Integrating high‐speed videos in capture‐mark‐recapture studies of insects

Capture–mark–recapture (CMR) studies have been used extensively in ecology and evolution. While it is feasible to apply CMR in some animals, it is considerably more challenging in small fast‐moving species such as insects. In these groups, low recapture rates can bias estimates of demographic parameters, thereby handicapping effective analysis and management of wild populations. Here, we use high‐speed videos (HSV) to capture two large dragonfly species, Anax junius and Rhionaeschna multicolor, that rarely land and, thus, are particularly challenging for CMR studies. We test whether HSV, compared to conventional “eye” observations, increases the “resighting” rates and, consequently, improves estimates of both survival rates and the effects of demographic covariates on survival. We show that the use of HSV increases the number of resights by 64% in A. junius and 48% in R. multicolor. HSV improved our estimates of resighting and survival probability which were either under‐ or overestimated with the conventional observations. Including HSV improved credible intervals for resighting rate and survival probability by 190% and 130% in A. junius and R. multicolor, respectively. Hence, it has the potential to open the door to a wide range of research possibilities on species that are traditionally difficult to monitor with distance sampling, including within insects and birds.     

Challenges and opportunities for comparative studies of survival rates: An example with male pinnipeds

Survival rates are a central component of life‐history strategies of large vertebrate species. However, comparative studies seldom investigate interspecific variation in survival rates with respect to other life‐history traits, especially for males. The lack of such studies could be due to the challenges associated with obtaining reliable datasets, incorporating information on the 0–1 probability scale, or dealing with several types of measurement error in life‐history traits, which can be a computationally intensive process that is often absent in comparative studies. We present a quantitative approach using a Bayesian phylogenetically controlled regression with the flexibility to incorporate uncertainty in estimated survival rates and quantitative life‐history traits while considering genetic similarity among species and uncertainty in relatedness. As with any comparative analysis, our approach makes several assumptions regarding the generalizability and comparability of empirical data from separate studies. Our model is versatile in that it can be applied to any species group of interest and include any life‐history traits as covariates. We used an unbiased simulation framework to provide “proof of concept” for our model and applied a slightly richer model to a real data example for pinnipeds. Pinnipeds are an excellent taxonomic group for comparative analysis, but survival rate data are scarce. Our work elucidates the challenges associated with addressing important questions related to broader ecological life‐history patterns and how survival–reproduction trade‐offs might shape evolutionary histories of extant taxa. Specifically, we underscore the importance of having high‐quality estimates of age‐specific survival rates and information on other life‐history traits that reasonably characterize a species for accurately comparing across species.     

Rapid contemporary evolution and clonal food web dynamics

Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or a sexual phase reshuffles the genetic material. When clones differ in traits affecting interspecific interactions, within-species clonal dynamics can have major effects on the population dynamics. We first consider a simple predator–prey system with two prey genotypes, parametrized with data from a well-studied experimental system, and explore how the extent of differences in defence against predation within the prey population determine dynamic stability versus instability of the system. We then explore how increased potential for evolution affects the community dynamics in a more general community model with multiple predator and multiple prey genotypes. These examples illustrate how microevolutionary ‘details’ that enhance or limit the potential for heritable phenotypic change can have significant effects on contemporaneous community-level dynamics and the persistence and coexistence of species.     

Individual variation in feeding morphology,not diet,can facilitate the success of generalist species in urban ecosystems

Generalist species dominate urban ecosystems. The success of urban generalists is often related to a plastic diet and feeding traits that allow them to take advantage of a variety of food resources provided by humans in cities. The classification of a species as a generalist is commonly based on mean estimates of diet‐ and feeding‐related traits. However, there is increasing evidence that a generalist population can consist of individual specialists. In such cases, estimates based on mean can hide important individual variation that can explain trophic ecology and the success of urban dwellers. Here, we focus on guppies, Poecilia reticulata, a widespread alien fish species which has invaded both urban and non‐urban systems, to explore the effect of urbanization on individual diet and feeding morphology (cranium shape). Our results show that guppies in urban and non‐urban populations are not individual specialists, having a similar generalist diet despite the high population density. However, there is important individual variation in cranium shape which allow urban guppies to feed more efficiently on highly nutritious food. Our data suggest that individual variation in feeding efficiency can be a critical overlooked trait that facilitates the success of urban generalists.     

