Production of organic chemicals (OCs) is increasing exponentially, and some OCs biomagnify through food webs to potentially toxic levels. Biomagnification under field conditions is best described by ...trophic magnification factors (TMFs; per trophic level change in log-concentration of a chemical) which have been measured for more than two decades. Syntheses of TMF behavior relative to chemical traits and ecosystem properties are lacking. We analyzed >1500 TMFs to identify OCs predisposed to biomagnify and to assess ecosystem vulnerability. The highest TMFs were for OCs that are slowly metabolized by animals (metabolic rate kM < 0.01 day(-1)) and are moderately hydrophobic (log KOW 6-8). TMFs were more variable in marine than freshwaters, unrelated to latitude, and highest in food webs containing endotherms. We modeled the probability that any OC would biomagnify as a combined function of KOW and kM. Probability is greatest (∼100%) for slowly metabolized compounds, regardless of KOW, and lowest for chemicals with rapid transformation rates (kM > 0.2 day(-1)). This probabilistic model provides a new global tool for screening existing and new OCs for their biomagnification potential.
Quantile regression is a way to estimate the conditional quantiles of a response variable distribution in the linear model that provides a more complete view of possible causal relationships between ...variables in ecological processes. Typically, all the factors that affect ecological processes are not measured and included in the statistical models used to investigate relationships between variables associated with those processes. As a consequence, there may be a weak or no predictive relationship between the mean of the response variable (y) distribution and the measured predictive factors (X). Yet there may be stronger, useful predictive relationships with other parts of the response variable distribution. This primer relates quantile regression estimates to prediction intervals in parametric error distribution regression models (eg least squares), and discusses the ordering characteristics, interval nature, sampling variation, weighting, and interpretation of the estimates for homogeneous and heterogeneous regression models.
In a recent Concepts paper in Ecology, Thomson et al. emphasized that assumptions of conventional correlation and regression analyses fundamentally conflict with the ecological concept of limiting ...factors, and they called for new statistical procedures to address this problem. The analytical issue is that unmeasured factors may be the active limiting constraint and may induce a pattern of unequal variation in the biological response variable through an interaction with the measured factors. Consequently, changes near the maxima, rather than at the center of response distributions, are better estimates of the effects expected when the observed factor is the active limiting constraint. Regression quantiles provide estimates for linear models fit to any part of a response distribution, including near the upper bounds, and require minimal assumptions about the form of the error distribution. Regression quantiles extend the concept of one-sample quantiles to the linear model by solving an optimization problem of minimizing an asymmetric function of absolute errors. Rank-score tests for regression quantiles provide tests of hypotheses and confidence intervals for parameters in linear models with heteroscedastic errors, conditions likely to occur in models of limiting ecological relations. We used selected regression quantiles (e.g., 5th, 10th,..., 95th) and confidence intervals to test hypotheses that parameters equal zero for estimated changes in average annual acorn biomass due to forest canopy cover of oak (Quercus spp.) and oak species diversity. Regression quantiles also were used to estimate changes in glacier lily (Erythronium grandiflorum) seedling numbers as a function of lily flower numbers, rockiness, and pocket gopher (Thomomys talpoides fossor) activity, data that motivated the query by Thomson et al. for new statistical procedures. Both example applications showed that effects of limiting factors estimated by changes in some upper regression quantile (e.g., 90-95th) were greater than if effects were estimated by changes in the means from standard linear model procedures. Estimating a range of regression quantiles (e.g., 5-95th) provides a comprehensive description of biological response patterns for exploratory and inferential analyses in observational studies of limiting factors, especially when sampling large spatial and temporal scales.
