A time‐series model for estimating temporal variation in phenotypic selection on laying dates in a Dutch great tit population

The Relative Contribution of Climatic, Demographic Factors, Disease Control Measures and Spatiotemporal Heterogeneity to Variation of Global COVID-19 Transmission

Despite a substantial number of COVID-19 related research papers published, it remains unclear as to which factors are associated with the observed variation in global transmission and what are their relative levels of importance. This study applies a rigorous statistical framework to provide robust estimations of the factor effects for a global and integrated perspective on this issue. We developed a mixed effect model exploring the relative importance of potential factors driving COVID-19 transmission while incorporating spatial and temporal heterogeneity of spread. We use an integrated data set for 87 countries across six continents for model specification and fitting. The best model accounts for 70.4% of the variance in the data analyzed: 10 fixed effect factors explain 20.5% of the variance, random temporal and spatial effects account for 50% of the variance. The fixed effect factors are classified into climatic, demographic and disease control groups. The explained variance in global transmission by the three groups are 0.6%, 1.1%, and 4.4% respectively. The high proportion of variance accounted for by random effects indicated striking differences in temporal transmission trajectories and effects of population mobility among the countries. In particular, the country-specific mobility-transmission relationship turns out to be the most important factor in explaining the observed global variation of transmission in the early phase of COVID-19 pandemic.

An estimator of the Opportunity for Selection that is independent of mean fitness

Variation among individuals in number of offspring (fitness, k) sets an upper limit to the evolutionary response to selection. This constraint is quantified by Crow's Opportunity for Selection (I), which is the variance in relative fitness (I = σ² _k /(u_k )² ). Crow's I has been widely used but remains controversial because it depends on mean offspring number in a sample ( k ¯ ). Here, I used a generalized Wright-Fisher model that allows for unequal probabilities of producing offspring to evaluate behavior of Crow's I and related indices under a wide range of sampling scenarios. Analytical and numerical results are congruent and show that rescaling the sample variance (s² _k ) to its expected value at a fixed k ¯ 2 removes dependence of I on mean offspring number, but the result still depends on choice of k ¯ 2 . A new index is introduced, Δ_I = Π- E(Î_drift ) = Π- 1/ k ¯ , which makes Î independent of sample k ¯ without the need for variance rescaling. Δ_I has a straightforward interpretation as the component of variance in relative fitness that exceeds that expected under a null model of random reproductive success. Δ_I can be used to directly compare estimates of the Opportunity for Selection for samples from different studies, different sexes, and different life stages.