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Annual plants under cyclic disturbance regime : better understanding through model aggregation
(2008)
In their application for conservation ecology, 'classical' analytical models and individual-based simulation models (IBMs) both entail their specific strengths and weaknesses, either in providing a detailed and realistic representation of processes or in regard to a comprehensive model analysis. This well-known dilemma may be resolved by the combination of both approaches when tackling certain problems of conservation ecology. Following this idea, we present the complementary use of both an IBM and a matrix population model in a case study on grassland conservation management. First, we develop a spatially explicit IBM to simulate the long-term response of the annual plant Thlaspi perfoliatum (Brassicaceae), claspleaf pennycress, to different management schemes (annual mowing vs. infrequent rototilling) based on field experiments. In order to complement the simulation results by further analyses, we aggregate the IBM to a spatially nonexplicit deterministic matrix population model. Within the periodic environment created by management regimes, population dynamics are described by periodic products of annual transition matrices. Such periodic matrix products provide a very conclusive framework to study the responses of species to different management return intervals. Thus, using tools of matrix model analysis (e.g., loop analysis), we can both identify dormancy within the age-structured seed bank as the pivotal strategy for persistence under cyclic disturbance regimes and reveal crucial thresholds in some less certain parameters. Results of matrix model analyses are therefore successfully tested by comparing their results to the respective IBM simulations. Their implications for an enhanced scientific basis for management decisions are discussed as well as some general benefits and limitations of the use of aggregating modeling approaches in conservation.
In undisturbed tropical montane rainforests massive organic layers accommodate the majority of roots and only a small fraction of roots penetrate the mineral soil. We investigated the contribution of vegetation to slope stability in such environments by modifying a standard model for slope stability to include an organic layer with distinct mechanical properties. The importance of individual model parameters was evaluated using detailed measurements of soil and vegetation properties to reproduce the observed depth of 11 shallow landslides in the Andes of southern Ecuador. By distinguishing mineral soil, organic layer and above-ground biomass, it is shown that in this environment vegetation provides a destabilizing effect mainly due to its contribution to the mass of the organic layer (up to 973 t ha-1 under wet conditions). Sensitivity analysis shows that the destabilizing effect of the mass of soil and vegetation can only be effective on slopes steeper than 37.9 degrees. This situation applies to 36% of the study area. Thus, on the steep slopes of this megadiverse ecosystem, the mass of the growing forest promotes landsliding, which in turn promotes a new cycle of succession. This feedback mechanism is worth consideration in further investigations of the impact of landslides on plant diversity in similar environments.
Collinearity a review of methods to deal with it and a simulation study evaluating their performance
(2013)
Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the folk lore'-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.
Predictive habitat models are an important tool for ecological research and conservation. A major cause of unreliable models is excessive model complexity, and regularization methods aim to improve the predictive performance by adequately constraining model complexity. We compare three regularization methods for logistic regression: variable selection, lasso, and ridge. They differ in the way model complexity is measured: variable selection uses the number of estimated parameters, the lasso uses the sum of the absolute values of the parameter estimates, and the ridge uses the sum of the squared values of the parameter estimates. We performed a simulation study with environmental data of a real landscape and artificial species occupancy data. We investigated the effect of three factors on relative model performance: (1) the number of parameters (16, 10, 6, 2) in the 'true' model that determined the distribution of the artificial species, (2) the prevalence, i.e. the proportion of sites occupied by the species, and (3) the sample size (measured in events per variable, EPV). Regularization improved model discrimination and calibration. However, no regularization method performed best under all circumstances: the ridge generally performed best in the 16-parameter scenario. The lasso generally performed best in the 10-parameter scenario. Variable selection with AIC was best at large sample sizes (EPV >= 10) when less than half of the variables influenced the species distribution. However, at low sample sizes (EPV < 10), ridge and lasso always performed best, regardless of the parameter scenario or prevalence. Overall, calibration was best in ridge models. Other methods showed overconfidence, particularly at low sample sizes. The percentage of correctly identified models was low for both lasso and variable selection. Variable selection should be used with caution. Although it can produce the best performing models under certain conditions, these situations are difficult to infer from the data. Ridge and lasso are risk-averse model strategies that can be expected to perform well under a wide range of underlying species-habitat relationships, particularly at small sample sizes.