We simulated the effects of missing information on statistical distributions of animal response that covaried with measured predictors of habitat to evaluate the utility and performance of quantile ...regression for providing more useful intervals of uncertainty in habitat relationships. These procedures were evaulated for conditions in which heterogeneity and hidden bias were induced by confounding with missing variables associated with other improtant processes, a problem common in statistical modeling of ecological phenomena. Simulations for a large (N = 10 000) finite population representing grid locations on a landscape demonstrated various forms of hidden bias that might occur when the effect of a measured habitat variable on some animal was confounded with the effect of another unmeasured variable. Quantile (0 ≤ τ ≤ 1) regression parameters for linear models that excluded the important, unmeasured variable revealed bias relative to parameters from the generating model. Depending on whether interactions of the measured and unmeasured variables were negative (interference interactions) or positive (facilitation interactions) in simulations without spatial structuring, either upper (τ > 0.5) or lower (τ < 0.5) quantile regression parameters were less biased than mean rate parameters. Heterogeneous, nonlinear response patterns occurred with correlations between the measured and unmeasured variables. When the unmeasured variable was spatially structured, variation in parameters across quantiles associated with heterogeneous effects of the habitat variable was reduced by modeling the spatial trend surface as a cubic polynomial of location coordinates, but substantial hidden bias remained. Sampling (n = 20-300) simulations demonstrated that regression quantile estimates and confidence intervals constructed by inverting weighted rank score tests provided valid coverage of these parameters. Local forms of quantile weighting were required for obtaining correct Type I error rates and confidence interval coverage. Quantile regression was used to estimate effects of physical habitat resources on a bivalve (Macomona liliana) in the spatially structured landscape on a sandflat in a New Zealand harbor. Confidence intervals around predicted 0.10 and 0.90 quantiles were used to estimate sampling intervals containing 80% of the variation in densities in relation to bed elevation. Spatially structured variation in bivalve counts estimated by a cubic polynomial trend surface remained after accounting for the nonlinear effects of bed elevation, indicating the existence of important spatially structured processes that were not adequately represented by the measured habitat variables.
The purpose of this study was to determine factors associated with early symptomatic acromial and scapular spine fractures in patients who underwent reverse total shoulder arthroplasty (RTSA).
We ...retrospectively evaluated all RTSAs performed by the senior author between 1/1/2013 and 6/1/2019. We evaluated patient demographics including gender, age, prevalence of comorbidities including osteoporosis, inflammatory arthritis, diabetes, and endocrine disorders such as hypothyroidism. We also evaluated preoperative and 2-week postoperative radiographs for center of rotation medialization (CORM) as distance between the center of the humeral head or glenosphere and the line of the deltoid, and distalization via the acromial-greater tuberosity distance (AGT). We evaluated inter- and intra-rater reliability via intraclass correlation coefficients.
We included 335 RTSAs with a minimum of 3 months of follow-up in the analysis. Reliability was acceptable with all intraclass correlation coefficients> 0.75. Symptomatic acromial and scapular spine stress fractures were significantly more common in those with inflammatory arthritis than those without (18% vs. 5%, P = 0.016). The rate of fracture was highest in patients with rheumatoid arthritis (24% vs. 5.2%, P = 0.003). There was no statistically significant association between symptomatic fractures and preoperative CORM or AGT (P = 0.557, P = 0.528) or postoperative CORM or AGT (P = 0.56, P = 0.102). There also was no statistically significant correlation between symptomatic stress fracture and patient age, gender, BMI, smoking, osteoporosis, gout, medical comorbidity, or previous shoulder surgery.
In this retrospective analysis of postoperative RTSA, symptomatic acromial and scapular stress fractures were significantly more common in patients with rheumatoid arthritis and thus precautions should be taken in these patients.
Many amphibians breed in water but live most of their lives in terrestrial habitats. Little is known, however, about the spatial distribution of these habitats or of the distances and directions ...amphibians move to reach breeding sites. The amphibian community at a small, temporary pond in northcentral Florida was monitored for 5 years. Based on captures and recaptures of more than 2500 striped newts (Notophthalmus perstriatus) and 5700 eastern narrow-mouthed toads (Gastrophryne carolinensis), we tabulated the angles of orientation that these amphibians entered and exited the pond basin. Our results showed that movements of these species between the pond and terrestrial habitats were nonrandom in orientation, but that narrow corridors did not appear to be used. Differences between the species likely reflect differences in habitat preferences, whereas intraspecific differences among years and between the sexes likely reflect variation among individuals. For terrestrial buffer zones to be effective at conserving pond-breeding amphibian communities, they need both a distance and a directional component. The determination of a directional component may be obscured if studies are carried out over a short time span. Conservation efforts for wetland-breeding amphibians that concentrate solely on the wetland likely will fail without consideration of the adjacent terrestrial habitat.