Moderate plant–soil feedbacks have small effects on the biodiversity–productivity relationship: A field experiment

Plant–soil feedback (PSF) has gained attention as a mechanism promoting plant growth and coexistence. However, most PSF research has measured monoculture growth in greenhouse conditions. Translating PSFs into effects on plant growth in field communities remains an important frontier for PSF research. Using a 4‐year, factorial field experiment in Jena, Germany, we measured the growth of nine grassland species on soils conditioned by each of the target species (i.e., 72 PSFs). Plant community models were parameterized with or without these PSF effects, and model predictions were compared to plant biomass production in diversity–productivity experiments. Plants created soils that changed subsequent plant biomass by 40%. However, because they were both positive and negative, the average PSF effect was 14% less growth on “home” than on “away” soils. Nine‐species plant communities produced 29 to 37% more biomass for polycultures than for monocultures due primarily to selection effects. With or without PSF, plant community models predicted 28%–29% more biomass for polycultures than for monocultures, again due primarily to selection effects. Synthesis: Despite causing 40% changes in plant biomass, PSFs had little effect on model predictions of plant community biomass across a range of species richness. While somewhat surprising, a lack of a PSF effect was appropriate in this site because species richness effects in this study were caused by selection effects and not complementarity effects (PSFs are a complementarity mechanism). Our plant community models helped us describe several reasons that even large PSF may not affect plant productivity. Notably, we found that dominant species demonstrated small PSF, suggesting there may be selective pressure for plants to create neutral PSF. Broadly, testing PSFs in plant communities in field conditions provided a more realistic understanding of how PSFs affect plant growth in communities in the context of other species traits.     

Closing the gap between rocks and clocks using total-evidence dating

Total-evidence dating (TED) allows evolutionary biologists to incorporate a wide range of dating information into a unified statistical analysis. One might expect this to improve the agreement between rocks and clocks but this is not necessarily the case. We explore the reasons for such discordance using a mammalian dataset with rich molecular, morphological and fossil information. There is strong conflict in this dataset between morphology and molecules under standard stochastic models. This causes TED to push divergence events back in time when using inadequate models or vague priors, a phenomenon we term ‘deep root attraction’ (DRA). We identify several causes of DRA. Failure to account for diversified sampling results in dramatic DRA, but this can be addressed using existing techniques. Inadequate morphological models also appear to be a major contributor to DRA. The major reason seems to be that current models do not account for dependencies among morphological characters, causing distorted topology and branch length estimates. This is particularly problematic for huge morphological datasets, which may contain large numbers of correlated characters. Finally, diversification and fossil sampling priors that do not incorporate all the available background information can contribute to DRA, but these priors can also be used to compensate for DRA. Specifically, we show that DRA in the mammalian dataset can be addressed by introducing a modest extra penalty for ghost lineages that are unobserved in the fossil record, for instance by assuming rapid diversification, rare extinction or high fossil sampling rate; any of these assumptions produces highly congruent divergence time estimates with a minimal gap between rocks and clocks. Under these conditions, fossils have a stabilizing influence on divergence time estimates and significantly increase the precision of those estimates, which are generally close to the dates suggested by palaeontologists.This article is part of the themed issue ‘Dating species divergences using rocks and clocks’.     

