Generalized linear and generalized additive models in studies of species distributions: setting the scene

An important statistical development of the last 30 years has been the advance in regression analysis provided by generalized linear models (GLMs) and generalized additive models (GAMs). Here we introduce a series of papers prepared within the framework of an international workshop entitled: Advances in GLMs/GAMs modeling: from species distribution to environmental management, held in Riederalp, Switzerland, 6-11 August 2001.We first discuss some general uses of statistical models in ecology, as well as provide a short review of several key examples of the use of GLMs and GAMs in ecological modeling efforts. We next present an overview of GLMs and GAMs, and discuss some of their related statistics used for predictor selection, model diagnostics, and evaluation. Included is a discussion of several new approaches applicable to GLMs and GAMs, such as ridge regression, an alternative to stepwise selection of predictors, and methods for the identification of interactions by a combined use of regression trees and several other approaches. We close with an overview of the papers and how we feel they advance our understanding of their application to ecological modeling.

A hierarchical approach to model parameter optimization for developmental systems.

In the context of Systems Biology, computer simulations of gene regulatory networks provide a powerful tool to validate hypotheses and to explore possible system behaviors. Nevertheless, modeling a system poses some challenges of its own: especially the step of model calibration is often difficult due to insufficient data. For example when considering developmental systems, mostly qualitative data describing the developmental trajectory is available while common calibration techniques rely on high-resolution quantitative data. Focusing on the calibration of differential equation models for developmental systems, this study investigates different approaches to utilize the available data to overcome these difficulties. More specifically, the fact that developmental processes are hierarchically organized is exploited to increase convergence rates of the calibration process as well as to save computation time. Using a gene regulatory network model for stem cell homeostasis in Arabidopsis thaliana the performance of the different investigated approaches is evaluated, documenting considerable gains provided by the proposed hierarchical approach.

The ghost of past species occurrence: improving species distribution models for presence-only data

1. Model-based approaches have been used increasingly in conservation biology over recent years. Species presence data used for predictive species distribution modelling are abundant in natural history collections, whereas reliable absence data are sparse, most notably for vagrant species such as butterflies and snakes. As predictive methods such as generalized linear models (GLM) require absence data, various strategies have been proposed to select pseudo-absence data. However, only a few studies exist that compare different approaches to generating these pseudo-absence data. 2. Natural history collection data are usually available for long periods of time (decades or even centuries), thus allowing historical considerations. However, this historical dimension has rarely been assessed in studies of species distribution, although there is great potential for understanding current patterns, i.e. the past is the key to the present. 3. We used GLM to model the distributions of three 'target' butterfly species, Melitaea didyma, Coenonympha tullia and Maculinea teleius, in Switzerland. We developed and compared four strategies for defining pools of pseudo-absence data and applied them to natural history collection data from the last 10, 30 and 100 years. Pools included: (i) sites without target species records; (ii) sites where butterfly species other than the target species were present; (iii) sites without butterfly species but with habitat characteristics similar to those required by the target species; and (iv) a combination of the second and third strategies. Models were evaluated and compared by the total deviance explained, the maximized Kappa and the area under the curve (AUC). 4. Among the four strategies, model performance was best for strategy 3. Contrary to expectations, strategy 2 resulted in even lower model performance compared with models with pseudo-absence data simulated totally at random (strategy 1). 5. Independent of the strategy model, performance was enhanced when sites with historical species presence data were not considered as pseudo-absence data. Therefore, the combination of strategy 3 with species records from the last 100 years achieved the highest model performance. 6. Synthesis and applications. The protection of suitable habitat for species survival or reintroduction in rapidly changing landscapes is a high priority among conservationists. Model-based approaches offer planning authorities the possibility of delimiting priority areas for species detection or habitat protection. The performance of these models can be enhanced by fitting them with pseudo-absence data relying on large archives of natural history collection species presence data rather than using randomly sampled pseudo-absence data.