We used regression quantiles to model potentially limiting relationships between the standing crop of cutthroat trout Oncorhynchus clarki and measures of stream channel morphology. Regression ...quantile models indicated that variation in fish density was inversely related to the width:depth ratio of streams but not to stream width or depth alone. The spatial and temporal stability of model predictions were examined across years and streams, respectively. Variation in fish density with width:depth ratio (10th‐90th regression quantiles) modeled for streams sampled in 1993‐1997 predicted the variation observed in 1998‐1999, indicating similar habitat relationships across years. Both linear and nonlinear models described the limiting relationships well, the latter performing slightly better. Although estimated relationships were transferable in time, results were strongly dependent on the influence of spatial variation in fish density among streams. Density changes with width:depth ratio in a single stream were responsible for the significant (P < 0.10) negative slopes estimated for the higher quantiles (>80th). This suggests that stream‐scale factors other than width:depth ratio play a more direct role in determining population density. Much of the variation in densities of cutthroat trout among streams was attributed to the occurrence of nonnative brook trout Salvelinus fontinalis (a possible competitor) or connectivity to migratory habitats. Regression quantiles can be useful for estimating the effects of limiting factors when ecological responses are highly variable, but our results indicate that spatiotemporal variability in the data should be explicitly considered. In this study, data from individual streams and stream‐specific characteristics (e.g., the occurrence of nonnative species and habitat connectivity) strongly affected our interpretation of the relationship between width:depth ratio and fish density.
Rates of change in final summer densities of two desert annuals, Eriogonum abertianum and Haplopappus gracilis, as constrained by their initial winter germination densities were estimated with ...regression quantiles and compared with mechanistic fits based on a self-thinning rule proposed by Guo et al. (1998); Oikos 83: 237-245). The allometric relation used was equivalent to S=Nf(Ni)-1=cf(Ni)-1, where S is the ratio of final to initial densities (survivorship), cf is a constant that is a final density specific to the species and environment, Ni is the initial plant density, and Nf is final plant density. We used regression quantiles to estimate cf assuming the exponent of - 1 was fixed (model 1, Nf(Ni)-1=cf(Ni)-1) and also obtained estimates by treating the exponent as a parameter to estimate (model 2, Nf(Ni)-1=cf(Ni)λ). Regression quantiles allow rates of change to be estimated through any part of a data distribution conditional on some linear function of covariates. We focused on estimates for upper (90-99th) quantiles near the boundary of the summer density distributions where we expected effects of self-thinning to operate as the primary constraint on plant performance. Allometric functions estimated with regression quantiles were similar to functions fit by Guo et al. (1998) when the exponent was constrained to - 1. However, the data were more consistent with estimates for model (2), where exponents were closer to - 0.4 than - 1, although model fit was not as good at higher initial plant densities as when the exponent was fixed at - 1. An exponential form (model 3, Nf(Ni)-1=cf(Ni)λ eγ Ni) that is a generalization of the discrete logistic growth function, where estimates of λ were - 0.23 to - 0.28 and estimates of γ were - 0.003 to - 0.006, provided better fit from low to high initial germination densities. Model 3 predictions were consistent with an interpretation that final summer densities were constrained by initial germination densities when these were low ($<40\ {\rm per}\ 0.25\ {\rm m}^{2}$ for Eriogonum and $<100\ {\rm per}\ 0.25\ {\rm m}^{2}$ for Haplopappus) and were constrained by the self-thinning process at higher germination densities. Our exponential model (3) estimated with regression quantiles had similar form to the mechanistic relation of Guo et al. (1998) when plotted as a survivorship function, but avoided the unrealistic assumption that all populations attained a similar final density, and was based on a statistical model that has formal rules for estimation and inference.
Equivalence testing and corresponding confidence interval estimates are used to provide more enlightened statistical statements about parameter estimates by relating them to intervals of effect sizes ...deemed to be of scientific or practical importance rather than just to an effect size of zero. Equivalence tests and confidence interval estimates are based on a null hypothesis that a parameter estimate is either outside (inequivalence hypothesis) or inside (equivalence hypothesis) an equivalence region, depending on the question of interest and assignment of risk. The former approach, often referred to as bioequivalence testing, is often used in regulatory settings because it reverses the burden of proof compared to a standard test of significance, following a precautionary principle for environmental protection. Unfortunately, many applications of equivalence testing focus on establishing average equivalence by estimating differences in means of distributions that do not have homogeneous variances. I discuss how to compare equivalence across quantiles of distributions using confidence intervals on quantile regression estimates that detect differences in heterogeneous distributions missed by focusing on means. I used one-tailed confidence intervals based on inequivalence hypotheses in a two-group treatment-control design for estimating bioequivalence of arsenic concentrations in soils at an old ammunition testing site and bioequivalence of vegetation biomass at a reclaimed mining site. Two-tailed confidence intervals based both on inequivalence and equivalence hypotheses were used to examine quantile equivalence for negligible trends over time for a continuous exponential model of amphibian abundance.
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