Semiparametric transformation models for interval‐censored data in the presence of a cure fraction

Mixed case interval‐censored data arise when the event of interest is known only to occur within an interval induced by a sequence of random examination times. Such data are commonly encountered in disease research with longitudinal follow‐up. Furthermore, the medical treatment has progressed over the last decade with an increasing proportion of patients being cured for many types of diseases. Thus, interest has grown in cure models for survival data which hypothesize a certain proportion of subjects in the population are not expected to experience the events of interest. In this article, we consider a two‐component mixture cure model for regression analysis of mixed case interval‐censored data. The first component is a logistic regression model that describes the cure rate, and the second component is a semiparametric transformation model that describes the distribution of event time for the uncured subjects. We propose semiparametric maximum likelihood estimation for the considered model. We develop an EM type algorithm for obtaining the semiparametric maximum likelihood estimators (SPMLE) of regression parameters and establish their consistency, efficiency, and asymptotic normality. Extensive simulation studies indicate that the SPMLE performs satisfactorily in a wide variety of settings. The proposed method is illustrated by the analysis of the hypobaric decompression sickness data from National Aeronautics and Space Administration.     

Niche models tell half the story: spatial context and life‐history traits influence species responses to global change

Aim While niche models are typically used to assess the vulnerability of species to climate change, they have been criticized for their limited assessment of threats other than climate change. We attempt to evaluate this limitation by combining niche models with life‐history models to investigate the relative influence of climate change and a range of fire regimes on the viability of a long‐lived plant population. Specifically, we investigate whether range shift due to climate change is a greater threat to an obligate seeding fire‐prone shrub than altered fire frequency and how these two threatening processes might interact. Location Australian sclerophyll woodland and heathland. Methods The study species is Leucopogon setiger, an obligate seeding fire‐prone shrub. A spatially explicit stochastic matrix model was constructed for this species and linked with a dynamic niche model and fire risk functions representing a suite of average fire return intervals. We compared scenarios with a variety of hypothetical patches, a patch framework based upon current habitat suitability and one with dynamic habitat suitability based on climate change scenarios A1FI and A2. Results Leucopogon setiger was found to be sensitive to fire frequency, with shorter intervals reducing expected minimum abundances (EMAs). Spatial decoupling of fires across the landscape reduced the vulnerability of the species to shortened fire frequencies. Shifting habitat, while reducing EMAs, was less of a threat to the species than frequent fire. Main conclusions Altered fire regime, in particular more frequent fires relative to the historical regime, was predicted to be a strong threat to this species, which may reflect a vulnerability of obligate seeders in general. Range shifts induced by climate change were a secondary threat when habitat reductions were predicted. Incorporating life‐history traits into habitat suitability models by linking species distribution models with population models allowed for the population‐level evaluation of multiple stressors that affect population dynamics and habitat, ultimately providing a greater understanding of the impacts of global change than would be gained by niche models alone. Further investigations of this type could elucidate how particular bioecological factors can affect certain types of species under global change.     

Wrong,but useful: regional species distribution models may not be improved by range‐wide data under biased sampling

Species distribution modeling (SDM) is an essential method in ecology and conservation. SDMs are often calibrated within one country's borders, typically along a limited environmental gradient with biased and incomplete data, making the quality of these models questionable. In this study, we evaluated how adequate are national presence‐only data for calibrating regional SDMs. We trained SDMs for Egyptian bat species at two different scales: only within Egypt and at a species‐specific global extent. We used two modeling algorithms: Maxent and elastic net, both under the point‐process modeling framework. For each modeling algorithm, we measured the congruence of the predictions of global and regional models for Egypt, assuming that the lower the congruence, the lower the appropriateness of the Egyptian dataset to describe the species' niche. We inspected the effect of incorporating predictions from global models as additional predictor (“prior”) to regional models, and quantified the improvement in terms of AUC and the congruence between regional models run with and without priors. Moreover, we analyzed predictive performance improvements after correction for sampling bias at both scales. On average, predictions from global and regional models in Egypt only weakly concur. Collectively, the use of priors did not lead to much improvement: similar AUC and high congruence between regional models calibrated with and without priors. Correction for sampling bias led to higher model performance, whatever prior used, making the use of priors less pronounced. Under biased and incomplete sampling, the use of global bats data did not improve regional model performance. Without enough bias‐free regional data, we cannot objectively identify the actual improvement of regional models after incorporating information from the global niche. However, we still believe in great potential for global model predictions to guide future surveys and improve regional sampling in data‐poor regions.     

