Integrated Population Modeling of Black Bears in Minnesota: Implications for Monitoring and Management

Background

Wildlife populations are difficult to monitor directly because of costs and logistical challenges associated with collecting informative abundance data from live animals. By contrast, data on harvested individuals (e.g., age and sex) are often readily available. Increasingly, integrated population models are used for natural resource management because they synthesize various relevant data into a single analysis.

Methodology/Principal Findings

We investigated the performance of integrated population models applied to black bears (Ursus americanus) in Minnesota, USA. Models were constructed using sex-specific age-at-harvest matrices (1980–2008), data on hunting effort and natural food supplies (which affects hunting success), and statewide mark–recapture estimates of abundance (1991, 1997, 2002). We compared this approach to Downing reconstruction, a commonly used population monitoring method that utilizes only age-at-harvest data. We first conducted a large-scale simulation study, in which our integrated models provided more accurate estimates of population trends than did Downing reconstruction. Estimates of trends were robust to various forms of model misspecification, including incorrectly specified cub and yearling survival parameters, age-related reporting biases in harvest data, and unmodeled temporal variability in survival and harvest rates. When applied to actual data on Minnesota black bears, the model predicted that harvest rates were negatively correlated with food availability and positively correlated with hunting effort, consistent with independent telemetry data. With no direct data on fertility, the model also correctly predicted 2-point cycles in cub production. Model-derived estimates of abundance for the most recent years provided a reasonable match to an empirical population estimate obtained after modeling efforts were completed.

Conclusions/Significance

Integrated population modeling provided a reasonable framework for synthesizing age-at-harvest data, periodic large-scale abundance estimates, and measured covariates thought to affect harvest rates of black bears in Minnesota. Collection and analysis of these data appear to form the basis of a robust and viable population monitoring program.     

Bayesian analysis of wildlife age-at-harvest data

SUMMARY: State and federal natural resource management agencies often collect age-structured harvest data. These data represent finite realizations of stochastic demographic and sampling processes and have long been used by biologists to infer population trends. However, different sources of data have been combined in ad hoc ways and these methods usually failed to incorporate sampling error. In this article, we propose a "hidden process" (or state-space) model for estimating abundance, survival, recovery rate, and recruitment from age-at-harvest data that incorporate both demographic and sampling stochasticity. To this end, a likelihood for age-at-harvest data is developed by embedding a population dynamics model within a model for the sampling process. Under this framework, the identification of abundance parameters can be achieved by conducting a joint analysis with an auxiliary data set. We illustrate this approach by conducting a Bayesian analysis of age-at-harvest and mark-recovery data from black bears (Ursus americanus) in Pennsylvania. Using a set of reasonable prior distributions, we demonstrate a substantial increase in precision when posterior summaries of abundance are compared to a bias-corrected Lincoln-Petersen estimator. Because demographic processes link consecutive abundance estimates, we also obtain a more realistic biological picture of annual changes in abundance. Because age-at-harvest data are often readily obtained, we argue that this type of analysis provides a valuable strategy for wildlife population monitoring.     

Calibrating Statistical Population Reconstruction Models Using Catch-Effort and Index Data

Abstract: This paper illustrates how age-at-harvest data, when combined with hunter-effort information routinely collected by state game management agencies, can be used to estimate and monitor trends in big game abundance. Twenty-four years of age-at-harvest data for black-tailed deer (Odocoileus hemionus) were analyzed to produce abundance estimates ranging from 1,281 adult females to 3,232 adult females on a 22,079-ha tree farm in Pierce County, Washington, USA. The annual natural survival probability was estimated to be 0.7293 ( = 0.0097) for this female population. The estimated abundance was highly correlated with an independent browse damage index (r = 0.8131, P < 0.001). A population reconstruction incorporating the browse index did not substantially improve the model fit but did provide an auxiliary model for predicting deer abundance. This population reconstruction illustrates a cost-effective alternative to expensive big game survey methods.     