History matters: relating paths and rates of landscape change to butterfly species decline

Western European landscapes have drastically changed since the 1950s, with agricultural intensifications and the spread of urban settlements considered the most important drivers of this land-use/land-cover change. Losses of habitat for fauna and flora have been a direct consequence of this development. In the present study, we relate butterfly occurrence to land-use/land-cover changes over five decades between 1951 and 2000. The study area covers the entire Swiss territory. The 10 explanatory variables originate from agricultural statistics and censuses. Both state as well as rate was used as explanatory variables. Species distribution data were obtained from natural history collections. We selected eight butterfly species: four species occur on wetlands and four occur on dry grasslands. We used cluster analysis to track land-use/land-cover changes and to group communes based on similar trajectories of change. Generalized linear models were applied to identify factors that were significantly correlated with the persistence or disappearance of butterfly species. Results showed that decreasing agricultural areas and densities of farms with more than 10 ha of cultivated land are significantly related with wetland species decline, and increasing densities of livestock seem to have favored disappearance of dry grassland species. Moreover, we show that species declines are not only dependent on land-use/land-cover states but also on the rates of change; that is, the higher the transformation rate from small to large farms, the higher the loss of dry grassland species. We suggest that more attention should be paid to the rates of landscape change as feasible drivers of species change and derive some management suggestions.

Do habitat suitability models reliably predict the recovery areas of threatened species?

1. Identifying those areas suitable for recolonization by threatened species is essential to support efficient conservation policies. Habitat suitability models (HSM) predict species' potential distributions, but the quality of their predictions should be carefully assessed when the species-environment equilibrium assumption is violated.2. We studied the Eurasian otter Lutra lutra, whose numbers are recovering in southern Italy. To produce widely applicable results, we chose standard HSM procedures and looked for the models' capacities in predicting the suitability of a recolonization area. We used two fieldwork datasets: presence-only data, used in the Ecological Niche Factor Analyses (ENFA), and presence-absence data, used in a Generalized Linear Model (GLM). In addition to cross-validation, we independently evaluated the models with data from a recolonization event, providing presences on a previously unoccupied river.3. Three of the models successfully predicted the suitability of the recolonization area, but the GLM built with data before the recolonization disagreed with these predictions, missing the recolonized river's suitability and badly describing the otter's niche. Our results highlighted three points of relevance to modelling practices: (1) absences may prevent the models from correctly identifying areas suitable for a species spread; (2) the selection of variables may lead to randomness in the predictions; and (3) the Area Under Curve (AUC), a commonly used validation index, was not well suited to the evaluation of model quality, whereas the Boyce Index (CBI), based on presence data only, better highlighted the models' fit to the recolonization observations.4. For species with unstable spatial distributions, presence-only models may work better than presence-absence methods in making reliable predictions of suitable areas for expansion. An iterative modelling process, using new occurrences from each step of the species spread, may also help in progressively reducing errors.5. Synthesis and applications. Conservation plans depend on reliable models of the species' suitable habitats. In non-equilibrium situations, such as the case for threatened or invasive species, models could be affected negatively by the inclusion of absence data when predicting the areas of potential expansion. Presence-only methods will here provide a better basis for productive conservation management practices.

Modelling the influence of change in fire regime on the local distribution of a Mediterranean pyrophytic plant species (Cistus salviifolius) at its northern range limit

