Application of the theory of evolutionary optimality to determine premature and excess mortality in the Lotka model

Within the framework of the Lotka model written in the form of McKendrik - Von Foerster equations, known as evolutionary optimality principle necessary conditions for stability of solutions, having nonzero values for survived populations, are presented in terms of excess mortality and of maximal life expectancy. Two variants of dependence of individual mortality on the population structure are analyzed: dependence on the total and on the relative with respect to the number of newborns. Substantial biological interpretations of the obtained mathematical results are discussed. In particular, the paradox of immortality and the need for a lively way cutting for maximal life expectancy are presented.