Many aspects of biology, such as population genetics and senescence, are predicated on identifying individuals and generations. Conventional demarcations of individuals and generations, such as physiological autonomy, unicellular bottlenecks, and alternation of generation, are rife with problems. Do physically separated cuttings or plant ramets constitute separate individuals or generations? Are chimaeras one or more individuals? To resolve these problems, Clarke : 321–361, 2012) proposed that individuals are circumscribed by mechanisms that constrain heritable variance in fitness. Simultaneously, Gorelick and Heng : (...) 1088–1098 2011) showed that sex constrains heritable variance Therefore, for eukaryotes, meiosis and karyogamy provide a consistent way to demarcate individuals and generations. Epigenetic reset associated with meiosis and karyogamy rejuvenates the next generation, but not the parent that engaged in the sex act. Wholesale epigenetic resets that probably only occur with meiosis and karyogamy imply that monozygotic twins are two different individuals, but apomictic progeny are diffuse parts of one disaggregated individual. Mitotic heritability circumscribes an individual, whereas meiotic heritability demarcates new individuals and generations. (shrink)

Extensive empirical work has shown that species richness decreases roughly exponentially or quadratically with latitude. What appears to be a latitudinal gradient in fact may simply be a negative correlation of latitude with area at that latitude, due to convergence of lines of meridian at the poles. There is simply less area at high latitudes, which means fewer niches and fewer opportunities for speciation, hence diminished biodiversity at high latitudes. Similarly, analytic geometry of a cone shows that species number should (...) decrease linearly with altitude on a conical mountain. Here, I provide an explicit mathematical model of the area hypothesis of species richness along latitude and altitude gradients. I re-analyze a previously published latitudinal gradient dataset and show that species number is a linear function of the predicted area and that species number is more fully explained by predicted area than by a quadratic function of latitude. However, analytic geometry is not needed if precise measures of area are known. (shrink)