Aims: To assess the potential distribution of an obligate seeder and active pyrophyte, Cistus salviifolius, a vulnerable species in the Swiss Red List; to derive scenarios by changing the fire return interval; and to discuss the results from a conservation perspective. A more general aim is to assess the impact of fire as a natural factor influencing the vegetation of the southern slopes of the Alps. Locations: Alps, southern Switzerland. Methods: Presence-absence data to fit the model were obtained from the most recent field mapping of C. salviifolius. The quantitative environmental predictors used in this study include topographic, climatic and disturbance (fire) predictors. Models were fitted by logistic regression and evaluated by jackknife and bootstrap approaches. Changes in fire regime were simulated by increasing the time-return interval of fire (simulating longer periods without fire). Two scenarios were considered: no fire in the past 15 years; or in the past 35 years. Results: Rock cover, slope, topographic position, potential evapotranspiration and time elapsed since the last fire were selected in the final model. The Nagelkerke R-2 of the model for C. salviifolius was 0.57 and the Jackknife area under the curve evaluation was 0.89. The bootstrap evaluation revealed model robustness. By increasing the return interval of fire by either up to 15 years, or 35 years, the modelled C. salviifolius population declined by 30-40%, respectively. Main conclusions: Although fire plays a significant role, topography and rock cover appear to be the most important predictors, suggesting that the distribution of C. salviifolius in the southern Swiss Alps is closely related to the availability of supposedly competition-free sites, such as emerging bedrock, ridge locations or steep slopes. Fire is more likely to play a secondary role in allowing C. salviifolius to extend its occurrence temporarily, by increasing germination rates and reducing the competition from surrounding vegetation. To maintain a viable dormant seed bank for C. salviifolius, conservation managers should consider carrying out vegetation clearing and managing wild fire propagation to reduce competition and ensure sufficient recruitment for this species.

Predicting future distributions of mountain plants under climate change: does dispersal capacity matter?

Many studies have investigated the impacts that climate change could potentially have on the distribution of plant species, but few have attempted to constrain projections through plant dispersal limitations. Instead, most studies published so far have been using the simplification of considering dispersal as either unlimited or null. However, depending on a species' dispersal capacity, landscape fragmentation, and the rate of climatic change, these assumptions can lead to serious over- or underestimation of a species' future distribution. To quantify the discrepancies between unlimited, realistic, and no dispersal scenarios, we carried out projections of future distribution over the 21st century for 287 mountain plant species in a study area of the Western Swiss Alps. For each species, simulations were run for four dispersal scenarios (unlimited dispersal, no dispersal, realistic dispersal and realistic dispersal with long-distance dispersal events) and under four climate change scenarios. Although simulations accounting for realistic dispersal limitations did significantly differ from those considering dispersal as unlimited or null in terms of projected future distribution, using the unlimited dispersal simplification nevertheless provided good approximations for species extinctions under more moderate climate change scenarios. Overall, simulations accounting for dispersal limitations produced, for our mountainous study area, results that were significantly closer to unlimited dispersal than to no dispersal. Finally, analyzing the temporal pattern of species extinctions over the entire 21st century showed that, due to the possibility of a large number of species shifting their distribution to higher elevation, important species extinctions for our study area might not occur before the 2080-2100 time periods.

Influence of weather, rank, and home advantage on football outcomes in the gulf region.

PURPOSE: The objective of this study was to investigate the effects of weather, rank, and home advantage on international football match results and scores in the Gulf Cooperation Council (GCC) region. METHODS: Football matches (n = 2008) in six GCC countries were analyzed. To determine the weather influence on the likelihood of favorable outcome and goal difference, generalized linear model with a logit link function and multiple regression analysis were performed. RESULTS: In the GCC region, home teams tend to have greater likelihood of a favorable outcome (P < 0.001) and higher goal difference (P < 0.001). Temperature difference was identified as a significant explanatory variable when used independently (P < 0.001) or after adjustment for home advantage and team ranking (P < 0.001). The likelihood of favorable outcome for GCC teams increases by 3% for every 1-unit increase in temperature difference. After inclusion of interaction with opposition, this advantage remains significant only when playing against non-GCC opponents. While home advantage increased the odds of favorable outcome (P < 0.001) and goal difference (P < 0.001) after inclusion of interaction term, the likelihood of favorable outcome for a GCC team decreased (P < 0.001) when playing against a stronger opponent. Finally, the temperature and wet bulb globe temperature approximation were found as better indicators of the effect of environmental conditions than absolute and relative humidity or heat index on match outcomes. CONCLUSIONS: In GCC region, higher temperature increased the likelihood of a favorable outcome when playing against non-GCC teams. However, international ranking should be considered because an opponent with a higher rank reduced, but did not eliminate, the likelihood of a favorable outcome.