Integrating growth and survival models for flexible estimation of size‐dependent survival in a cryptic,endangered snake

Estimates of demographic rates for animal populations and individuals have many applications for ecological and conservation research. In many animals, survival is size‐dependent, but estimating the form of the size–survival relationship presents challenges. For elusive species with low recapture rates, individuals’ size will be unknown at many points in time. Integrating growth and capture–mark–recapture models in a Bayesian framework empowers researchers to impute missing size data, with uncertainty, and include size as a covariate of survival, capture probability, and presence on‐site. If there is no theoretical expectation for the shape of the size–survival relationship, spline functions can allow for fitting flexible, data‐driven estimates. We use long‐term capture–mark–recapture data from the endangered San Francisco gartersnake (Thamnophis sirtalis tetrataenia) to fit an integrated growth–survival model. Growth models showed that females reach longer asymptotic lengths than males and that the magnitude of sexual size dimorphism differed among populations. The capture probability and availability of San Francisco gartersnakes for capture increased with snout–vent length. The survival rate of female snakes exhibits a nonlinear relationship with snout–vent length (SVL), with survival flat between 300 mm and 550 mm SVL before decreasing for females between 550 mm and 700 mm SVL. For male snakes, survival decreased for adult males >550 mm SVL. The survival rates of the smallest and largest San Francisco gartersnakes were highly uncertain because recapture rates were very low for these sizes. By integrating growth and survival models and using penalized splines, we found support for size‐dependent survival in San Francisco gartersnakes. Our results have applications for devising management activities for this endangered subspecies, and our methods could be applied broadly to the study of size‐dependent demography among animals.     

Network robustness and structure depend on the phenological characteristics of plants and pollinators

Many structural patterns have been found to be important for the stability and robustness of mutualistic plant–pollinator networks. These structural patterns are impacted by a suite of variables, including species traits, species abundances, their spatial configuration, and their phylogenetic history. Here, we consider a specific trait: phenology, or the timing of life history events. We expect that timing and duration of activity of pollinators, or of flowering in plants, could greatly affect the species'' roles within networks in which they are embedded. Using plant–pollinator networks from 33 sites in southern British Columbia, Canada, we asked (a) how phenological species traits, specifically timing of first appearance in the network and duration of activity in a network, were related to species'' roles within a network, and (b) how those traits affected network robustness to phenologically biased species loss. We found that long duration of activity increased connection within modules for both pollinators and plants and among modules for plants. We also found that date of first appearance was positively related to interaction strength asymmetry in plants but negatively related to pollinators. Networks were generally more robust to the loss of pollinators than plants, and robustness increased if the models allow new interactions to form when old ones are lost, constrained by overlapping phenology of plants and pollinators. Robustness declined with the loss of late‐flowering plants, which tended to have higher interaction strength asymmetry. In addition, robustness declined with loss of early‐flying or long‐duration pollinators. These pollinators tended to be among‐module connectors. Our results point to networks being limited by early‐flying pollinators. If plants flower earlier due to climate change, plant fitness may decline as they will depend on early emerging pollinators, unless pollinators also emerge earlier.     

Favoring recruitment as a conservation strategy to improve the resilience of long‐lived reptile populations: Insights from a population viability analysis

In long‐lived species, although adult survival typically has the highest elasticity, temporal variations in less canalized demographic parameters are the main drivers of population dynamics. Targeting recruitment rates may thus be the most effective strategy to manage these species. We analyzed 1,136 capture–recapture histories collected over 9 years in an isolated population of the critically endangered Lesser Antillean iguana, using a robust design Pradel model to estimate adult survival and recruitment rates. From an adult population size estimated at 928 in 2013, we found a yearly decline of 4% over the 8‐year period. As expected under the canalization hypothesis for a long‐lived species, adult survival was high and constant, with little possibility for improvement, whereas the recruitment rate varied over time and likely drove the observed population decline. We then used a prospective perturbation analysis to explore whether managing the species’ immature cohorts would at least slow the population decline. The prospective perturbation analysis suggested that a significant and sustained conservation effort would be needed to achieve a recruitment rate high enough to slow the population decline. We posit that the high recruitment rate achieved in 2014—likely due to the maintenance in 2012 of the main nesting sites used by this population—would be sufficient to slow this population''s decline if it was sustained each year. Based on the results of diverse pilot studies we conducted, we identified the most likely threats targeting the eggs and immature cohorts, stressing the need to improve reproductive success and survival of immature iguanas. The threats we identified are also involved in the decline of several reptile species, and species from other taxa such as ground‐nesting birds. These findings on a little‐studied taxon provide further evidence that focusing on the immature life stages of long‐lived species can be key to their conservation.     