An Evaluation of Sex-Age-Kill (SAK) Model Performance

ABSTRACT The sex-age-kill (SAK) model is widely used to estimate abundance of harvested large mammals, including white-tailed deer (Odocoileus virginianus). Despite a long history of use, few formal evaluations of SAK performance exist. We investigated how violations of the stable age distribution and stationary population assumption, changes to male or female harvest, stochastic effects (i.e., random fluctuations in recruitment and survival), and sampling efforts influenced SAK estimation. When the simulated population had a stable age distribution and λ > 1, the SAK model underestimated abundance. Conversely, when λ < 1, the SAK overestimated abundance. When changes to male harvest were introduced, SAK estimates were opposite the true population trend. In contrast, SAK estimates were robust to changes in female harvest rates. Stochastic effects caused SAK estimates to fluctuate about their equilibrium abundance, but the effect dampened as the size of the surveyed population increased. When we considered both stochastic effects and sampling error at a deer management unit scale the resultant abundance estimates were within ±121.9% of the true population level 95% of the time. These combined results demonstrate extreme sensitivity to model violations and scale of analysis. Without changes to model formulation, the SAK model will be biased when λ ≠ 1. Furthermore, any factor that alters the male harvest rate, such as changes to regulations or changes in hunter attitudes, will bias population estimates. Sex-age-kill estimates may be precise at large spatial scales, such as the state level, but less so at the individual management unit level. Alternative models, such as statistical age-at-harvest models, which require similar data types, might allow for more robust, broad-scale demographic assessments.     

Using Statistical Population Reconstruction to Estimate Demographic Trends in Small Game Populations

ABSTRACT Statistical population reconstruction offers a robust approach to demographic assessment for harvested populations, but current methods are restricted to big-game species with multiple age classes. We extended this approach to small game and analyzed 14 years of age-at-harvest data for greater sage-grouse (Centrocercus urophasianus) in Oregon, USA, in conjunction with radiotelemetry data to reconstruct annual abundance levels, recruitment, and natural survival probabilities. Abundance estimates ranged from a low of 26,236 in 1995 to a high of 39,492 in 2004. Annual abundance estimates for adult males were correlated with a spring lek count index (r = 0.849, P < 0.029). We estimated the average annual harvest mortality for the population to be 0.028, ranging from 0.021 to 0.031 across years. We estimated the probability of natural survival of adult females to be 0.818 ( = 0.052), somewhat higher than that of adult males (Ŝ = 0.609, = 0.163). Our precision in reconstructing the population was hampered by low harvest rates and the few birds tagged in the radiotelemetry investigations. Despite these issues, our analysis illustrates how modern statistical reconstruction procedures offer a flexible framework for demographic assessment using commonly collected data. This approach offers a useful alternative to small-game indices and would be most appropriate for species with 5 or more years of age-at-harvest data and moderate-to-heavy harvest rates.     

Estimating abundance using mark-resight when sampling is with replacement or the number of marked individuals is unknown

Summary .  Although mark–resight methods can often be a less expensive and less invasive means for estimating abundance in long-term population monitoring programs, two major limitations of the estimators are that they typically require sampling without replacement and/or the number of marked individuals available for resighting to be known exactly. These requirements can often be difficult to achieve. Here we address these limitations by introducing the Poisson log and zero-truncated Poisson log-normal mixed effects models (PNE and ZPNE, respectively). The generalized framework of the models allow the efficient use of covariates in modeling resighting rate and individual heterogeneity parameters, information-theoretic model selection and multimodel inference, and the incorporation of individually unidentified marks. Both models may be implemented using standard statistical computing software, but they have also been added to the mark–recapture freeware package Program MARK . We demonstrate the use and advantages of (Z)PNE using black-tailed prairie dog data recently collected in Colorado. We also investigate the expected relative performance of the models in simulation experiments. Compared to other available estimators, we generally found (Z)PNE to be more precise with little or no loss in confidence interval coverage. With the recent introduction of the logit-normal mixed effects model and (Z)PNE, a more flexible and efficient framework for mark–resight abundance estimation is now available for the sampling conditions most commonly encountered in these studies.     

Accounting for spatial pattern when modeling organism-environment interactions

Statistical models of environment-abundance relationships may be influenced by spatial autocorrelation in abundance, environmental variables, or both. Failure to account for spatial autocorrelation can lead to incorrect conclusions regarding both the absolute and relative importance of environmental variables as determinants of abundance. We consider several classes of statistical models that are appropriate for modeling environment-abundance relationships in the presence of spatial autocorrelation, and apply these to three case studies: 1) abundance of voles in relation to habitat characteristics; 2) a plant competition experiment; and 3) abundance of Orbatid mites along environmental gradients. We find that when spatial pattern is accounted for in the modeling process, conclusions about environmental control over abundance can change dramatically. We conclude with five lessons: 1) spatial models are easy to calculate with several of the most common statistical packages; 2) results from spatially-structured models may point to conclusions radically different from those suggested by a spatially independent model; 3) not all spatial autocorrelation in abundances results from spatial population dynamics; it may also result from abundance associations with environmental variables not included in the model; 4) the different spatial models do have different mechanistic interpretations in terms of ecological processes – thus ecological model selection should take primacy over statistical model selection; 5) the conclusions of the different spatial models are typically fairly similar – making any correction is more important than quibbling about which correction to make.     

