Measures of individual uncertainty for ecological models: Variance and entropy

Little information loss with red-green color deficient vision in natural environments

Inherited color vision deficiency affects red-green discrimination in about one in twelve men from European populations. Its effects have been studied mainly in primitive foraging but also in detecting blushing and breaking camouflage. Yet there is no obvious relationship between these specific tasks and vision in the real world. The aim here was to quantify the impact of color vision deficiency by estimating computationally the information available to observers about colored surfaces in natural scenes. With representative independent sets of 50 and 100 hyperspectral images, estimated information was found to be only a little less in red-green color vision deficiency than in normal trichromacy. Colorimetric analyses revealed the importance of large lightness variations within scenes, small redness-greenness variations, and uneven frequencies of different colored surfaces. While red-green color vision deficiency poses challenges in some tasks, it has much less effect on gaining information from natural environments.

Estimating ectopic beat probability with simplified statistical models that account for experimental uncertainty

Ectopic beats (EBs) are cellular arrhythmias that can trigger lethal arrhythmias. Simulations using biophysically-detailed cardiac myocyte models can reveal how model parameters influence the probability of these cellular arrhythmias, however such analyses can pose a huge computational burden. Here, we develop a simplified approach in which logistic regression models (LRMs) are used to define a mapping between the parameters of complex cell models and the probability of EBs (P(EB)). As an example, in this study, we build an LRM for P(EB) as a function of the initial value of diastolic cytosolic Ca²⁺ concentration ([Ca²⁺]_iⁱⁿⁱ), the initial state of sarcoplasmic reticulum (SR) Ca²⁺ load ([Ca²⁺]_SRⁱⁿⁱ), and kinetic parameters of the inward rectifier K⁺ current (I_K1) and ryanodine receptor (RyR). This approach, which we refer to as arrhythmia sensitivity analysis, allows for evaluation of the relationship between these arrhythmic event probabilities and their associated parameters. This LRM is also used to demonstrate how uncertainties in experimentally measured values determine the uncertainty in P(EB). In a study of the role of [Ca²⁺]_SRⁱⁿⁱ uncertainty, we show a special property of the uncertainty in P(EB), where with increasing [Ca²⁺]_SRⁱⁿⁱ uncertainty, P(EB) uncertainty first increases and then decreases. Lastly, we demonstrate that I_K1 suppression, at the level that occurs in heart failure myocytes, increases P(EB).

An ectopic beat is an abnormal cellular electrical event which can trigger dangerous arrhythmias in the heart. Complex biophysical models of the cardiac myocyte can be used to reveal how cell properties affect the probability of ectopic beats. However, such analyses can pose a huge computational burden. We develop a simplified approach that enables a highly complex biophysical model to be reduced to a rather simple statistical model from which the functional relationship between myocyte model parameters and the probability of an ectopic beat is determined. We refer to this approach as arrhythmia sensitivity analysis. Given the efficiency of our approach, we also use it to demonstrate how uncertainties in experimentally measured myocyte model parameters determine the uncertainty in ectopic beat probability. We find that, with increasing model parameter uncertainty, the uncertainty in probability of ectopic beat first increases and then decreases. In general, our approach can efficiently analyze the relationship between cardiac myocyte parameters and the probability of ectopic beats and can be used to study how uncertainty of these cardiac myocyte parameters influences the ectopic beat probability.

A simple model suggesting economically rational sample-size choice drives irreproducibility

Several systematic studies have suggested that a large fraction of published research is not reproducible. One probable reason for low reproducibility is insufficient sample size, resulting in low power and low positive predictive value. It has been suggested that insufficient sample-size choice is driven by a combination of scientific competition and 'positive publication bias'. Here we formalize this intuition in a simple model, in which scientists choose economically rational sample sizes, balancing the cost of experimentation with income from publication. Specifically, assuming that a scientist's income derives only from 'positive' findings (positive publication bias) and that individual samples cost a fixed amount, allows to leverage basic statistical formulas into an economic optimality prediction. We find that if effects have i) low base probability, ii) small effect size or iii) low grant income per publication, then the rational (economically optimal) sample size is small. Furthermore, for plausible distributions of these parameters we find a robust emergence of a bimodal distribution of obtained statistical power and low overall reproducibility rates, both matching empirical findings. Finally, we explore conditional equivalence testing as a means to align economic incentives with adequate sample sizes. Overall, the model describes a simple mechanism explaining both the prevalence and the persistence of small sample sizes, and is well suited for empirical validation. It proposes economic rationality, or economic pressures, as a principal driver of irreproducibility and suggests strategies to change this.

Calculation Formulas and Simulation Algorithms for Entropy of Function of LR Fuzzy Intervals

Entropy has continuously arisen as one of the pivotal issues in optimization, mainly in portfolios, as an indicator of risk measurement. Aiming to simplify operations and extending applications of entropy in the field of LR fuzzy interval theory, this paper first proposes calculation formulas for the entropy of function via the inverse credibility distribution to directly calculate the entropy of linear function or simple nonlinear function of LR fuzzy intervals. Subsequently, to deal with the entropy of complicated nonlinear function, two novel simulation algorithms are separately designed by combining the uniform discretization process and the numerical integration process with the proposed calculation formulas. Compared to the existing simulation algorithms, the numerical results show that the advantage of the algorithms is well displayed in terms of stability, accuracy, and speed. On the whole, the simplified calculation formulas and the effective simulation algorithms proposed in this paper provide a powerful tool for the LR fuzzy interval theory, especially in entropy optimization.