

Modelling populations on an individual-by-individual basis has proven to be a fruitful approach. Many complex patterns that are observed on the population level have been shown to arise from simple interactions between individuals. However, a major problem with these models is that the typically large number of individuals needed requires impractically large computation times. The common solution, reduction of the number of individuals in the model, can lead to loss of variation, irregular dynamics, and large sensitivity to the value of random generator seeds. As a solution to these problems, we propose to add an extra variable feature to each model individual, namely the number of real individuals it actually represents. This approach allows zooming from a real individual-by-individual model to a cohort representation or ultimately an all-animals-are-equal view without changing the model formulation. Therefore, the super-individual concept offers easy possibilities to check whether the observed behaviour is an artifact of following a limited number of individuals or of lumping individuals, and also to verify whether individual variability is indeed an essential ingredient for the observed behaviour. In addition the approach offers arbitrarily large computational advantages. As an example the super-individual approach is applied to a generic model of the dynamics of a size-distributed consumer cohort as well as to an elaborate applied simulation model of the recruitment of striped bass.     

Nutrient transfer functions: the site of integration between feeding behaviour and nutritional physiology

Summary. We describe and extend a graphical approach to quantitative nutrition that focuses on the interplay between behavioural and physiological components of nutritional regulation. The site of integration is the nutrient transfer function, which is the function describing the time course of nutrient transfer between serially connected nutritional compartments (e.g., from the gut to the blood). The relationship between the shape of the nutrient transfer function and the temporal patterns of feeding determines the values of two key quantitative parameters of nutrition: the rate ('power') and the efficiency of nutrient acquisition. The approach can be extended to consider, in addition to the short-term behavioural and physiological decisions made by animals, some ecological determinants and longer-term, life history consequences of such decisions. Most importantly, this category of models can provide insights into the interplay among the various nutrients in an animal's diet. We illustrate this using hypothetical examples, and also present preliminary data for the power-efficiency relationships of protein and digestible carbohydrates in locusts. Finally, we consider existing evidence for the various means available to these and other insects for regulating such relationships. Received 24 September 1997; accepted 9 December 1997.     

Regional Consequences of Local Population Demography and Genetics in Relation to Habitat Management in Gentiana pneumonanthe

Abstract:  A joint demographic and population genetics stage-based model for a subdivided population was applied to Gentiana pneumonanthe , an early successional perennial herb, at a regional (metapopulation) scale. We used numerical simulations to determine the optimal frequency of habitat disturbance (sod cutting) and the intensity of gene flow among populations of G. pneumonanthe to manage both population viability and genetic diversity in this species. The simulations showed that even small populations that initially had near-equal allele frequencies could, if managed properly through sod cutting every 6 to 7 years, sustain their high genetic variation over the long run without gene flow. The more the allele frequencies in the small populations are skewed, however, the higher the probability that in the absence of gene flow, some alleles will be lost and within-population genetic variation will decrease even under proper management. This implies that although local population dynamics should be the major target for management, regional dynamics become important when habitat fragmentation and decreased population size lead to the loss of local genetic diversity. The recommended strategy to improve genetic composition of small populations is the introduction of seeds or seedlings of nonlocal origin.     

Development of the gap model ZELIG-CFS to predict the dynamics of North American mixed forest types with complex structures

When the development of gap models began about three decades ago, they became a new category of forest productivity models. Compared with traditional growth and yield models, which aim at deriving empirical relationships that best fit data, gap models use semi-theoretical relationships to simulate biotic and abiotic processes in forest stands, including the effects of photosynthetic active radiation interception, site fertility, temperature and soil moisture on tree growth and seedling establishment. While growth and yield models are appropriate to predict short-term stemwood production, gap models may be used to predict the natural course of species replacement for several generations. Because of the poor availability of historical data and knowledge on species-specific allometric relationships, species replacement and death rate, it has seldom been possible to develop and evaluate the most representative algorithms to predict growth and mortality with a high degree of accuracy. For this reason, the developers of gap models focused more on developing simulation tools to improve the understanding of forest succession than predicting growth and yield accurately.In a previous study, the predictions of simulations in two southeastern Canadian mixed ecosystem types using the ZELIG gap model were compared with long-term historical data. This exercise highlighted model components that needed modifications to improve the predictive capacity of ZELIG. The updated version of the model, ZELIG-CFS, includes modifications in the modelling of crown interaction effects, survival rate and regeneration. Different algorithms representing crown interactive effects between crowns were evaluated and species-specific model components that compute individual-tree mortality probability rate were derived. The results of the simulations were compared using long-term remeasurement data obtained from sample plots located in La Mauricie National Park of Canada in Quebec. In the present study, three forest types were studied: (1) red spruce-balsam fir-yellow birch, (2) yellow birch-sugar maple-balsam fir, and (3) red spruce-balsam fir-white birch mixed ecosystems. Among the seven algorithms that represented individual crown interactions, two better predicted the changes in basal area and individual-tree growth: (1) the mean available light growing factor (ALGF), which is computed from the proportion of light intercepted at different levels of individual crowns adjusted by the species-specific shade tolerance index, and (2) the ratio of mean ALGF to crown width. The long-term predicted patterns of change in basal area were consistent with the life history of the different species.     

Estimating influence of stocking regimes on livestock grazing distributions

Livestock often concentrate grazing in particular regions of landscapes while partly or wholly avoiding other regions. Dispersing livestock from the heavily grazed regions is a central challenge in grazing land management. Position data gathered from GPS-collared livestock hold potential for increasing knowledge of factors driving livestock aggregation patterns, but advances in gathering the data have outpaced advancements in analyzing and learning from it. We fit a hierarchical seemingly unrelated regression (SUR) model to explore how season of stocking and the location where cattle entered a pasture influenced grazing distributions. Stocking alternated between summer on one side of the pasture one year and fall on another side of the pasture the next year for 18 years. Waypoints were recorded on cattle for 50 d each year. We focused our analysis on the pasture's 10 most heavily grazed 4-ha units, because these units were the most prone to negative grazing impacts. Though grazing of the study units was always disproportionately heavy, it was much heavier with the summer than fall stocking regime: Bayesian confidence intervals indicate summer grazing of study units was approximately double the average fall grazing value. This is our core result, and it illustrates the strong effect stocking season or date or both can have on grazing distributions. We fit three additional models to explore the relative importance of stocking season versus location. According to this analysis, stocking season played a role, but stocking location was the main driver. Ostensibly minor factors (e.g. stocking location) can greatly influence livestock distributions.