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The DNA technology applied to forensic science has improved significantly in recent years. As a result of these advancements, DNA profiles can be generated from a low-template amount of DNA. This advancement, however, can lead to more complex mixtures due to the instrumentation picking up trace amounts of DNA. This leads to the need for these more challenging profiles to be interpreted. Due to the lack of standardization in DNA profile interpretation, one complex DNA profile is likely to draw several different conclusions from DNA analysts when assessing the number of contributors (NoC). Probabilistic genotyping software (PGS) is a possible solution to the problems of complex DNA profile interpretations. DNA-View® Mixture Solution™, developed by Dr. Charles Brenner, is a continuous modelling PGS that considers genotypes, peak height, stutter, dropout, and other artifacts that result from stochastic effects in the interpretation of DNA profiles. Mixture Solution has the potential to minimize some of the uncertainty inherent in DNA analysis of profiles having multiple contributors. In this project, DNA mixture analysis with Mixture Solution was applied to two and three-person mixtures having ratios ranging from 1:1 to 8:1 and 1:1:1 to 8:1:8. Two scenarios with several hypotheses were tested regarding each contributor as if they were the person of interest (POI) in a real case. Mixture Solution assigns the most favorable hypothesis for and against the POI and calculates an LR representing the comparison of those two hypotheses. In the final reports, trends previously observed in two-person mixture ratios were also observed in three-person mixtures. The main factor driving low LR assignment in three-person mixtures is low template DNA. Low peak heights and dropout are the factors driving low LR assignment. The factors that make manual DNA profile interpretation challenging can also challenge PGS. However, the robustness of Mixture Solution was demonstrated throughout the project with complex three-person mixtures.

Investigation of stains from crime scenes are commonly used in the search for criminals. At The National Laboratory of Forensic Science, where these stains are examined, a number of questions of theoretical and practical interest regarding the databases of DNA profiles and the strength of DNA evidence against a suspect in a trial are not fully investigated. The first part of this thesis deals with how a sample of DNA profiles from a population is used in the process of estimating the strength of DNA evidence in a trial, taking population genetic factors into account. We then consider how to combine hypotheses regarding the relationship between a suspect and other possible donors of the stain from the crime scene by two applications of Bayes’ theorem. After that we assess the DNA profiles that minimize the strength of DNA evidence against a suspect, and investigate how the strength is affected by sampling error using the bootstrap method and a Bayesian method. In the last part of the thesis we examine discrepancies between different databases of DNA profiles by both descriptive and inferential statistics, including likelihood ratio tests and Bayes factor tests. Little evidence of major differences is found.

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