Estimating Mountain Lion Abundance in Arizona Using Statistical Population Reconstruction

Directly monitoring abundance of cryptic species, such as mountain lions (Puma concolor), over large areas is a challenge for wildlife managers because traditional population estimation techniques may be impractical and expensive. We generated annual estimates of mountain lion abundance in Arizona, USA, for 2004–2018 by employing statistical population reconstruction methods, which use available age-at-harvest data and auxiliary information such as estimated survival rates, harvest probabilities, and hunter effort. Using PopRecon 2.0 software, we estimated that the statewide abundance of all mountain lions including kittens ranged from 1,848 (95% CI = 650–3,046) to 4,661 (95% CI = 393–9,030) during 2004–2018. Abundance for subadults and adults was more stable and precisely estimated, ranging from 1,166 (95% CI = 622–1,709) to 1,715 (95% CI = 872–2,558). Our results suggest a stable statewide mountain lion population. This approach provides a practical and cost-effective option for monitoring Arizona's mountain lion population, and will improve the ability of managers to monitor the population annually to respond to changes in abundance and to evaluate factors that influence mountain lion abundance. © 2019 The Authors. Journal of Wildlife Management published by Wiley Periodicals, Inc. on behalf of The Wildlife Society.     

Assessing Ecoregional-Scale Habitat Suitability Index Models for Priority Landbirds

ABSTRACT Emerging methods in habitat and wildlife population modeling promise new horizons in conservation but only if these methods provide robust population-habitat linkages. We used Breeding Bird Survey (BBS) data to verify and validate newly developed habitat suitability index (HSI) models for 40 priority landbird species in the Central Hardwoods and West Gulf Coastal Plain/Ouachitas Bird Conservation Regions. We considered a species’ HSI model verified if there was a significant rank correlation between mean predicted HSI score and mean observed BBS abundance across the 88 ecological subsections within these Bird Conservation Regions. When we included all subsections, correlations verified 37 models. Models for 3 species were unverified. Rank correlations for an additional 5 species were not significant when analyses included only subsections with BBS abundance >0. To validate models, we developed generalized linear models with mean observed BBS abundance as the response variable and mean HSI score and Bird Conservation Region as predictor variables. We considered verified models validated if the overall model was an improvement over an intercept-only null model and the coefficient on the HSI variable in the model was >0. Validation provided a more rigorous assessment of model performance than verification, and models for 12 species that we verified failed validation. Species whose models failed validation were either poorly sampled by BBS protocols or associated with woodland and shrubland habitats embedded within predominantly open landscapes. We validated models for 25 species. Habitat specialists and species reaching their highest densities in predominantly forested landscapes were more likely to have validated models. In their current form, validated models are useful for conservation planning of priority landbirds and offer both insight into limiting factors at ecoregional scales and a framework for monitoring priority landbird populations from readily available national data sets.     

Comparison of statistical population reconstruction using full and pooled adult age-class data

Background

Age-at-harvest data are among the most commonly collected, yet neglected, demographic data gathered by wildlife agencies. Statistical population construction techniques can use this information to estimate the abundance of wild populations over wide geographic areas and concurrently estimate recruitment, harvest, and natural survival rates. Although current reconstruction techniques use full age-class data (0.5, 1.5, 2.5, 3.5, … years), it is not always possible to determine an animal''s age due to inaccuracy of the methods, expense, and logistics of sample collection. The ability to inventory wild populations would be greatly expanded if pooled adult age-class data (e.g., 0.5, 1.5, 2.5+ years) could be successfully used in statistical population reconstruction.

Methodology/Principal Findings

We investigated the performance of statistical population reconstruction models developed to analyze full age-class and pooled adult age-class data. We performed Monte Carlo simulations using a stochastic version of a Leslie matrix model, which generated data over a wide range of abundance levels, harvest rates, and natural survival probabilities, representing medium-to-big game species. Results of full age-class and pooled adult age-class population reconstructions were compared for accuracy and precision. No discernible difference in accuracy was detected, but precision was slightly reduced when using the pooled adult age-class reconstruction. On average, the coefficient of variation increased by 0.059 when the adult age-class data were pooled prior to analyses. The analyses and maximum likelihood model for pooled adult age-class reconstruction are illustrated for a black-tailed deer (Odocoileus hemionus) population in Washington State.

