The face of evolutionary biology is changing: from reconstructing and analysing the past to
predicting future evolutionary processes. Recent developments include prediction of …

Evolution is a quest for innovation. Organisms adapt to changing natural selection by evolving
new phenotypes. Can we read this dynamics in their genomes? Not every mutation under …

Seasonal influenza is controlled through vaccination campaigns. Evolution of influenza
virus antigens means that vaccines must be updated to match novel strains, and vaccine …

… Each strain has a multiplicity m i in our data set, which counts the number of sequences
with HA genotype a i and season of observation t i (sequences observed in the same season …

… , samples were crosslinked in 1% HCHO (prepared in 1× DPBS) at room temperature for 10
min, and HCHO was quenched by the addition of glycine at a final concentration of 0.125 M. …

… r m gives the point where the binding probability reaches a maximum (crater landscape),
or else values close to 1 (mesa landscape). r s approximately indicates the onset of selection, …

… and k', m kk' pairs interact is , where g kk' gives the probability for a cross-interaction. are the
binomial coefficients. The probability p for observing for each pair k ≤ k' m kk' interactions in …

… Next we evaluate the internal link numbers L α = L(c α ) and the pairwise mismatches M
αβ , defined as the minimum of M(c α , c β ) over all pairwise alignments of the subgraphs G α …

… These enjoy the relation with scalar products v 2 and m 2 defined in SI Text. We now consider
the reverse history x T = (x 0 T , …, x n T ), which is given by x i T = x n –i (i = 0, …, n), and, …

A fraction of COVID-19 convalescent individuals mount a potent antibody response to SARS-CoV-2
with cross-reactivity to SARS-CoV-1. To uncover their humoral response in detail, we …