Unravelling angiosperm genome evolution by phylogenetic analysis of chromosomal duplication events

L are assigned values to give a basic reproduction number, R 0 , for local transmission in a patch of 5, R 0 for mass-action transmission in a patch of 0.4, and an R 0 of 0.02 between any two patches. Seasonal variation in contact rates is characterized by 1 p , and is assumed to be opposite in phase for the Northern and Southern hemispheres (represented by setting 1 p ¼ þ0:25 for 1 , p # M=2; and 1 p ¼ 20:25 for M=2 , p # M). The probability that a host is infected upon exposure depends on the strain s, and the host's immune history. Each strain is characterized by A epitopes, each consisting of C codons (three nucleotide bases). Immunity is assumed to be specific to the set of amino acids to which the host has been exposed at each codon, and for simplicity, no functional constraints are imposed on the amino acid sequences. For the default values of A ¼ 4 and C ¼ 3 used here, a total of 4 £ 10 15 strains are possible. Antigenic distance, d(s,H) between a strain s and the immune history of a host, H, is then simply defined as the number of codons in strain s for which the amino acid has not been previously encountered by the host. The level of cross-protection from infection provided at a certain antigenic distance is given by the function f (d), where we assume f ðdÞ ¼ v 1 þ ðv 0 2 v 1 Þðd 2 n t Þ=ðAC 2 n t Þ for d $ n t ; f ðdÞ ¼ v 1 for 0 , d , n t ; and f(d) ¼ 1 for d ¼ 0. n t (¼2) is the threshold level of change necessary for cross-protection to drop below the maximal level set by v 1 (¼0.99), and v 0 (¼0.25) is the minimal level of cross-protection mounted against a strain with no similarity to a previously encountered strain at the codons modelled (¼0 for no cross-protection). These assumptions reflect empirical studies suggesting that two or more substitutions at key antigenic sites are required to escape pre-existing immunity 26,27. The probability that a host will be infected by a strain following exposure is given by where t (¼270 days) is the decay timescale (half-life ¼ t 1/2 ¼ 187 days < 6 …

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