Various distance metrics and their induced norms are employed in the quantitative modeling of evolutionary dynamics. Minimization of these distance metrics when applied to evolutionary optimization are hypothesized to result in different outcomes. Here, we apply the different distance metrics to the evolutionary trait dynamics brought about by the interaction between two competing species infected by parasites (exploiters). We present deterministic cases showing the distinctive selection outcomes under the Manhattan, Euclidean and Chebyshev norms. Specifically, we show how they differ in the time of convergence to the desired optima (e.g., no disease), and in the egalitarian sharing of carrying capacity between the competing species. However, when randomness is introduced to the population dynamics of parasites and to the trait dynamics of the competing species, the distinctive characteristics of the outcomes under the three norms become indistinguishable. Our results provide theoretical cases when evolutionary dynamics using different distance metrics exhibit similar outcomes.

This article argues for five correctives to the current ethical debate about speciesism, and proposes normative, conceptual, methodological and experimental avenues to move this debate forward. Firstly, it clarifies the Principle of Equal Consideration of Interests and points out limitations of its scope. Secondly, it disambiguates between ‘favouritist’ and ‘species-relative’ views about moral treatment. Thirdly, it argues that not all moral intuitions about speciesism should be given equal weight. Fourthly, it emphasizes the importance of empirical research to corroborate statements about ‘folk speciesism’. Fifthly, it disambiguates between the moral significance of species and the moral status of their individual members. For each of these issues, it is shown that they have either been overlooked, or been given inapt treatment, in recent contributions to the debate. Building on the correctives, new directions are proposed for ethical inquiry into the moral relevance of species and species membership.