DeWayne R. Derryberry

Model selection for ecologists: the worldviews of AIC and BIC

Ecologists frequently ask questions that are best addressed with a model comparison approach. Under this system, the merit of several models is considered without necessarily requiring that (1) models are nested, (2) one of the models is true, and (3) only current data be used. This is in marked contrast to the pragmatic blend of Neyman-Pearson and Fisherian significance testing conventionally emphasized in biometric texts (Christensen 2005), in which (1) just two hypotheses are under consideration, representing a pairwise comparison of models, (2) one of the models, H0, is assumed to be true, and (3) a single data set is used to quantify evidence concerning H0. As Murtaugh (2014) noted, null hypothesis testing can be extended to certain highly structured multi-model situations (nested with a clear sequence of tests), such as extra sums of squares approaches in general linear models, and drop in deviance tests in generalized linear models. This is especially true when there is the expectation that higher order interactions are not significant or nonexistent, and the testing of main effects does not depend on the order of the tests (as with completely balanced designs). There are, however, three scientific frameworks that are poorly handled by traditional hypothesis testing. First, in questions requiring model comparison and selection, the null hypothesis testing paradigm becomes strained. Candidate models may be non-nested, a wide number of plausible models may exist, and all of the models may be approximations to reality. In this context, we are not assessing which model is correct (since none are correct), but which model has the best predictive accuracy, in particular, which model is expected to fit future observations well. Extensive ecological examples can be found in Johnson and Omland (2004), Burnham and Anderson (2002), and Anderson (2008). Second, the null hypothesis testing paradigm is often inadequate for making inferences concerning the falsification or confirmation of scientific claims because it does not explicitly consider prior information. Scientists often do not consider a single data set to be adequate for research hypothesis rejection (Quinn and Keough 2002:35), particularly for complex hypotheses with a low degree of falsifiability (i.e., Popper 1959:266). Similarly, the support of hypotheses in the generation of scientific theories requires repeated corroboration (Ayala et al. 2008). Third, ecologists and other scientists are frequently concerned with the plausibility of existing or default models, what statistician would consider null hypotheses (e.g., the ideal free distribution, classic insular biogeography, mathematic models for species interactions, archetypes for community succession and assembly, etc.). However, null hypothesis testing is structured in such a way that the null hypothesis cannot be directly supported by evidence. Introductory statistical and biometric textbooks go to great lengths to make this conceptual point (e.g., DeVeaux et al. 2013:511, 618, Moore 2010:376, Devore and Peck 1997:300–303).

Small-Footprint Lidar Estimations of Sagebrush Canopy Characteristics

The height and shape of shrub canopies are critical measurements for characterizing shrub steppe rangelands. Remote sensing technologies might provide an efficient method to acquire these measurements across large areas. This study compared point-cloud and rasterized lidar data to field-measured sagebrush height and shape to quantify the correlation between field-based and lidar-derived estimates. The results demonstrated that discrete return, small-footprint lidar with high point density (9.46 points/m 2 ) can provide strong predictions of true sagebrush height (R 2 of 0.84 to 0.86), but with a consistent underestimation of approximately 30 percent. Our results provided the first successful lidar-based descriptors of sagebrush shape with R 2 values of 0.65, 0.74, and 0.78 for respective predictions of shortest canopy diameter, longest canopy diameter, and canopy area. Future studies can extend lidar-derived shrub height and shape measurements to canopy volume, cover, and biomass estimates.

Vegetation and Slope Effects on Accuracy of a LiDAR-Derived DEM in the Sagebrush Steppe

This study analysed the errors associated with vegetation cover type and slope in a Light Detection and Ranging (LiDAR) derived digital elevation model (DEM) in a semiarid environment in southwest Idaho, USA. Reference data were collected over a range of vegetation cover types and slopes. Reference data were compared to bare-ground raster values and root mean square error (RMSE) and mean signed error (MSE) were used to quantify errors. Results indicate that vegetation cover type and slope have statistically significant effects on the accuracy of a LiDAR-derived bare-earth DEM. RMSE and MSE ranged from 0.072 to 0.220 m and from −0.154 to 0.017 m, respectively, with the largest errors associated with herbaceous cover and steep slopes. The lowest errors were associated with low sagebrush and low-slope environments. Although the RMSEs in this study were lower than those reported by others, further refinement of the accuracy of LiDAR systems may be needed for fine-scale vegetation and terrain applications in rangeland environments.