Conclusions/Significance

Inventorying wild populations is one of the greatest challenges of wildlife agencies. These new statistical population reconstruction models should expand the demographic capabilities of wildlife agencies that have already collected pooled adult age-class data or are seeking a cost-effective method for monitoring the status and trends of our wild resources.     

Classification in conservation biology: A comparison of five machine-learning methods

Classification is one of the most widely applied tasks in ecology. Ecologists have to deal with noisy, high-dimensional data that often are non-linear and do not meet the assumptions of conventional statistical procedures. To overcome this problem, machine-learning methods have been adopted as ecological classification methods. We compared five machine-learning based classification techniques (classification trees, random forests, artificial neural networks, support vector machines, and automatically induced rule-based fuzzy models) in a biological conservation context. The study case was that of the ocellated turkey (Meleagris ocellata), a bird endemic to the Yucatan peninsula that has suffered considerable decreases in local abundance and distributional area during the last few decades. On a grid of 10 × 10 km cells that was superimposed to the peninsula we analysed relationships between environmental and social explanatory variables and ocellated turkey abundance changes between 1980 and 2000. Abundance was expressed in three (decrease, no change, and increase) and 14 more detailed abundance change classes, respectively. Modelling performance varied considerably between methods with random forests and classification trees being the most efficient ones as measured by overall classification error and the normalised mutual information index. Artificial neural networks yielded the worst results along with linear discriminant analysis, which was included as a conventional statistical approach. We not only evaluated classification accuracy but also characteristics such as time effort, classifier comprehensibility and method intricacy—aspects that determine the success of a classification technique among ecologists and conservation biologists as well as for the communication with managers and decision makers. We recommend the combined use of classification trees and random forests due to the easy interpretability of classifiers and the high comprehensibility of the method.     

Sharing detection heterogeneity information among species in community models of occupancy and abundance can strengthen inference

1. The estimation of abundance and distribution and factors governing patterns in these parameters is central to the field of ecology. The continued development of hierarchical models that best utilize available information to inform these processes is a key goal of quantitative ecologists. However, much remains to be learned about simultaneously modeling true abundance, presence, and trajectories of ecological communities.
2. Simultaneous modeling of the population dynamics of multiple species provides an interesting mechanism to examine patterns in community processes and, as we emphasize herein, to improve species‐specific estimates by leveraging detection information among species. Here, we demonstrate a simple but effective approach to share information about observation parameters among species in hierarchical community abundance and occupancy models, where we use shared random effects among species to account for spatiotemporal heterogeneity in detection probability.
3. We demonstrate the efficacy of our modeling approach using simulated abundance data, where we recover well our simulated parameters using N‐mixture models. Our approach substantially increases precision in estimates of abundance compared with models that do not share detection information among species. We then expand this model and apply it to repeated detection/non‐detection data collected on six species of tits (Paridae) breeding at 119 1 km² sampling sites across a P. montanus hybrid zone in northern Switzerland (2004–2020). We find strong impacts of forest cover and elevation on population persistence and colonization in all species. We also demonstrate evidence for interspecific competition on population persistence and colonization probabilities, where the presence of marsh tits reduces population persistence and colonization probability of sympatric willow tits, potentially decreasing gene flow among willow tit subspecies.
4. While conceptually simple, our results have important implications for the future modeling of population abundance, colonization, persistence, and trajectories in community frameworks. We suggest potential extensions of our modeling in this paper and discuss how leveraging data from multiple species can improve model performance and sharpen ecological inference.

     

Using statistics to design and estimate vital rates in matrix population models for a perennial herb

Matrix population models are widely used to assess population status and to inform management decisions. Despite existing theories for building such models, model construction is often partially based on expert opinion. So far, model structure has received relatively little attention, although it may affect estimates of population dynamics. Here, we assessed the consequences of two published matrix structures (a 4 × 4 matrix based on expert opinion and a 10 × 10 matrix based on statistical modeling) for estimates of vital rates and stochastic population dynamics of the long-lived herb Astragalus scaphoides. We explored the ways in which choice of model structure alters the accuracy (i.e., mean) and precision (i.e., variance) of predicted population dynamics. We found that model structure had a negligible effect on the accuracy and precision of vital rates and stochastic stage distribution. However, the 10 × 10 matrix produced lower estimates of stochastic population growth rates than the 4 × 4 matrix, and more accurately predicted the observed trends in population abundance for three out of four study populations. Moreover, estimates of realized variation in population growth rate due to fluctuations in population stage structure over time were occasionally sensitive to matrix structure, suggesting differential roles of transient dynamics. Our study indicates that statistical modeling for choosing categories in matrix models might be preferable over expert opinion to accurately predict population trends and can provide a more objective way for model construction when the biological knowledge of the species is limited.     

