Stationary Populations

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  Stationary Populations
  Arni S.R. Srinivasa Rao
  Understanding the properties of stationary populations is treated in this talk from the perspective of mathematical history of population dynamics as well as modern experiments conducted on insects longevity. The subject of population dynamics is hundreds of years old and is been studied by famous mathematicians such as Fibinocci, Alambert Daniel Bernoulli, Euler, etc, Concepts such as stability and stationarity of population are essential pillars of population dynamics. In the last century the works by Alfred Lotka laid the foundation for the population stability theory, which was developed further by William Feller through renewal equations. Ansley Coale and Norman Ryder (during 1960s and 1970s) brought several properties of stationary populations from the Life Table perspective. table perspective. During the last decade (early 2000s) new identities of stationary populations have emerged regarding life-lived and left, first with work by James Carey and his UC Davis colleagues Hans Mueller and Jane-Ling Wang, followed by contributions by James Vaupel (who coined the identity Carey's Equality) and Josh Goldstein. Rao & Carey (2013) have proved a fundamental theorem in stationary population using insights from Carey's equality by blending with algebraic and combinatory principles. These newer results bring similar patterns that are comparable to renewal type of theory due to Lotka, Feller and others. This talk concludes with implications of Carey's equality in other areas of population dynamics, including in non-stationary populations and direction of research in stationary populations.