MOTIVATION: Recombination is a fundamental process in molecular evolution, and the identification of recombinant sequences is thus of major interest. However, current methods for detecting recombinants are primarily designed for aligned sequences. Thus, they struggle with analyses of highly diverse genes, such as the var genes of the malaria parasite Plasmodium falciparum, which are known to diversify primarily through recombination. RESULTS: We introduce an algorithm to detect recent recombinant sequences from a dataset without a full multiple alignment. Our algorithm can handle thousands of gene-length sequences without the need for a reference panel. We demonstrate the accuracy of our algorithm through extensive numerical simulations; in particular, it maintains its effectiveness in the presence of insertions and deletions. We apply our algorithm to a dataset of 17 335 DBLα types in var genes from Ghana, observing that sequences belonging to the same ups group or domain subclass recombine amongst themselves more frequently, and that non-recombinant DBLα types are more conserved than recombinant ones. AVAILABILITY AND IMPLEMENTATION: Source code is freely available at https://github.com/qianfeng2/detREC_program. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

We analyse the capacity of several 2-D constraint families-the exclusion, coloring, parity, and charge model families. Using Baxter's corner transfer matrix formalism combined with the corner transfer matrix renormalization group method of Nishino and Okunishi, we calculate very tight lower bounds and estimates on the growth rates of these models. Our results strongly improve previous known lower bounds and lead to the surprising conjecture that the capacity of the even and charge(3) constraints are identical.