Using mixture of Gamma distributions for Bayesian analysis in an M/G/1 queue with optional second service

Pedigree analysis and estimates of effective breeding size characterize sea lamprey reproductive biology

The sea lamprey (Petromyzon marinus) is an invasive species in the Great Lakes and the focus of a large control and assessment program. Current assessment methods provide information on the census size of spawning adult sea lamprey in a small number of streams, but information characterizing reproductive success of spawning adults is rarely available. We used RAD-capture sequencing to genotype single nucleotide polymorphism (SNP) loci for ~1600 sea lamprey larvae collected from three streams in northern Michigan (Black Mallard, Pigeon, and Ocqueoc Rivers). Larval genotypes were used to reconstruct family pedigrees, which were combined with Gaussian mixture analyses to identify larval age classes for estimation of spawning population size. Two complementary estimates of effective breeding size (N b), as well as the extrapolated minimum number of spawners (N s), were also generated for each cohort. Reconstructed pedigrees highlighted inaccuracies of cohort assignments from traditionally used mixture analyses. However, combining genotype-based pedigree information with length-at-age assignment of cohort membership greatly improved cohort identification accuracy. Population estimates across all three streams sampled in this study indicate a small number of successfully spawning adults when barriers were in operation, implying that barriers limited adult spawning numbers but were not completely effective at blocking access to spawning habitats. Thus, the large numbers of larvae present in sampled systems were a poor indicator of spawning adult abundance. Overall, pedigree-based N b and N s estimates provide a promising and rapid assessment tool for sea lamprey and other species.