Comparing survival among species with imperfect detection using multilevel analysis of mark—recapture data: a case study on bats

For comparative demography studies, 2 prerequisites are usually needed: 1) using typical parameter values for species, 2) correctly accounting for the uncertainty in the species specific estimates. However, although within‐species variability may be essential, it is typically not considered in analytical procedures, resulting in parameter estimates that may not be representative of the species. Further, data are analysed in 2 steps, first separately for each species, then estimates are compared among species. Accounting for the uncertainty in the species specific estimates is then difficult. Here we propose the application of multilevel Bayesian models on mark—recapture (MR) data for comparative studies on survival probabilities that solves these problems. Our models account for within‐species variability in space and time in the form of random effects. Models reflecting different biological predictions related to the species’ ecology and life‐history traits may further be contrasted. To illustrate our approach, we used long‐term data from 5 temperate tree‐roosting bat species and compared their survival probabilities. Results suggest that species foraging in open space, high reproductive output and short longevity records have lower survival than species foraging at short distances, with low reproductive output and high longevity records. Multilevel models provided relatively precise estimates, away from the edges of the parameter space, even for species with low encounter rates and short study duration. This is particularly valuable for less studied taxa such as bats for which available data are often more sparse. Our approach can be easily extended to include additional groups or levels of interest and effects at the individual level (e.g. sex or age). Different hypotheses regarding differences or similarities in parameters among species can be tested through the application of different models. Overall, it offers a flexible tool to ecologists, and population and evolutionary biologists for comparative studies, explicitly accounting for multilevel structures often encountered in MR data.     

Modeling the demography of species providing extended parental care: A capture–recapture multievent model with a case study on polar bears (Ursus maritimus)

1. In species providing extended parental care, one or both parents care for altricial young over a period including more than one breeding season. We expect large parental investment and long‐term dependency within family units to cause high variability in life trajectories among individuals with complex consequences at the population level. So far, models for estimating demographic parameters in free‐ranging animal populations mostly ignore extended parental care, thereby limiting our understanding of its consequences on parents and offspring life histories.
2. We designed a capture–recapture multievent model for studying the demography of species providing extended parental care. It handles statistical multiple‐year dependency among individual demographic parameters grouped within family units, variable litter size, and uncertainty on the timing at offspring independence. It allows for the evaluation of trade‐offs among demographic parameters, the influence of past reproductive history on the caring parent''s survival status, breeding probability, and litter size probability, while accounting for imperfect detection of family units. We assess the model performance using simulated data and illustrate its use with a long‐term dataset collected on the Svalbard polar bears (Ursus maritimus).
3. Our model performed well in terms of bias and mean square error and in estimating demographic parameters in all simulated scenarios, both when offspring departure probability from the family unit occurred at a constant rate or varied during the field season depending on the date of capture. For the polar bear case study, we provide estimates of adult and dependent offspring survival rates, breeding probability, and litter size probability. Results showed that the outcome of the previous reproduction influenced breeding probability.
4. Overall, our results show the importance of accounting for i) the multiple‐year statistical dependency within family units, ii) uncertainty on the timing at offspring independence, and iii) past reproductive history of the caring parent. If ignored, estimates obtained for breeding probability, litter size, and survival can be biased. This is of interest in terms of conservation because species providing extended parental care are often long‐living mammals vulnerable or threatened with extinction.

