Compositional data and Simpson's paradox

Simpson's paradox, also known as amalgamation or aggregation paradox, appears whendealing with proportions. Proportions are by construction parts of a whole, which canbe interpreted as compositions assuming they only carry relative information. TheAitchison inner product space structure of the simplex, the sample space of compositions, explains the appearance of the paradox, given that amalgamation is a nonlinearoperation within that structure. Here we propose to use balances, which are specificelements of this structure, to analyse situations where the paradox might appear. Withthe proposed approach we obtain that the centre of the tables analysed is a naturalway to compare them, which avoids by construction the possibility of a paradox.Key words: Aitchison geometry, geometric mean, orthogonal projection

Overcoming the rare species modelling paradox: test of a novel hierarchical framework with an Iberian endemic plant

Rare species have restricted geographic ranges, habitat specialization, and/or small population sizes. Datasets on rare species distribution usually have few observations, limited spatial accuracy and lack of valid absences; conversely they provide comprehensive views of species distributions allowing to realistically capture most of their realized environmental niche. Rare species are the most in need of predictive distribution modelling but also the most difficult to model. We refer to this contrast as the "rare species modelling paradox" and propose as a solution developing modelling approaches that deal with a sufficiently large set of predictors, ensuring that statistical models aren't overfitted. Our novel approach fulfils this condition by fitting a large number of bivariate models and averaging them with a weighted ensemble approach. We further propose that this ensemble forecasting is conducted within a hierarchic multi-scale framework. We present two ensemble models for a test species, one at regional and one at local scale, each based on the combination of 630 models. In both cases, we obtained excellent spatial projections, unusual when modelling rare species. Model results highlight, from a statistically sound approach, the effects of multiple drivers in a same modelling framework and at two distinct scales. From this added information, regional models can support accurate forecasts of range dynamics under climate change scenarios, whereas local models allow the assessment of isolated or synergistic impacts of changes in multiple predictors. This novel framework provides a baseline for adaptive conservation, management and monitoring of rare species at distinct spatial and temporal scales.

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Skeletal muscle triglycerides, diacylglycerols, and ceramides in insulin resistance: another paradox in endurance-trained athletes?

OBJECTIVE-Chronic exercise and obesity both increase intra-myocellular triglycerides (IMTGs) despite having opposing effects on insulin sensitivity. We hypothesized that chronically exercise-trained muscle would be characterized by lower skeletal muscle diacylglycerols (DAGs) and ceramides despite higher IMTGs and would account for its higher insulin sensitivity. We also hypothesized that the expression of key skeletal muscle proteins involved in lipid droplet hydrolysis, DAG formation, and fatty-acid partitioning and oxidation would be associated with the lipotoxic phenotype.RESEARCH DESIGN AND METHODS-A total of 14 normal-weight, endurance-trained athletes (NWA group) and 7 normal-weight sedentary (NWS group) and 21 obese sedentary (OBS group) volunteers were studied. Insulin sensitivity was assessed by glucose clamps. IMTGs, DAGs, ceramides, and protein expression were measured in muscle biopsies.RESULTS-DAG content in the NWA group was approximately twofold higher than in the OBS group and similar to 50% higher than in the NWS group, corresponding to higher insulin sensitivity. While certain DAG moieties clearly were associated with better insulin sensitivity, other species were not. Ceramide content was higher in insulin-resistant obese muscle. The expression of OXPAT/perilipin-5, adipose triglyceride lipase, and stearoyl-CoA desaturase protein was higher in the NWA group, corresponding to a higher mitochondrial content, proportion of type 1 myocytes, DAGs, and insulin sensitivity.CONCLUSIONS-Total myocellular DAGs were markedly higher in highly trained athletes, corresponding with higher insulin sensitivity, and suggest a more complex role for DAGs in insulin action. Our data also provide additional evidence in humans linking ceramides to insulin resistance. Finally, this study provides novel evidence supporting a role for specific skeletal muscle proteins involved in intramyocellular lipids, mitochondrial oxidative capacity, and insulin resistance. Diabetes 60:2588-2597, 2011

Self-avoiding random walks and Olbers' paradox

In this paper, we prove that a self-avoiding walk of infinite length provides a structure that would resolve Olbers' paradox. That is, if the stars of a universe were distributed like the vertices of an infinite random walk with each segment length of about a parsec, then the night sky could be as dark as actually observed on the Earth. Self-avoiding random walk structure can therefore resolve the Olbers' paradox even in a static universe.

Signalling value of maternal and paternal melanism in the barn owl : implication for the resolution of the lek paradox

Secondary sexual characters often signal qualities such as physiological processes associated with resistance to various sources of stress. When the expression of an ornament is not sex-limited, we can identify the costs and benefits of displaying a trait that is typical of its own sex or of the other sex. Indeed, the magnitude and sign of the covariation between physiology and the extent to which an ornament is expressed could differ between males and females if, for instance, the regulation of physiological processes is sensitive to sex hormones. Using data collected over 14 years in the nocturnal barn owl Tyto alba, we investigated how nestling body mass covaries with a heritable melanin-based sex-trait, females displaying on average larger black feather spots than males. Independently of nestling sex, year and time of the day large-spotted nestlings were heavier than small-spotted nestlings. In contrast, the magnitude and sign of the covariation between nestling body mass and the size of parental spots varied along the day in a way that depended on the year and parental gender. In poor years, offspring of smaller-spotted mothers were heavier throughout the resting period; in the morning, offspring sired by larger-spotted fathers were heavier than offspring of smaller-spotted fathers, while in the evening the opposite pattern was found. Thus, maternal and paternal coloration is differentially associated with behaviour or physiology, processes that are sensitive to time of the day and environmental factors. Interestingly, the covariation between offspring body mass and paternal coloration is more sensitive to these environmental factors than the covariation with maternal coloration. This indicates that the benefit of pairing with differently spotted males may depend on environmental conditions, which could help maintain genetic variation in the face of intense directional (sexual) selection.

Asset freezing, corporate political resources and the Tullock paradox

In 1967, Gordon Tullock asked why firms do not spend more on campaign contributions, despite the large rents that could be generated from political activities. We suggest in this paper that part of the puzzle could come from the fact that one important type of political activity has been neglected by the literature which focuses on campaign contributions or political connections. We call this neglected activity "asset freezing": situations in which firms delay lay-offs or invest in specific technologies to support local politicians' re-election objectives. In doing so, firms bear a potentially significant cost as they do not use a portion of their economic assets in the most efficient or productive way. The purpose of this paper is to provide a first theoretical exploration of this phenomenon. Building on the literature on corporate political resources, we argue that a firm's economic assets can be evaluated based on their degree of "political freezability," which depends on the flexibility of their use and on their value for policy-makers. We then develop a simple model in which financial contributions and freezing assets are alternative options for a firm willing to lawfully influence public policy-making, and derive some of our initial hypotheses more formally.