A Model for Evolution and Extinction

Abstract

This article gives a brief introduction to the mathematical modeling of large-scale biological evolution and extinction. We give three examples of simple models in this field: the coevolutionary avalanche model of Bak and Sneppen, the environmental stress model of Newman, and the increasing fitness model of Sibani, Schmidt, and Alstrøm. We describe the features of real evolution which these models are intended to explain and compare the results of simulations against data drawn from the fossil record.

Research of Newman’s Biological Evolution Model

“…Следуя работам [3][4][5][6][7][8], воспользуемся приближением среднего по-ля, пренебрегая флуктуациями распределения видов по устойчивости r( ). Темп его изменения с течением времени определяется формулой…”

“…Второй подход, базирующийся на том, что эволюция связана с экзогенными причинами, был развит М. Ньюманом в модели с ко-герентным шумом [3][4][5][6][7][8], исследованию которой посвящена настоя-щая работа. Модель построена в предположении отсутствия какого-либо взаимодействия между видами.…”

Biodiverzitet - Pojam i fenomenologija / Biodiversity - Notion and Phenomenology

“…Tokom procesa evolucije taksoni se pojavljuju i nestaju; u tipičnom slučaju, pojedina vrsta se izgubi oko 10 miliona godina nakon prve pojave u geološkim slojevima (Roberts & Newman 1996). Izumiranje živih oblika je normalan sastavni dio evolucije, iako nije uvijek pouzdano utvrđen faktor koji je u tome bio presudan, "loši geni ili loša sreća" (Raup 1991).…”

Selective advantage of topological disorder in biological evolution

“…The list of models studied starts with large-scale properties of the evolutionary process-massive global extinctions-and ends with the works which are aimed at following the replicative behavior of the chemical structures holding information, namely DNA molecules. A lot of effort has been devoted to this area recently [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] and still new fruitful ideas emerge [17,18,19].…”