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The genealogy process is typically the most time-consuming part of-and a limiting factor in the success of-forensic genetic genealogy, which is a new approach to solving violent crimes and identifying human remains. We formulate a stochastic dynamic program that-given the list of matches and their genetic distances to the unknown target-chooses the best decision at each point in time: which match to investigate (i.e., find its ancestors and look for most recent common ancestors between the match and the target), which set of potential most recent common ancestors to descend from (i.e., find its descendants, with the goal of identifying a marriage between the maternal and paternal sides of the target's family tree), or whether to terminate the investigation. The objective is to maximize the probability of finding the target minus a cost associated with the expected size of the final family tree. We estimate the parameters of our model using data from 17 cases (eight solved, nine unsolved) from the DNA Doe Project. We assess the Proposed Strategy using simulated versions of the 17 DNA Doe Project cases, and compare it to a Benchmark Strategy that ranks matches by their genetic distance to the target and only descends from known common ancestors between a pair of matches. The Proposed Strategy solves cases ≈10 - fold faster than the Benchmark Strategy, and does so by aggressively descending from a set of potential most recent common ancestors between the target and a match even when this set has a low probability of containing the correct most recent common ancestor. Our analysis provides a mathematical foundation for improving the genealogy process in forensic genetic genealogy.

Significance Within the context of sexual assaults, we address a fundamental issue in criminal investigations: how much evidence to collect and process. Using data from the San Francisco Police Department, we show that machine learning algorithms outperform sexual assault forensic examiners at identifying probative samples. Relative to selective testing of samples, testing all DNA samples in a sexual assault kit more than doubles the number of sexual assault kits generating a DNA profile that can be entered into the criminal DNA database, at only a slightly lower benefit-to-cost ratio. Our results suggest that the yield of DNA profiles for the database would increase another 47.2% by collecting samples from the three most probative locations (as deemed by the machine learning algorithm)., Although the backlog of untested sexual assault kits in the United States is starting to be addressed, many municipalities are opting for selective testing of samples within a kit, where only the most probative samples are tested. We use data from the San Francisco Police Department Criminalistics Laboratory, which tests all samples but also collects information on the samples flagged by sexual assault forensic examiners as most probative, to build a standard machine learning model that predicts (based on covariates gleaned from sexual assault kit questionnaires) which samples are most probative. This model is embedded within an optimization framework that selects which samples to test from each kit to maximize the Combined DNA Index System (CODIS) yield (i.e., the number of kits that generate at least one DNA profile for the criminal DNA database) subject to a budget constraint. Our analysis predicts that, relative to a policy that tests only the samples deemed probative by the sexual assault forensic examiners, the proposed policy increases the CODIS yield by 45.4% without increasing the cost. Full testing of all samples has a slightly lower cost-effectiveness than the selective policy based on forensic examiners, but more than doubles the yield. In over half of the sexual assaults, a sample was not collected during the forensic medical exam from the body location deemed most probative by the machine learning model. Our results suggest that electronic forensic records coupled with machine learning and optimization models could enhance the effectiveness of criminal investigations of sexual assaults.

We analyze confirmed cases and new hospitalizations in Wisconsin in the weeks surrounding the April 7, 2020 election, and find no evidence of a surge in SARS-CoV-2 transmission.

Motivated by the debate over how to deal with the huge backlog of untested sexual assault kits in the U.S.A., we construct and analyze a mathematical model that predicts the expected number of hits (i.e., a new DNA profile matches a DNA sample in the criminal database) as a function of both the proportion of the backlog that is tested and whether the victim-offender relationship is used to prioritize the kits that are tested. Refining the results in Ref. (Criminol Public Policy, 2016, 15, 555), we use data from Detroit, where government funding was used to process ≈15% of their backlog, to predict that prioritizing stranger kits over nonstranger kits leads to only a small improvement in performance (a 0.034 increase in the normalized area under the curve of the hits vs. proportion of backlog tested curve). Two rough but conservative cost-benefit analyses-one for testing the entire backlog and a marginal one for testing kits from nonstranger assaults-suggest that testing all sexual assault kits in the backlog is quite cost-effective: for example, spending ≈$1641 to test a kit averts sexual assaults costing ≈$133,484 on average.