     

Patterns and processes in shorebird survival rates: a global review

Changes in demographic rates underpin changes in population size, and understanding demographic rates can greatly aid the design and development of strategies to maintain populations in the face of environmental changes. However, acquiring estimates of demographic parameters at relevant spatial scales is difficult. Measures of annual survival rates can be particularly challenging to obtain because large‐scale, long‐term tracking of individuals is difficult and the resulting data contain many inherent biases. In recent years, advances in both tracking and analytical techniques have meant that, for some taxonomic groups, sufficient numbers of survival estimates are available to allow variation within and among species to be explored. Here we review published estimates of annual adult survival rates in shorebird species across the globe, and construct models to explore the phylogenetic, geographical, seasonal and sex‐based variation in survival rates. Models of 295 survival estimates from 56 species show that survival rates calculated from recoveries of dead individuals or from return rates of marked individuals are significantly lower than estimates from mark–recapture models. Survival rates also vary across flyways, largely as a consequence of differences in the genera that have been studied and the analytical methods used, with published estimates from the Americas and from smaller shorebirds (Actitis, Calidris and Charadrius spp.) tending to be underestimated. By incorporating the analytical method used to generate each estimate within a mixed model framework, we provide method‐corrected species‐specific and genus‐specific adult annual survival estimates for 52 species of 15 genera.     

Multiple coping strategies maintain stability of a small mammal population in a resource‐restricted environment

In semi‐arid environments, aperiodic rainfall pulses determine plant production and resource availability for higher trophic levels, creating strong bottom‐up regulation. The influence of climatic factors on population vital rates often shapes the dynamics of small mammal populations in such resource‐restricted environments. Using a 21‐year biannual capture–recapture dataset (1993 to 2014), we examined the impacts of climatic factors on the population dynamics of the brush mouse (Peromyscus boylii) in semi‐arid oak woodland of coastal‐central California. We applied Pradel''s temporal symmetry model to estimate capture probability (p), apparent survival (φ), recruitment (f), and realized population growth rate (λ) of the brush mouse and examined the effects of temperature, rainfall, and El Niño on these demographic parameters. The population was stable during the study period with a monthly realized population growth rate of 0.993 ± SE 0.032, but growth varied over time from 0.680 ± 0.054 to 1.450 ± 0.083. Monthly survival estimates averaged 0.789 ± 0.005 and monthly recruitment estimates averaged 0.175 ± 0.038. Survival probability and realized population growth rate were positively correlated with rainfall and negatively correlated with temperature. In contrast, recruitment was negatively correlated with rainfall and positively correlated with temperature. Brush mice maintained their population through multiple coping strategies, with high recruitment during warmer and drier periods and higher survival during cooler and wetter conditions. Although climatic change in coastal‐central California will likely favor recruitment over survival, varying strategies may serve as a mechanism by which brush mice maintain resilience in the face of climate change. Our results indicate that rainfall and temperature are both important drivers of brush mouse population dynamics and will play a significant role in predicting the future viability of brush mice under a changing climate.     

Quantifying Extinction Probabilities from Sighting Records: Inference and Uncertainties

Methods are needed to estimate the probability that a population is extinct, whether to underpin decisions regarding the continuation of a invasive species eradication program, or to decide whether further searches for a rare and endangered species could be warranted. Current models for inferring extinction probability based on sighting data typically assume a constant or declining sighting rate. We develop methods to analyse these models in a Bayesian framework to estimate detection and survival probabilities of a population conditional on sighting data. We note, however, that the assumption of a constant or declining sighting rate may be hard to justify, especially for incursions of invasive species with potentially positive population growth rates. We therefore explored introducing additional process complexity via density-dependent survival and detection probabilities, with population density no longer constrained to be constant or decreasing. These models were applied to sparse carcass discoveries associated with the recent incursion of the European red fox (Vulpes vulpes) into Tasmania, Australia. While a simple model provided apparently precise estimates of parameters and extinction probability, estimates arising from the more complex model were much more uncertain, with the sparse data unable to clearly resolve the underlying population processes. The outcome of this analysis was a much higher possibility of population persistence. We conclude that if it is safe to assume detection and survival parameters are constant, then existing models can be readily applied to sighting data to estimate extinction probability. If not, methods reliant on these simple assumptions are likely overstating their accuracy, and their use to underpin decision-making potentially fraught. Instead, researchers will need to more carefully specify priors about possible population processes.     