Spatial trends of breast and prostate cancers in the United States between 2000 and 2005

BackgroundBreast cancer in females and prostate cancer in males are two of the most common cancers in the United States, and the literature suggests that they share similar features. However, it is unknown whether the occurrence of these two cancers at the county level in the United States is correlated. We analyzed Caucasian age-adjusted county level average annual incidence rates for breast and prostate cancers from the National Cancer Institute and State Cancer Registries to determine whether there was a spatial correlation between the two conditions and whether the two cancers had similar spatial patterns.ResultsThere was a significant correlation between breast and prostate cancers by county (r = 0.332, p < 0.001). This relationship was more pronounced when we performed a geographically-weighted regression (GWR) analysis (r = 0.552) adjusting for county unemployment rates. There was variation in the parameter estimates derived with the GWR; however, the majority of the estimates indicted a positive association. The strongest relationship between breast and prostate cancer was in the eastern parts of the Midwest and South, and the Southeastern U.S. We also observed a north-south pattern for both cancers with our cluster analyses. Clusters of counties with high cancer incidence rates were more frequently found in the North and clusters of counties with low incidence rates were predominantly in the South.ConclusionOur analyses suggest breast and prostate cancers cluster spatially. This finding corroborates other studies that have found these two cancers share similar risk factors. The north-south distribution observed for both cancers warrants further research to determine what is driving this spatial pattern.

Estrogen receptor positive breast cancers and their association with environmental factors

BackgroundEpidemiological studies to assess risk factors for breast cancer often do not differentiate between different types of breast cancers. We applied a general linear model to determine whether data from the Surveillance, Epidemiology, and End Results Program on annual county level age-adjusted incidence rates of breast cancer with and without estrogen receptors (ER+ and ER-) were associated with environmental pollutants.ResultsOur final model explained approximately 38% of the variation in the rate of ER+ breast cancer. In contrast, we were only able to explain 14% of the variation in the rate of ER- breast cancer with the same set of environmental variables. Only ER+ breast cancers were positively associated with the EPAs estimated risk of cancer based on toxic air emissions and the proportion of agricultural land in a county. Meteorological variables, including short wave radiation, temperature, precipitation, and water vapor pressure, were also significantly associated with the rate of ER+ breast cancer, after controlling for age, race, premature mortality from heart disease, and unemployment rate.ConclusionsOur findings were consistent with what we expected, given the fact that many of the commonly used pesticides and air pollutants included in the EPA cancer risk score are classified as endocrine disruptors and ER+ breast cancers respond more strongly to estrogen than ER- breast cancers. The findings of this study suggest that ER+ and ER- breast cancers have different risk factors, which should be taken into consideration in future studies that seek to understand environmental risk factors for breast cancer.

New Interatheres (Mammalia, Notoungulata) from the Late Oligocene Salla Beds of Bolivia

Abstract Two new Deseadan interatheriine genera (Interatheriidae, Notoungulata) from the late Oligocene Salla Beds of Bolivia are described. Both are monotypic and one is known from a partial skeleton, a rarity among known pre-Santacrucian interathere taxa. Phylogenetically, both taxa nest well within Interatheriinae, showing characteristically bilobed p3–4. Both taxa also have derived characters (hypselodont cheeckteeth, persistent lingual sulcus on upper molars) relative to basal interatheriines such as Santiagorothia and Proargyrohyrax but are clearly plesiomorphic with respect to younger, more highly derived Santacrucian interatheriine taxa such as Interatherium and Protypotherium. New species Brucemacfaddenia boliviensis is on average larger than the other new Salla interatheriine, Federicoanaya sallaensis, although they do overlap in size. Distinguishing between the two new taxa based purely on molar morphology is confounded by lack of diagnostic characters on the molar teeth and the overlap in size between the taxa. We overcome this difficulty of identifying specimens that preserve only molars by using discriminant analysis. We present a few of the simpler yet still robust discriminant functions we used so that future workers have a means of identifying problematic specimens. Analysis of Salla interathere specimens and stratigraphic provenance indicates both taxa experienced a modest increase in body size upsection, the driving mechanism for which remains unknown, but could be environmental changes or simple drift. These two new taxa help emphasize the fact that while the Salla fauna shares elements with roughly contemporaneous Deseadan faunas from more southerly latitudes, important faunal distinctions mark the two regions as well.

