In 2011, Lake Erie experienced the largest harmful algal bloom in its recorded history, with a peak intensity over three times greater than any previously observed bloom. Here we show that long-term trends in agricultural practices are consistent with increasing phosphorus loading to the western basin of the lake, and that these trends, coupled with meteorological conditions in spring 2011, produced record-breaking nutrient loads. An extended period of weak lake circulation then led to abnormally long residence times that incubated the bloom, and warm and quiescent conditions after bloom onset allowed algae to remain near the top of the water column and prevented flushing of nutrients from the system. We further find that all of these factors are consistent with expected future conditions. If a scientifically guided management plan to mitigate these impacts is not implemented, we can therefore expect this bloom to be a harbinger of future blooms in Lake Erie.

Likelihood-based parentage inference depends on the distribution of a likelihood-ratio statistic, which, in most cases of interest, cannot be exactly determined, but only approximated by Monte Carlo simulation. We provide importance-sampling algorithms for efficiently approximating very small tail probabilities in the distribution of the likelihood-ratio statistic. These importance-sampling methods allow the estimation of small false-positive rates and hence permit likelihood-based inference of parentage in large studies involving a great number of potential parents and many potential offspring. We investigate the performance of these importance-sampling algorithms in the context of parentage inference using single-nucleotide polymorphism (SNP) data and find that they may accelerate the computation of tail probabilities >1 millionfold. We subsequently use the importance-sampling algorithms to calculate the power available with SNPs for large-scale parentage studies, paying particular attention to the effect of genotyping errors and the occurrence of related individuals among the members of the putative mother–father–offspring trios. These simulations show that 60–100 SNPs may allow accurate pedigree reconstruction, even in situations involving thousands of potential mothers, fathers, and offspring. In addition, we compare the power of exclusion-based parentage inference to that of the likelihood-based method. Likelihood-based inference is much more powerful under many conditions; exclusion-based inference would require 40% more SNP loci to achieve the same accuracy as the likelihood-based approach in one common scenario. Our results demonstrate that SNPs are a powerful tool for parentage inference in large managed and/or natural populations.

Estimating the accuracy of genetic stock identification (GSI) that can be expected given a previously collected baseline requires simulation. The conventional method involves repeatedly simulating mixtures by resampling from the baseline, simulating new baselines by resampling from the baseline, and analyzing the simulated mixtures with the simulated baselines. We show that this overestimates the predicted accuracy of GSI. The bias is profound for closely related populations and increases as more genetic data (loci and (or) alleles) are added to the analysis. We develop a new method based on leave-one-out cross validation and show that it yields essentially unbiased estimates of GSI accuracy. Applying both our method and the conventional method to a coastwide baseline of 166 Chinook salmon ( Oncorhynchus tshawytscha ) populations shows that the conventional method provides severely biased predictions of accuracy for some individual populations. The bias for reporting units (aggregations of closely related populations) is moderate, but still present.