Advanced MRI unravels the nature of tissue alterations in early multiple sclerosis.

INTRODUCTION: In patients with multiple sclerosis (MS), conventional magnetic resonance imaging (MRI) provides only limited insights into the nature of brain damage with modest clinic-radiological correlation. In this study, we applied recent advances in MRI techniques to study brain microstructural alterations in early relapsing-remitting MS (RRMS) patients with minor deficits. Further, we investigated the potential use of advanced MRI to predict functional performances in these patients. METHODS: Brain relaxometry (T1, T2, T2*) and magnetization transfer MRI were performed at 3T in 36 RRMS patients and 18 healthy controls (HC). Multicontrast analysis was used to assess for microstructural alterations in normal-appearing (NA) tissue and lesions. A generalized linear model was computed to predict clinical performance in patients using multicontrast MRI data, conventional MRI measures as well as demographic and behavioral data as covariates. RESULTS: Quantitative T2 and T2* relaxometry were significantly increased in temporal normal-appearing white matter (NAWM) of patients compared to HC, indicating subtle microedema (P = 0.03 and 0.004). Furthermore, significant T1 and magnetization transfer ratio (MTR) variations in lesions (mean T1 z-score: 4.42 and mean MTR z-score: -4.09) suggested substantial tissue loss. Combinations of multicontrast and conventional MRI data significantly predicted cognitive fatigue (P = 0.01, Adj-R (2) = 0.4), attention (P = 0.0005, Adj-R (2) = 0.6), and disability (P = 0.03, Adj-R (2) = 0.4). CONCLUSION: Advanced MRI techniques at 3T, unraveled the nature of brain tissue damage in early MS and substantially improved clinical-radiological correlations in patients with minor deficits, as compared to conventional measures of disease.

An improved approach for predicting the distribution of rare and endangered species from occurrence and pseudo-absence data

1. Few examples of habitat-modelling studies of rare and endangered species exist in the literature, although from a conservation perspective predicting their distribution would prove particularly useful. Paucity of data and lack of valid absences are the probable reasons for this shortcoming. Analytic solutions to accommodate the lack of absence include the ecological niche factor analysis (ENFA) and the use of generalized linear models (GLM) with simulated pseudo-absences. 2. In this study we tested a new approach to generating pseudo-absences, based on a preliminary ENFA habitat suitability (HS) map, for the endangered species Eryngium alpinum. This method of generating pseudo-absences was compared with two others: (i) use of a GLM with pseudo-absences generated totally at random, and (ii) use of an ENFA only. 3. The influence of two different spatial resolutions (i.e. grain) was also assessed for tackling the dilemma of quality (grain) vs. quantity (number of occurrences). Each combination of the three above-mentioned methods with the two grains generated a distinct HS map. 4. Four evaluation measures were used for comparing these HS maps: total deviance explained, best kappa, Gini coefficient and minimal predicted area (MPA). The last is a new evaluation criterion proposed in this study. 5. Results showed that (i) GLM models using ENFA-weighted pseudo-absence provide better results, except for the MPA value, and that (ii) quality (spatial resolution and locational accuracy) of the data appears to be more important than quantity (number of occurrences). Furthermore, the proposed MPA value is suggested as a useful measure of model evaluation when used to complement classical statistical measures. 6. Synthesis and applications. We suggest that the use of ENFA-weighted pseudo-absence is a possible way to enhance the quality of GLM-based potential distribution maps and that data quality (i.e. spatial resolution) prevails over quantity (i.e. number of data). Increased accuracy of potential distribution maps could help to define better suitable areas for species protection and reintroduction.

A systematic review of the surgical treatment of large incisional hernia.