Correlations between meteorological parameters and prostate cancer

BackgroundThere exists a north-south pattern to the distribution of prostate cancer in the U.S., with the north having higher rates than the south. The current hypothesis for the spatial pattern of this disease is low vitamin D levels in individuals living at northerly latitudes; however, this explanation only partially explains the spatial distribution in the incidence of this cancer. Using a U.S. county-level ecological study design, we provide evidence that other meteorological parameters further explain the variation in prostate cancer across the U.S.ResultsIn general, the colder the temperature and the drier the climate in a county, the higher the incidence of prostate cancer, even after controlling for shortwave radiation, age, race, snowfall, premature mortality from heart disease, unemployment rate, and pesticide use. Further, in counties with high average annual snowfall (>75 cm/yr) the amount of land used to grow crops (a proxy for pesticide use) was positively correlated with the incidence of prostate cancer.ConclusionThe trends found in this USA study suggest prostate cancer may be partially correlated with meteorological factors. The patterns observed were consistent with what we would expect given the effects of climate on the deposition, absorption, and degradation of persistent organic pollutants including pesticides. Some of these pollutants are known endocrine disruptors and have been associated with prostate cancer.

Spectroscopic Detection of Nitrogen Concentrations in Sagebrush

The ability to estimate foliar nitrogen in semi-arid landscapes can yield information on nutritional status and improve our limited understanding of controls on canopy photosynthesis. We examined two spectroscopic methods for estimating sagebrush dried leaf and live shrub nitrogen content: first derivative reflectance (FDR) and continuum removal. Both methods used partial least squares (PLS) regression to select wavebands most significantly correlated with nitrogen concentrations in the samples. Sagebrush dried leaf spectra produced PLS models (R 2 = 0.76–0.86) that could predict nitrogen concentrations within the data set more accurately than PLS models generated from live shrub spectra (R 2 = 0.41–0.63). Inclusion of wavelengths associated with leaf water in the FDR transformations appeared to improve regression results. These findings are encouraging and warrant further exploration into sagebrush reflectance spectra to characterize nitrogen concentrations.

A simple framework for assessing the sensitivity of mountain watersheds to warming‐driven snowpack loss

The common observation that snowpack increases with elevation suggests that a catchments elevation distribution should be a robust indicator of its potential to store snow and its sensitivity to snowpack loss. To capture a wide range of potential elevation-based responses, we used Monte Carlo methods to simulate 20,000 watershed elevation distributions. We applied a simple function relating warming, elevation, and snowpack to explore snowpack losses from the simulated elevation distributions. Regression analyses demonstrate that snowpack loss is best described by three parameters that identify the central tendency, variance, and shape of each catchments elevation distribution. Equal amounts of snowpack loss can occur even when catchments are centered within different elevation zones; this stresses the value of also measuring the variance and shape of elevation distributions. Responses of the simulated elevation distributions to warming are nonlinear and emphasize that the sensitivity of mountain forests to snowpack loss will likely be watershed dependent.

A graphical framework for model selection criteria and significance tests: refutation, confirmation and ecology

Summary 1.In this paper we use a novel graphical heuristic to compare the way four methods: significance testing, two popular information-theoretic approaches (AIC and BIC), and Goods Bayes/Non-Bayes compromise (an underutilized hypothesis testing approach whose demarcation criterion adjusts for n) evaluate the merit of competing hypotheses, e.g., H0 and HA. 2.A primary goal of our work is to clarify the concept of strong consistency in model selection. Explicit considerations of this principle (including the strong consistency of BIC) are currently limited to technical derivations, inaccessible to most ecologists. We use our graphical framework to demonstrate, in simple terms, the strong consistency of both BIC and Goods compromise. 3.Our framework also locates the evaluated metrics (and ICs in general) along a conceptual continuum of hypothesis refutation/confirmation that considers n, parameter number, and effect size. Along this continuum, significance testing, and particularly AIC are refutative for H0, whereas Goods compromise, and particularly BIC are confirmatory for the true hypothesis. 4.Our work graphically demonstrates the well-known asymptotic bias of significance tests for HA, and the incorrectness of using statistically non-consistent methods for point hypothesis testing. To address these issues we recommend: 1) dedicated confirmatory methods with strong consistency like BIC for use in point hypothesis testing and confirmatory model selection; 2) significance tests for use in exploratory/refutative hypothesis testing, particularly when conjoined with rational approaches (e.g., Goods compromise, power analyses) to account for the effect of n on P-values; and 3) asymptotically efficient methods like AIC for exploratory model selection. This article is protected by copyright. All rights reserved.