Using species distribution models to define nesting habitat of the eastern metapopulation of double‐crested cormorants

When organisms with similar phenotypes have conflicting management and conservation initiatives, approaches are needed to differentiate among subpopulations or discrete groups. For example, the eastern metapopulation of the double‐crested cormorant (Phalacrocorax auritus) has a migratory phenotype that is culled because they are viewed as a threat to commercial and natural resources, whereas resident birds are targeted for conservation. Understanding the distinct breeding habitats of resident versus migratory cormorants would aid in identification and management decisions. Here, we use species distribution models (SDM: Maxent) of cormorant nesting habitat to examine the eastern P. auritus metapopulation and the predicted breeding sites of its phenotypes. We then estimate the phenotypic identity of breeding colonies of cormorants where management plans are being developed. We transferred SDMs trained on data from resident bird colonies in Florida and migratory bird colonies in Minnesota to South Carolina in an effort to identify the phenotype of breeding cormorants there based on the local landscape characteristics. Nesting habitat characteristics of cormorant colonies in South Carolina more closely resembled those of the Florida phenotype than those of birds of the Minnesota phenotype. The presence of the resident phenotype in summer suggests that migratory and resident cormorants will co‐occur in South Carolina in winter. Thus, there is an opportunity for separate management strategies for the two phenotypes in that state. We found differences in nesting habitat characteristics that could be used to refine management strategies and reduce human conflicts with abundant winter migrants and, at the same time, conserve less common colonies of resident cormorants. The models we use here show potential for advancing the study of geographically overlapping phenotypes with differing conservation and management priorities.     

Semiparametric frailty models for zero‐inflated event count data in the presence of informative dropout

Recurrent events data are commonly encountered in medical studies. In many applications, only the number of events during the follow‐up period rather than the recurrent event times is available. Two important challenges arise in such studies: (a) a substantial portion of subjects may not experience the event, and (b) we may not observe the event count for the entire study period due to informative dropout. To address the first challenge, we assume that underlying population consists of two subpopulations: a subpopulation nonsusceptible to the event of interest and a subpopulation susceptible to the event of interest. In the susceptible subpopulation, the event count is assumed to follow a Poisson distribution given the follow‐up time and the subject‐specific characteristics. We then introduce a frailty to account for informative dropout. The proposed semiparametric frailty models consist of three submodels: (a) a logistic regression model for the probability such that a subject belongs to the nonsusceptible subpopulation; (b) a nonhomogeneous Poisson process model with an unspecified baseline rate function; and (c) a Cox model for the informative dropout time. We develop likelihood‐based estimation and inference procedures. The maximum likelihood estimators are shown to be consistent. Additionally, the proposed estimators of the finite‐dimensional parameters are asymptotically normal and the covariance matrix attains the semiparametric efficiency bound. Simulation studies demonstrate that the proposed methodologies perform well in practical situations. We apply the proposed methods to a clinical trial on patients with myelodysplastic syndromes.     

Runoff and the longitudinal distribution of macroinvertebrates in a glacier‐fed stream: implications for the effects of global warming

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The mid‐domain effect matters: simulation analyses of range‐size distribution data from Mount Kinabalu,Borneo

Aim In simulation exercises, mid‐domain peaks in species richness arise as a result of the random placement of modelled species ranges within simulated geometric constraints. This has been called the mid‐domain effect (MDE). Where close correspondence is found between such simulations and empirical data, it is not possible to reject the hypothesis that empirical species richness patterns result from the MDE rather than being the outcome (wholly or largely) of other factors. To separate the influence of the MDE from other factors we therefore need to evaluate variables other than species richness. The distribution of range sizes gives different predictions between models including the MDE or not. Here, we produce predictions for species richness and distribution of range sizes from one model without the MDE and from two MDE models: a classical MDE model encompassing only species with their entire range within the domain (range‐restricted MDE), and a model encompassing all species with the theoretical midpoint within the domain (midpoint‐restricted MDE). These predictions are compared with observations from the elevational pattern of range‐size distributions and species richness of vascular plants. Location Mount Kinabalu, Borneo. Methods The data set analysed comprises more than 28,000 plant specimens with information on elevation. Species ranges are simulated with various assumptions for the three models, and the species simulated are subsequently subjected to a sampling that simulates the actual collection of species on Mount Kinabalu. The resulting pattern of species richness and species range‐size distributions are compared with the observed pattern. Results The comparison of simulated and observed patterns indicates that an underlying monotonically decreasing trend in species richness with elevation is essential to explain fully the observed pattern of richness and range size. When the underlying trend is accounted for, the MDE model that restricts the distributions of theoretical midpoints performs better than both the classical MDE model and the model that does not incorporate geometric constraints. Main conclusions Of the three models evaluated here, the midpoint‐restricted MDE model is found to be the best for explaining species richness and species range‐size distributions on Mount Kinabalu.     