Abundance of rare and elusive species: Empirical investigation of closed versus spatially explicit capture–recapture models with lynx as a case study

Effective conservation and management require reliable monitoring methods and estimates of abundance to prioritize human and financial investments. Camera trapping is a non-invasive sampling method allowing the use of capture–recapture (CR) models to estimate abundance while accounting for the difficulty of detecting individuals in the wild. We investigated the relative performance of standard closed CR models and spatially explicit CR models (SECR) that incorporate spatial information in the data. Using simulations, we considered 4 scenarios comparing low versus high detection probability and small versus large populations and contrasted abundance estimates obtained from both approaches. Standard CR and SECR models both provided minimally biased abundance estimates, but precision was improved when using SECR models. The associated confidence intervals also provided better coverage than their non-spatial counterpart. We concluded SECR models exhibit better statistical performance than standard closed CR models and allow for sound management strategies based on density maps of activity centers. To illustrate the comparison, we considered the Eurasian lynx (Lynx lynx) as a case study that provided the first abundance estimates of a local population in France. © 2012 The Wildlife Society.     

An integrated population model for a long‐lived ungulate: more efficient data use with Bayesian methods

We develop an integrated population model for Svalbard reindeer Rangifer tarandus platyrhynchus, and demonstrate how this type of model can be used to extract more information from the data and separate different sources of variability in population estimates. Our model combines individual mark–recapture data with population counts and harvesting data within a Bayesian model framework, and accounts for observation error, environmental and demographic stochasticity, and age structure. From this model we obtain annual estimates of age‐specific population size, survival and fecundity. The model provides estimates of age structure at a finer scale than that found in the census data, and enables us to estimate survival for the period before calves are first caught and marked, i.e. before they enter the individual mark–recapture data. The modeling framework provides an improved approach to studying age‐structured populations that are imperfectly censused and where the demography of only a sample of individuals is known. We use data from independent censuses of the same population to evaluate population estimates obtained from the model, and show that it is successful at correcting for different types of observation error. Based on our model results, we suggest that allocating resources to the collection of supplementary mark–recapture data could improve the reliability of population projections more than making regular population censuses as exhaustive as possible. Our work demonstrates how integrated Bayesian population modeling can be used to increase the amount of information extracted from collections of data, identifying and disentangling sources of variation in individual performance and population size. This represents an important step towards increasing the predictive ability of population growth models for long‐lived species experiencing changes in environmental conditions and harvesting regimes.     

Partitioning Detectability Components in Populations Subject to Within-Season Temporary Emigration Using Binomial Mixture Models

Detectability of individual animals is highly variable and nearly always < 1; imperfect detection must be accounted for to reliably estimate population sizes and trends. Hierarchical models can simultaneously estimate abundance and effective detection probability, but there are several different mechanisms that cause variation in detectability. Neglecting temporary emigration can lead to biased population estimates because availability and conditional detection probability are confounded. In this study, we extend previous hierarchical binomial mixture models to account for multiple sources of variation in detectability. The state process of the hierarchical model describes ecological mechanisms that generate spatial and temporal patterns in abundance, while the observation model accounts for the imperfect nature of counting individuals due to temporary emigration and false absences. We illustrate our model’s potential advantages, including the allowance of temporary emigration between sampling periods, with a case study of southern red-backed salamanders Plethodon serratus. We fit our model and a standard binomial mixture model to counts of terrestrial salamanders surveyed at 40 sites during 3–5 surveys each spring and fall 2010–2012. Our models generated similar parameter estimates to standard binomial mixture models. Aspect was the best predictor of salamander abundance in our case study; abundance increased as aspect became more northeasterly. Increased time-since-rainfall strongly decreased salamander surface activity (i.e. availability for sampling), while higher amounts of woody cover objects and rocks increased conditional detection probability (i.e. probability of capture, given an animal is exposed to sampling). By explicitly accounting for both components of detectability, we increased congruence between our statistical modeling and our ecological understanding of the system. We stress the importance of choosing survey locations and protocols that maximize species availability and conditional detection probability to increase population parameter estimate reliability.     

