Since ancient times, a natural number has been called perfect if it equals the sum of its proper divisors; e.g., 6 = 1+2+3 is a perfect number. In 1913, Dickson showed that for each fixed k, there are only finitely many odd perfect numbers with at most k distinct prime factors. We show how this result, and many like it, follow from embedding the natural numbers in the supernatural numbers and i...

Kin selection theory predicts altruism between related individuals, which requires the ability to recognize kin from non-kin. In insects, kin discrimination associated with altruistic behaviour is well-known in clonal and social species but in very few solitary insects. Here, we report that the solitary larvae of a non-social insect Aleochara bilineata Gyll. (Coleoptera; Staphylinidae) show kin...

BACKGROUND Authorship of peer-reviewed publications can create conflict among academics. OBJECTIVE To document authorship conflicts of academics at a tertiary faculty. METHODS An anonymous questionnaire eliciting authorship conflicts and knowledge of authorship criteria was administered online to 154 academic staff members at a New Zealand university. RESULTS 43 academics responded, a res...

In many organisms, individuals behave more altruistically towards relatives than towards unrelated individuals. Here, we conducted a study to determine if the performance of Arabidopsis thaliana is influenced by whether individuals are in competition with kin or non-kin. We selected seven pairs of genetically distinct accessions that originated from local populations throughout Europe. We measu...

What drives seemingly sellsh individuals in multi-agent systems to cooperate with each other? Our answer to the question is \kin preference." Kin preference helps to establish \habitats" that are composed of kin in population of rational agents. These habitats are resistant to invasion of enemies { that is, of non-kin. Results show the importance of kin preference in promoting cooperation and s...

Kin recognition is a useful ability for animals, facilitating cooperation among relatives and avoidance of excessive kin competition or inbreeding. In meerkats, Suricata suricatta, encounters between unfamiliar kin are relatively frequent, and kin recognition by phenotype matching is expected to avoid inbreeding with close relatives. Here, we investigate whether female meerkats are able to disc...

The proposition is advanced that many current measures of kinship strength may paradoxically indicate inadequate or weakened kinship structures. That is so because they rely on measures that emphasize continuous proximity. This curious paradox is a consequence of inattention to the relationship between technology, services, and proximity. This article presents nonproximity indicators of kinship...