Rethinking long‐term vegetation dynamics: multiple glacial refugia and local expansion of a species complex

Evidence is accumulating that some arcto‐boreal plant taxa persisted through the last glacial maximum (LGM) in Alaska and adjacent Canada. However, the spatial patterns of glacial persistence and associated postglacial colonization remain largely unknown. In this study, we investigated the LGM refugia of an alder (Alnus) species complex (n = 3 taxa) and assess the spatiotemporal dynamics of Alnus in this vast region. Specifically, we conducted high‐throughput DNA sequencing (ddRADseq) on Alnus foliar samples collected from a dense population network to investigate patterns of genetic structure and infer the presence of glacial lineages. Species distribution modeling (SDM) was used to investigate the probability and possible locations of glacial persistence. These analyses were integrated and then compared with fossil pollen data to identify the locations of refugial populations and spatial patterns of postglacial colonization. Our genetic analyses revealed two glacial lineages with separate geographic origins for each Alnus taxon, suggesting that the genus persisted in multiple LGM refugia. Non‐overlapping hindcast distributions based on SDMs further support the presence of multiple, spatially distinct refugia. These ddRADseq and SDM results, in conjunction with reassessment of fossil pollen records, suggest that Alnus expanded from several population nuclei that existed during the LGM and coalesced during the Holocene to form its present range. These results challenge the unidirectional model for postglacial vegetation expansion, implying that climate buffering associated with landscape heterogeneity and adaptation to millennial‐scale environmental variability played important roles in driving late‐Quaternary population dynamics.     

Climate‐induced changes in the distribution of freshwater fish: observed and predicted trends

1. Climate change could be one of the main threats faced by aquatic ecosystems and freshwater biodiversity. Improved understanding, monitoring and forecasting of its effects are thus crucial for researchers, policy makers and biodiversity managers. 2. Here, we provide a review and some meta‐analyses of the literature reporting both observed and predicted climate‐induced effects on the distribution of freshwater fish. After reviewing three decades of research, we summarise how methods in assessing the effects of climate change have evolved, and whether current knowledge is geographically or taxonomically biased. We conducted multispecies qualitative and quantitative analyses to find out whether the observed responses of freshwater fish to recent changes in climate are consistent with those predicted under future climate scenarios. 3. We highlight the fact that, in recent years, freshwater fish distributions have already been affected by contemporary climate change in ways consistent with anticipated responses under future climate change scenarios: the range of most cold‐water species could be reduced or shift to higher altitude or latitude, whereas that of cool‐ and warm‐water species could expand or contract. 4. Most evidence about the effects of climate change is underpinned by the large number of studies devoted to cold‐water fish species (mainly salmonids). Our knowledge is still incomplete, however, particularly due to taxonomic and geographic biases. 5. Observed and expected responses are well correlated among families, suggesting that model predictions are supported by empirical evidence. The observed effects are of greater magnitude and show higher variability than the predicted effects, however, indicating that other drivers of changes may be interacting with climate and seriously affecting freshwater fish. 6. Finally, we suggest avenues of research required to address current gaps in what we know about the climate‐induced effects on freshwater fish distribution, including (i) the need for more long‐term data analyses, (ii) the assessment of climate‐induced effects at higher levels of organisation (e.g. assemblages), (iii) methodological improvements (e.g. accounting for uncertainty among projections and species’ dispersal abilities, combining both distributional and empirical approaches and including multiple non‐climatic stressors) and (iv) systematic confrontation of observed versus predicted effects across multi‐species assemblages and at several levels of biological organisation (i.e. populations and assemblages).     

Predicting potential distribution of poorly known species with small database: the case of four‐horned antelope Tetracerus quadricornis on the Indian subcontinent

Information gaps on the distribution of data deficient and rare species such as four‐horned antelope (FHA) in Nepal may impair their conservation. We aimed to empirically predict the distribution of FHA in Nepal with the help of data from the Indian subcontinent. Additionally, we wanted to identify core areas and gaps within the reported range limits and to assess the degree of isolation of known Nepalese populations from the main distribution areas in India. The tropical part of the Indian subcontinent (65°–90° eastern longitude, 5°–30° northern latitude), that is, the areas south of the Himalayan Mountains. Using MaxEnt and accounting for sampling bias, we developed predictive distribution models from environmental and topographical variables, and known presence locations of the study species in India and Nepal. We address and discuss the use of target group vs. random background. The prediction map reveals a disjunct distribution of FHA with core areas in the tropical parts of central to southern–western India. At the scale of the Indian subcontinent, suitable FHA habitat area in Nepal was small. The Indo‐Gangetic Plain isolates Nepalese from the Indian FHA populations, but the distribution area extends further south than proposed by the current IUCN map. A low to intermediate temperature seasonality as well as low precipitation during the dry and warm season contributed most to the prediction of FHA distribution. The predicted distribution maps confirm other FHA range maps but also indicate that suitable areas exist south of the known range. Results further highlight that small populations in the Nepalese Terai Arc are isolated from the Indian core distribution and therefore might be under high extinction risk.     

