Species abundance distributions (SADs) follow one of ecology's oldest and most universal laws - every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just ...a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science.
Background
The mesial surface of the first permanent molar is the most caries‐susceptible proximal surface of the permanent dentition in children under the age of 12.
Aim
The aim of this study was to ...determine the association between caries progression on the mesial surface of the first permanent molar (T6M) and caries on the distal surface of the primary second molar (t5D) and the occlusal surface of the first permanent molar (T6O).
Design
Children (between 5 and 13 years old; N = 565) that had participated in a 4‐year longitudinal caries study that at baseline had at least one T6 fully erupted with a t5 in proximal contact, with no restoration or sealant on T6O and t5D, and adequate bitewing radiographs were included. Clinical data using the International Caries Detection and Assessment System (ICDAS) and radiographs were used to determine the caries status of T6M, T6O, and t5D.
Results
Baseline caries presence on t5D and T6O were highly significantly associated with follow‐up caries presence on T6M (P < .001). The adjusted odds ratios corresponding to t5D and T6O were 3.94 (95% CI: 1.78, 8.71) and 3.26 (95% CI: 1.46, 7.31), respectively.
Conclusion
These findings highlight the need for prevention and management of caries on T6O and t5D.
Counts from heterogeneous populations are often modeled using mixture distributions. These models assume that observations are generated from multiple unobserved subpopulations and estimate ...parameters having latent class interpretations. When interest is to make inferences about marginal means and incidence density ratios for the effects of risk factors in the overall population, regression coefficients obtained from common mixture models do not provide direct interpretations for these population-level parameters. While indirect techniques such as the use of post-modeling transformations may be employed to estimate the marginal effects of explanatory variables of interest, there are many instances where latent class model formulations fail to fully explain relationships between covariates and population-wide parameters (Preisser et al., 2012; Long et al., 2014). First, we employ two-component mixtures of non-degenerate count data distributions to estimate the overall effects of exposure variables on marginal means of zero-inflated and other heterogeneous counts. The models are examined using simulations and further applied to a double-blind dental caries incidence trial. Next, we develop a marginalized model for bivariate zero-inflated counts that allows the estimation of parameters for the overall effects of exposure variables on the marginal means of the two correlated outcomes. The model employs four-component mixture distributions and estimates marginally interpretable regression coefficients. We demonstrate the application of the method by using simulations and dental caries indices of primary and permanent teeth among children from a school-based fluoride mouthrinse study. Finally, extending earlier approaches, we propose an estimation method for marginalized zero-inflated count models when covariates are missing at random. The method, which can also be applied to other missing data problems, is illustrated and compared with complete case analysis by using simulations and dental data.
REVIEW AND SYNTHESIS McGill, Brian J; Etienne, Rampal S; Gray, John S ...
Ecology letters,
10/2007, Volume:
10, Issue:
10
Journal Article
Peer reviewed
Species abundance distributions (SADs) follow one of ecology's oldest and most universal laws - every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just ...a few common species. Here, we review theoretical, empirical and statistical developments in the study of SADs. Several key points emerge. (i) Literally dozens of models have been proposed to explain the hollow curve. Unfortunately, very few models are ever rejected, primarily because few theories make any predictions beyond the hollow-curve SAD itself. (ii) Interesting work has been performed both empirically and theoretically, which goes beyond the hollow-curve prediction to provide a rich variety of information about how SADs behave. These include the study of SADs along environmental gradients and theories that integrate SADs with other biodiversity patterns. Central to this body of work is an effort to move beyond treating the SAD in isolation and to integrate the SAD into its ecological context to enable making many predictions. (iii) Moving forward will entail understanding how sampling and scale affect SADs and developing statistical tools for describing and comparing SADs. We are optimistic that SADs can provide significant insights into basic and applied ecological science. Ecology Letters (2007) 10: 995-1015 PUBLICATION ABSTRACT
PDF