PURPOSE: Incisional hernia (IH) is one of the most frequent postoperative complications. Of all patients undergoing IH repair, a vast amount have a hernia which can be defined as a large incisional hernia (LIH). The aim of this study is to identify the preferred technique for LIH repair. METHODS: A systematic review of the literature was performed and studies describing patients with IH with a diameter of 10 cm or a surface of 100 cm2 or more were included. Recurrence hazards per year were calculated for all techniques using a generalized linear model. RESULTS: Fifty-five articles were included, containing 3,945 LIH repairs. Mesh reinforced techniques displayed better recurrence rates and hazards than techniques without mesh reinforcement. Of all the mesh techniques, sublay repair, sandwich technique with sublay mesh and aponeuroplasty with intraperitoneal mesh displayed the best results (recurrence rates of <3.6%, recurrence hazard <0.5% per year). Wound complications were frequent and most often seen after complex LIH repair. CONCLUSIONS: The use of mesh during LIH repair displayed the best recurrence rates and hazards. If possible mesh in sublay position should be used in cases of LIH repair.

A multi-contrast MRI study of microstructural brain damage in patients with mild cognitive impairment.

OBJECTIVES: The aim of this study was to investigate pathological mechanisms underlying brain tissue alterations in mild cognitive impairment (MCI) using multi-contrast 3 T magnetic resonance imaging (MRI). METHODS: Forty-two MCI patients and 77 healthy controls (HC) underwent T1/T2* relaxometry as well as Magnetization Transfer (MT) MRI. Between-groups comparisons in MRI metrics were performed using permutation-based tests. Using MRI data, a generalized linear model (GLM) was computed to predict clinical performance and a support-vector machine (SVM) classification was used to classify MCI and HC subjects. RESULTS: Multi-parametric MRI data showed microstructural brain alterations in MCI patients vs HC that might be interpreted as: (i) a broad loss of myelin/cellular proteins and tissue microstructure in the hippocampus (p ≤ 0.01) and global white matter (p < 0.05); and (ii) iron accumulation in the pallidus nucleus (p ≤ 0.05). MRI metrics accurately predicted memory and executive performances in patients (p ≤ 0.005). SVM classification reached an accuracy of 75% to separate MCI and HC, and performed best using both volumes and T1/T2*/MT metrics. CONCLUSION: Multi-contrast MRI appears to be a promising approach to infer pathophysiological mechanisms leading to brain tissue alterations in MCI. Likewise, parametric MRI data provide powerful correlates of cognitive deficits and improve automatic disease classification based on morphometric features.

Multicontrast MRI Quantification of Focal Inflammation and Degeneration in Multiple Sclerosis.

INTRODUCTION: Local microstructural pathology in multiple sclerosis patients might influence their clinical performance. This study applied multicontrast MRI to quantify inflammation and neurodegeneration in MS lesions. We explored the impact of MRI-based lesion pathology in cognition and disability. METHODS: 36 relapsing-remitting MS subjects and 18 healthy controls underwent neurological, cognitive, behavioural examinations and 3 T MRI including (i) fluid attenuated inversion recovery, double inversion recovery, and magnetization-prepared gradient echo for lesion count; (ii) T1, T2, and T2(*) relaxometry and magnetisation transfer imaging for lesion tissue characterization. Lesions were classified according to the extent of inflammation/neurodegeneration. A generalized linear model assessed the contribution of lesion groups to clinical performances. RESULTS: Four lesion groups were identified and characterized by (1) absence of significant alterations, (2) prevalent inflammation, (3) concomitant inflammation and microdegeneration, and (4) prevalent tissue loss. Groups 1, 3, 4 correlated with general disability (Adj-R (2) = 0.6; P = 0.0005), executive function (Adj-R (2) = 0.5; P = 0.004), verbal memory (Adj-R (2) = 0.4; P = 0.02), and attention (Adj-R (2) = 0.5; P = 0.002). CONCLUSION: Multicontrast MRI provides a new approach to infer in vivo histopathology of plaques. Our results support evidence that neurodegeneration is the major determinant of patients' disability and cognitive dysfunction.