Grazing alters species relative abundance by affecting plant functional traits in a Tibetan subalpine meadow

Domestic livestock grazing has caused dramatic changes in plant community composition across the globe. However, the response of plant species abundance in communities subject to grazing has not often been investigated through a functional lens, especially for belowground traits. Grazing directly impacts aboveground plant tissues, but the relationships between above‐ and belowground traits, and their influence on species abundance are also not well known. We collected plant trait and species relative abundance data in the grazed and nongrazed meadow plant communities in a species‐rich subalpine ecosystem of the Qinghai–Tibet Plateau. We measured three aboveground traits (leaf photosynthesis rate, specific leaf area, and maximum height) and five belowground traits (root average diameter, root biomass, specific root length, root tissue density, and specific root area). We tested for shifts in the relationship between species relative abundance and among all measured traits under grazing compared with the nongrazed meadow. We also compared the power of above‐ and belowground traits to predict species relative abundance. We observed a significant shift from a resource conservation strategy to a resource acquisition strategy. Moreover, this resource conservation versus resource acquisition trade‐off can also determine species relative abundance in the grazed and nongrazed plant communities. Specifically, abundant species in the nongrazed meadow had aboveground and belowground traits that are associated with high resource conservation, whereas aboveground and belowground traits that are correlated with high resource acquisition determined species relative abundance in the grazed meadow. However, belowground traits were found to explain more variances in species relative abundance than aboveground traits in the nongrazed meadow, while aboveground and belowground traits had comparable predictive power in the grazed meadow. We show that species relative abundance in both the grazed and the nongrazed meadows can be predicted by both aboveground traits and belowground traits associated with a resource acquisition versus conservation trade‐off. More importantly, we show that belowground traits have higher predictive power of species relative abundance than aboveground traits in the nongrazed meadow, whereas in the grazed meadows, above‐ and belowground traits had comparable high predictive power.     

Understanding the impact of correlation within pair‐bonds on Cormack–Jolly–Seber models

1. The Cormack–Jolly–Seber (CJS) model and its extensions have been widely applied to the study of animal survival rates in open populations. The model assumes that individuals within the population of interest have independent fates. It is, however, highly unlikely that a pair of animals which have formed a long‐term pairing have dissociated fates.
2. We examine a model extension which allows animals who have formed a pair‐bond to have correlated survival and recapture fates. Using the proposed extension to generate data, we conduct a simulation study exploring the impact that correlated fate data has on inference from the CJS model. We compute Monte Carlo estimates for the bias, range, and standard errors of the parameters of the CJS model for data with varying degrees of survival correlation between mates. Furthermore, we study the likelihood ratio test of sex effects within the CJS model by simulating densities of the deviance. Finally, we estimate the variance inflation factor c^ for CJS models that incorporate sex‐specific heterogeneity.
3. Our study shows that correlated fates between mated animals may result in underestimated standard errors for parsimonious models, significantly deflated likelihood ratio test statistics, and underestimated values of c^ for models taking sex‐specific effects into account.
4. Underestimated standard errors can result in lowered coverage of confidence intervals. Moreover, deflated test statistics will provide overly conservative test results. Finally, underestimated variance inflation factors can lead researchers to make incorrect conclusions about the level of extra‐binomial variation present in their data.