Rejoinder for discussion on “Horseshoe-based Bayesian nonparametric estimation of effective population size trajectories”

Phylodynamics is an area of population genetics that uses genetic sequence data to estimate past population dynamics. Modern state-of-the-art Bayesian nonparametric methods for recovering population size trajectories of unknown form use either change-point models or Gaussian process priors. Change-point models suffer from computational issues when the number of change-points is unknown and needs to be estimated. Gaussian process-based methods lack local adaptivity and cannot accurately recover trajectories that exhibit features such as abrupt changes in trend or varying levels of smoothness. We propose a novel, locally adaptive approach to Bayesian nonparametric phylodynamic inference that has the flexibility to accommodate a large class of functional behaviors. Local adaptivity results from modeling the log-transformed effective population size a priori as a horseshoe Markov random field, a recently proposed statistical model that blends together the best properties of the change-point and Gaussian process modeling paradigms. We use simulated data to assess model performance, and find that our proposed method results in reduced bias and increased precision when compared to contemporary methods. We also use our models to reconstruct past changes in genetic diversity of human hepatitis C virus in Egypt and to estimate population size changes of ancient and modern steppe bison. These analyses show that our new method captures features of the population size trajectories that were missed by the state-of-the-art methods.     

Improving removal-based estimates of abundance by sampling a population of spatially distinct subpopulations

A statistical modeling framework is described for estimating the abundances of spatially distinct subpopulations of animals surveyed using removal sampling. To illustrate this framework, hierarchical models are developed using the Poisson and negative-binomial distributions to model variation in abundance among subpopulations and using the beta distribution to model variation in capture probabilities. These models are fitted to the removal counts observed in a survey of a federally endangered fish species. The resulting estimates of abundance have similar or better precision than those computed using the conventional approach of analyzing the removal counts of each subpopulation separately. Extension of the hierarchical models to include spatial covariates of abundance is straightforward and may be used to identify important features of an animal's habitat or to predict the abundance of animals at unsampled locations.     

Increasing the resolution of the Broad Spectrum Revolution in the Southern Levantine Epipaleolithic (19-12 ka)

We analyze terminal Pleistocene archaeofaunal diversity trends in the Southern Levant by examining eight Epipaleolithic (ca. 19-12 ka) assemblages from the Western Galilee/Mt. Carmel, Israel subregion. We test predictions from a Broad Spectrum Revolution model of the population dynamics of human foragers and their prey. The study emphasizes control over geographic variability and archaeological recovery and recording methods, as we analyze a time series that samples the Epipaleolithic more fully than have previous studies. This provides a new opportunity to examine human population and economic change in the long-term transition to sedentism and agriculture.We use the Mantel test to evaluate the significance of temporal trends in body-size-based big game diversity, as well as in diversity of small game prey types. Results demonstrate a highly significant decline through time in the relative abundance of medium and large big game, measured relative to small big game. This suggests that the apparent “gazelle specialization” by Late Epipaleolithic (Natufian) hunters reflects longer-term anthropogenic overexploitation of the largest prey types in the spectrum. While large and medium big game abundance declined, our results show small game increased in economic importance over time.Considered with associated climate change data, the results provide substantial support for the hypothesis that local human populations expanded rapidly in size after the Last Glacial Maximum (LGM). We suggest that following the post-LGM population pulse, human foragers adopted a shifting series of intensification strategies mediated by changes in residential mobility.     

Natural and orthogonal interaction framework for modeling gene-environment interactions with application to lung cancer

Objectives: We aimed at extending the Natural and Orthogonal Interaction (NOIA) framework, developed for modeling gene-gene interactions in the analysis of quantitative traits, to allow for reduced genetic models, dichotomous traits, and gene-environment interactions. We evaluate the performance of the NOIA statistical models using simulated data and lung cancer data. Methods: The NOIA statistical models are developed for additive, dominant, and recessive genetic models as well as for a binary environmental exposure. Using the Kronecker product rule, a NOIA statistical model is built to model gene-environment interactions. By treating the genotypic values as the logarithm of odds, the NOIA statistical models are extended to the analysis of case-control data. Results: Our simulations showed that power for testing associations while allowing for interaction using the NOIA statistical model is much higher than using functional models for most of the scenarios we simulated. When applied to lung cancer data, much smaller p values were obtained using the NOIA statistical model for either the main effects or the SNP-smoking interactions for some of the SNPs tested. Conclusion: The NOIA statistical models are usually more powerful than the functional models in detecting main effects and interaction effects for both quantitative traits and binary traits.