Cox proportional hazards models with left truncation and time‐varying coefficient: Application of age at event as outcome in cohort studies

When analyzing time‐to‐event cohort data, two different ways of choosing a time scale have been discussed in the literature: time‐on‐study or age at onset of disease. One advantage of choosing the latter is interpretability of the hazard ratio as a function of age. To handle the analysis of age at onset in a principled manner, we present an analysis of the Cox Proportional Hazards model with time‐varying coefficient for left‐truncated and right‐censored data. In the analysis of Northern Manhattan Study (NOMAS) with age at onset of stroke as outcome, we demonstrate that well‐established risk factors may be important only around a certain age span and less established risk factors can have a strong effect in a certain age span.     

No‐analog climates and shifting realized niches during the late quaternary: implications for 21st‐century predictions by species distribution models

Empirically derived species distributions models (SDMs) are increasingly relied upon to forecast species vulnerabilities to future climate change. However, many of the assumptions of SDMs may be violated when they are used to project species distributions across significant climate change events. In particular, SDM's in theory assume stable fundamental niches, but in practice, they assume stable realized niches. The assumption of a fixed realized niche relative to climate variables remains unlikely for various reasons, particularly if novel future climates open up currently unavailable portions of species’ fundamental niches. To demonstrate this effect, we compare the climate distributions for fossil‐pollen data from 21 to 15 ka bp (relying on paleoclimate simulations) when communities and climates with no modern analog were common across North America to observed modern pollen assemblages. We test how well SDMs are able to project 20th century pollen‐based taxon distributions with models calibrated using data from 21 to 15 ka. We find that taxa which were abundant in areas with no‐analog late glacial climates, such as Fraxinus, Ostrya/Carpinus and Ulmus, substantially shifted their realized niches from the late glacial period to present. SDMs for these taxa had low predictive accuracy when projected to modern climates despite demonstrating high predictive accuracy for late glacial pollen distributions. For other taxa, e.g. Quercus, Picea, Pinus strobus, had relatively stable realized niches and models for these taxa tended to have higher predictive accuracy when projected to present. Our findings reinforce the point that a realized niche at any one time often represents only a subset of the climate conditions in which a taxon can persist. Projections from SDMs into future climate conditions that are based solely on contemporary realized distributions are potentially misleading for assessing the vulnerability of species to future climate change.     

Biogeography of the Amazon molly: ecological niche and range limits of an asexual hybrid species

Aim To understand the relative contributions of environmental factors, dispersal limitations and the presence of sperm donors in determining the distribution of the Amazon molly (Poecilia formosa), a sperm‐dependent unisexual fish species of hybrid origin. To explore niche similarities and/or differences between the hybrid and parental species. To evaluate whether large‐scale abiotic factors can explain a successful introduction of both P. formosa and Poecilia latipinna. Location South‐east United States, Mexico and Central America. Methods We used abiotic variables in ecological niche modelling (ENM) to identify regions with suitable conditions for the presence of the Amazon molly and its two parental species (P. latipinna and Poecilia mexicana). We also used a recently developed metric to calculate the degree of niche overlap between the hybrid and its parental species. Results ENM produced highly significant models [all area under the curve (AUC) > 0.99 for the three species]. Annual mean temperature and minimum temperature of the coldest month were the variables that best explained the distribution of the Amazon molly. With the exception of south Florida, few areas beyond the known distribution of the species were predicted to have suitable environmental conditions. The hybrid species niche overlaps partially with the parental species. However, given the available data, it is neither more similar nor more different than expected by chance. Main conclusions Two different processes are acting to limit the distribution of P. formosa. At the northern limit, although a sperm donor species is present further north, suitable environmental conditions are absent from nearby locations. At the southern limit, a sperm donor species is present and areas with good environmental conditions are present at nearby locations, suggesting that dispersal ability is the limiting factor. We found that the hybrid species overlaps in a similar way with both parental species while still having its own niche identity. This result may be explained by the fact that hybrid species inherit characteristics of two ecologically divergent species, which can result in intermediate or even transgressive phenotypes. These results support recent work on the role of hybridization in diversification.