For each gene, we characterised the distribution of sequence convergence between pairs of branches in the species phylogeny following the approach described by Castoe et al. (2009) implemented in the ...

Only some bats and toothed whales rely on sophisticated echolocation, in which they emit sonar pulses and process returning echoes, to detect and track down small prey. Now, two new studies show that ...

Convergent evolution—where distinct species independently evolve similar traits or functions, such as the wings of birds and bats—has long fascinated biologists. Now, a research team led by Prof. Zou ...

Given a decreasing sequence {aⁿ} of nonnegative terms, we prove that there exist subsequences {nk } of {n} such that ∑k=1∞nk+1−nkank and ∑n=1∞an have the same convergence. In particular, ∑n=1∞an ...

High-throughput sequencing of related individuals has become an important tool for studying human disease. However, owing to technical complexity and lack of available tools, most pedigree-based ...

This is a preview. Log in through your library . Journal Information This monthly journal, begun in 1950, is devoted entirely to research in pure and applied mathematics, principally to the ...