     

Evolution in plant populations as a driver of ecological changes in arthropod communities

Heritable variation in traits can have wide-ranging impacts on species interactions, but the effects that ongoing evolution has on the temporal ecological dynamics of communities are not well understood. Here, we identify three conditions that, if experimentally satisfied, support the hypothesis that evolution by natural selection can drive ecological changes in communities. These conditions are: (i) a focal population exhibits genetic variation in a trait(s), (ii) there is measurable directional selection on the trait(s), and (iii) the trait(s) under selection affects variation in a community variable(s). When these conditions are met, we expect evolution by natural selection to cause ecological changes in the community. We tested these conditions in a field experiment examining the interactions between a native plant (Oenothera biennis) and its associated arthropod community (more than 90 spp.). Oenothera biennis exhibited genetic variation in several plant traits and there was directional selection on plant biomass, life-history strategy (annual versus biennial reproduction) and herbivore resistance. Genetically based variation in biomass and life-history strategy consistently affected the abundance of common arthropod species, total arthropod abundance and arthropod species richness. Using two modelling approaches, we show that evolution by natural selection in large O. biennis populations is predicted to cause changes in the abundance of individual arthropod species, increases in the total abundance of arthropods and a decline in the number of arthropod species. In small O. biennis populations, genetic drift is predicted to swamp out the effects of selection, making the evolution of plant populations unpredictable. In short, evolution by natural selection can play an important role in affecting the dynamics of communities, but these effects depend on several ecological factors. The framework presented here is general and can be applied to other systems to examine the community-level effects of ongoing evolution.     

Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model

Interval mapping using normal mixture models has been an important tool for analyzing quantitative traits in experimental organisms. When the primary phenotype is time-to-event, it is natural to use survival models such as Cox's proportional hazards model instead of normal mixtures to model the phenotype distribution. An extra challenge for modeling time-to-event data is that the underlying population may consist of susceptible and nonsusceptible subjects. In this article, we propose a semiparametric proportional hazards mixture cure model which allows missing covariates. We discuss applications to quantitative trait loci (QTL) mapping when the primary trait is time-to-event from a population of mixed susceptibility. This model can be used to characterize QTL effects on both susceptibility and time-to-event distribution, and to estimate QTL location. The model can naturally incorporate covariate effects of other risk factors. Maximum likelihood estimates for the parameters in the model as well as their corresponding variance estimates can be obtained numerically using an EM-type algorithm. The proposed methods are assessed by simulations under practical settings and illustrated using a real data set containing survival times of mice after infection with Listeria monocytogenes. An extension to multiple intervals is also discussed.     

A General and Robust Framework for Secondary Traits Analysis

Case–control designs are commonly employed in genetic association studies. In addition to the case–control status, data on secondary traits are often collected. Directly regressing secondary traits on genetic variants from a case–control sample often leads to biased estimation. Several statistical methods have been proposed to address this issue. The inverse probability weighting (IPW) approach and the semiparametric maximum-likelihood (SPML) approach are the most commonly used. A new weighted estimating equation (WEE) approach is proposed to provide unbiased estimation of genetic associations with secondary traits, by combining observed and counterfactual outcomes. Compared to the existing approaches, WEE is more robust against biased sampling and disease model misspecification. We conducted simulations to evaluate the performance of the WEE under various models and sampling schemes. The WEE demonstrated robustness in all scenarios investigated, had appropriate type I error, and was as powerful or more powerful than the IPW and SPML approaches. We applied the WEE to an asthma case–control study to estimate the associations between the thymic stromal lymphopoietin gene and two secondary traits: overweight status and serum IgE level. The WEE identified two SNPs associated with overweight in logistic regression, three SNPs associated with serum IgE levels in linear regression, and an additional four SNPs that were missed in linear regression to be associated with the 75th quantile of IgE in quantile regression. The WEE approach provides a general and robust secondary analysis framework, which complements the existing approaches and should serve as a valuable tool for identifying new associations with secondary traits.