Within the field of species distribution modelling an apparent dichotomy exists between process-based and correlative approaches, where the processes are explicit in the former and implicit in the latter. However, these intuitive distinctions can become blurred when comparing species distribution modelling approaches in more detail. In this review article, we contrast the extremes of the correlativeprocess spectrum of species distribution models with respect to core assumptions, model building and selection strategies, validation, uncertainties, common errors and the questions they are most suited to answer. The extremes of such approaches differ clearly in many aspects, such as model building approaches, parameter estimation strategies and transferability. However, they also share strengths and weaknesses. We show that claims of one approach being intrinsically superior to the other are misguided and that they ignore the processcorrelation continuum as well as the domains of questions that each approach is addressing. Nonetheless, the application of process-based approaches to species distribution modelling lags far behind more correlative (process-implicit) methods and more research is required to explore their potential benefits. Critical issues for the employment of species distribution modelling approaches are given, together with a guideline for appropriate usage. We close with challenges for future development of process-explicit species distribution models and how they may complement current approaches to study species distributions.
Substantial investment in climate change research has led to dire predictions of the impacts and risks to biodiversity. The Intergovernmental Panel on Climate Change fourth assessment report(1) cites 28,586 studies demonstrating significant biological changes in terrestrial systems(2). Already high extinction rates, driven primarily by habitat loss, are predicted to increase under climate change(3-6). Yet there is little specific advice or precedent in the literature to guide climate adaptation investment for conserving biodiversity within realistic economic constraints(7). Here we present a systematic ecological and economic analysis of a climate adaptation problem in one of the world's most species-rich and threatened ecosystems: the South African fynbos. We discover a counterintuitive optimal investment strategy that switches twice between options as the available adaptation budget increases. We demonstrate that optimal investment is nonlinearly dependent on available resources, making the choice of how much to invest as important as determining where to invest and what actions to take. Our study emphasizes the importance of a sound analytical framework for prioritizing adaptation investments(4). Integrating ecological predictions in an economic decision framework will help support complex choices between adaptation options under severe uncertainty. Our prioritization method can be applied at any scale to minimize species loss and to evaluate the robustness of decisions to uncertainty about key assumptions.
Questions: Which are the factors that influence forest and shrubland loss and regeneration and their underlying drivers?
Location: Central Chile, a world biodiversity hotspot.
Methods: Using land-cover data from the years 1975, 1985, 1999 and 2008, we fitted classification trees and multiple logistic regression models to account for the relationship between different trajectories of vegetation change and a range of biophysical and socio-economic factors.
Results: The variables that most consistently showed significant effects on vegetation change across all time-intervals were slope and distance to primary roads. We found that forest and shrubland loss on one side and regeneration on the other often displayed opposite patterns in relation to the different explanatory variables. Deforestation was positively related to distance to primary roads and to distance within forest edges and was favoured by a low insolation and a low slope. In turn, forest regeneration was negatively related to the distance to primary roads and positively to the distance to the nearest forest patch, insolation and slope. Shrubland loss was positively influenced by slope and distance to cities and primary roads and negatively influenced by distance to rivers. Conversely, shrubland regeneration was negatively related to slope, distance to cities and distance to primary roads and positively related to distance from existing forest patches and distance to rivers.
Conclusions: This article reveals how biophysical and socioeconomic factors influence vegetation cover change and the underlying social, political and economical drivers. This assessment provides a basis for management decisions, considering the crucial role of perennial vegetation cover for sustaining biodiversity and ecosystem services.