The inconclusive category, entropy, and forensic firearm identification.

There has been extensive recent discussion of the difficulty in estimating meaningful error rates in forensic firearms examinations, and other areas of pattern evidence. The 2016 President's Council of Advisors on Science and Technology (PCAST) report was clear in criticizing many forensic disciplines as lacking the types of studies that would provide error rate measurements seen in other scientific fields. However, there is a substantial lack of consensus on the approach to measuring an "error rate" for fields such as forensic firearm examination that include in the conclusion scale the "inconclusive" category, as occurs in the Association of Firearm and Tool Mark Examiners (AFTE) Range of Conclusions and many other such fields. Many authors appear to assume the error rate calculated in the binary decision model is the only appropriate way to report errors, but there have been attempts made to adapt the error rate from the binary decision model to scientific fields in which the inconclusive category is viewed as a meaningful outcome of the examination process. In this study we present three neural networks of differing complexity and performance trained to classify the outlines of ejector marks on cartridge cases fired from different firearm models, as a model system for examining the performance of various metrics of error in systems using the inconclusive category. We also discuss an entropy, or information, based method to assess the similarity of classifications to ground truth that is applicable to range of conclusion scales, even when the inconclusive category is used.

Phenotypic plasticity, heterochrony and ontogenetic repatterning during juvenile development of divergent Arctic charr (Salvelinus alpinus).

Phenotypic plasticity is a developmental process that plays a role as a source of variation for evolution. Models of adaptive divergence make the prediction that increasing ecological specialization should be associated with lower levels of plasticity. We tested for differences in the magnitude, rate and trajectory of morphological plasticity in two lake populations of Arctic charr (Salvelinus alpinus) that exhibited variation in the degree of resource polymorphism. We reared offspring on diet treatments that mimicked benthic and pelagic prey. Offspring from the more divergent population had lower levels of morphological plasticity. Allometry influenced the rate of shape change over ontogeny, with differences in rate among ecomorphs being minimal when allometric variation was removed. However, plasticity in the spatial trajectory of development was extensive across ecomorphs, both with and without the inclusion of allometric variation, suggesting that different aspects of shape development can evolve independently.

Why the null matters: statistical tests, random walks and evolution.

A number of statistical tests have been developed to determine what type of dynamics underlie observed changes in morphology in evolutionary time series, based on the pattern of change within the time series. The theory of the 'scaled maximum', the 'log-rate-interval' (LRI) method, and the Hurst exponent all operate on the same principle of comparing the maximum change, or rate of change, in the observed dataset to the maximum change expected of a random walk. Less change in a dataset than expected of a random walk has been interpreted as indicating stabilizing selection, while more change implies directional selection. The 'runs test' in contrast, operates on the sequencing of steps, rather than on excursion. Applications of these tests to computer generated, simulated time series of known dynamical form and various levels of additive noise indicate that there is a fundamental asymmetry in the rate of type II errors of the tests based on excursion: they are all highly sensitive to noise in models of directional selection that result in a linear trend within a time series, but are largely noise immune in the case of a simple model of stabilizing selection. Additionally, the LRI method has a lower sensitivity than originally claimed, due to the large range of LRI rates produced by random walks. Examination of the published results of these tests show that they have seldom produced a conclusion that an observed evolutionary time series was due to directional selection, a result which needs closer examination in light of the asymmetric response of these tests.

Spatiotemporal reorganization of growth rates in the evolution of ontogeny.

Heterochrony, evolutionary changes in rate or timing of development producing parallelism between ontogeny and phylogeny, is viewed as the most common type of evolutionary change in development. Alternative hypotheses such as heterotopy, evolutionary change in the spatial patterning of development, are rarely entertained. We examine the evidence for heterochrony and heterotopy in the evolution of body shape in two clades of piranhas. One of these is the sole case of heterochrony previously reported in the group; the others were previously interpreted as cases of heterotopy. To compare ontogenies of shape, we computed ontogenetic trajectories of shape by multivariate regression of geometric shape variables (i.e., partial warp scores and shape coordinates) on centroid size. Rates of development relative to developmental age and angles between the trajectories were compared statistically. We found a significant difference in developmental rate between species of Serrasalmus, suggesting that heterochrony is a partial explanation for the evolution of body shape, but we also found a significant difference between their ontogenetic transformations; the direction of the difference between them suggests that heterotopy also plays a role in this group. In Pygocentrus we found no difference in developmental rate among species, but we did find a difference in the ontogenies, suggesting that heterotopy, but not heterochrony, is the developmental basis for shape diversification in this group. The prevalence of heterotopy as a source of evolutionary novelty remains largely unexplored and will not become clear until the search for developmental explanations looks beyond heterochrony.