Outcome Prediction of Consciousness Disorders in the Acute Stage Based on a Complementary Motor Behavioural Tool.

INTRODUCTION: Attaining an accurate diagnosis in the acute phase for severely brain-damaged patients presenting Disorders of Consciousness (DOC) is crucial for prognostic validity; such a diagnosis determines further medical management, in terms of therapeutic choices and end-of-life decisions. However, DOC evaluation based on validated scales, such as the Revised Coma Recovery Scale (CRS-R), can lead to an underestimation of consciousness and to frequent misdiagnoses particularly in cases of cognitive motor dissociation due to other aetiologies. The purpose of this study is to determine the clinical signs that lead to a more accurate consciousness assessment allowing more reliable outcome prediction. METHODS: From the Unit of Acute Neurorehabilitation (University Hospital, Lausanne, Switzerland) between 2011 and 2014, we enrolled 33 DOC patients with a DOC diagnosis according to the CRS-R that had been established within 28 days of brain damage. The first CRS-R assessment established the initial diagnosis of Unresponsive Wakefulness Syndrome (UWS) in 20 patients and a Minimally Consciousness State (MCS) in the remaining13 patients. We clinically evaluated the patients over time using the CRS-R scale and concurrently from the beginning with complementary clinical items of a new observational Motor Behaviour Tool (MBT). Primary endpoint was outcome at unit discharge distinguishing two main classes of patients (DOC patients having emerged from DOC and those remaining in DOC) and 6 subclasses detailing the outcome of UWS and MCS patients, respectively. Based on CRS-R and MBT scores assessed separately and jointly, statistical testing was performed in the acute phase using a non-parametric Mann-Whitney U test; longitudinal CRS-R data were modelled with a Generalized Linear Model. RESULTS: Fifty-five per cent of the UWS patients and 77% of the MCS patients had emerged from DOC. First, statistical prediction of the first CRS-R scores did not permit outcome differentiation between classes; longitudinal regression modelling of the CRS-R data identified distinct outcome evolution, but not earlier than 19 days. Second, the MBT yielded a significant outcome predictability in the acute phase (p<0.02, sensitivity>0.81). Third, a statistical comparison of the CRS-R subscales weighted by MBT became significantly predictive for DOC outcome (p<0.02). DISCUSSION: The association of MBT and CRS-R scoring improves significantly the evaluation of consciousness and the predictability of outcome in the acute phase. Subtle motor behaviour assessment provides accurate insight into the amount and the content of consciousness even in the case of cognitive motor dissociation.

A general linear relaxometry model of R1 using imaging data.

PURPOSE: The longitudinal relaxation rate (R1 ) measured in vivo depends on the local microstructural properties of the tissue, such as macromolecular, iron, and water content. Here, we use whole brain multiparametric in vivo data and a general linear relaxometry model to describe the dependence of R1 on these components. We explore a) the validity of having a single fixed set of model coefficients for the whole brain and b) the stability of the model coefficients in a large cohort. METHODS: Maps of magnetization transfer (MT) and effective transverse relaxation rate (R2 *) were used as surrogates for macromolecular and iron content, respectively. Spatial variations in these parameters reflected variations in underlying tissue microstructure. A linear model was applied to the whole brain, including gray/white matter and deep brain structures, to determine the global model coefficients. Synthetic R1 values were then calculated using these coefficients and compared with the measured R1 maps. RESULTS: The model's validity was demonstrated by correspondence between the synthetic and measured R1 values and by high stability of the model coefficients across a large cohort. CONCLUSION: A single set of global coefficients can be used to relate R1 , MT, and R2 * across the whole brain. Our population study demonstrates the robustness and stability of the model. Magn Reson Med, 2014. © 2014 The Authors. Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. Magn Reson Med 73:1309-1314, 2015. © 2014 Wiley Periodicals, Inc.