Title: Creative extinction: emergent patterns by extinction dynamics of large communities
Author: Kei Tokita
Affiliation: Cybermedia Center, Graduate School of Science and Graduate School of Frontier Biosciences, Osaka University

Abstract: While extinction is negatively interpreted in nature conservation, it can be worth examining that extinction also plays a positive role for emergent patterns of a community, such as hierarchy structures of interaction webs, selection patterns about which species becomes extinct and survives, and typical forms of species abundance distributions (SADs). These patterns are actually "natural sculptures" and the chisel may be termed "creative extinction", an imitation of the economic term "creative destruction" to denote a "process of industrial mutation that incessantly revolutionizes the economic structure from within, incessantly destroying the old one, incessantly creating a new one [1]". To illuminate the creative extinction, the present study focuses on several emergent patterns of community, which are developed by extinction dynamics of three types of a random community model [2,3] with asymmetric [4], antisymmetric [5] and symmetric [6,7] interspecies interactions, respectively. The theory of the random community model has had a great impacts on community ecology [2,3]. Although a random community is not believed to evolve in nature, it can be accidentally created by environmental or artificial causes, such as biotic fusion [4] occurring at various scales from an introduction or an invasion of a single exotic species to large-scale integration of isolated biotas by, e.g. a canal construction or isthmus formation. In the context of mathematical sciences, the random community model is well worth studying because the dynamics shows every possible complex behavior such as chaos. One of the significant features of extinction dynamics of a random community model is an uncertainty of survivors, that is, the dynamics is too chaotic to predict a composition of non-extinct species even if it starts from almost same initial states. The system therefore has a large number of equilibrium states and their basin-size distribution obeys power law [4], meaning that there exists no typical survivor. Second characteristic is a hierarchical community structure self-organized through extinction dynamics [5,7]. Thirdly, well-known SADs are emerged after mass extinction. In the case of food-web models [5], after mass extinction of about 50% species, the resulting SAD covers the three most widely applied models: the lognormal distribution [8], Fisher's logseries [9] and MacArthur's broken stick model [10]. Also for a plant community [7], SAD like a left-skewed lognormal distribution [11] is observed after mass extinctions in which more than 95% of species get extinct. Extinction moreover can trigger off diversification in some cases [6], which is another significance of creative extinction exemplified by community assembly model with extinction and mutation. Implications and predictions of the present theoretical framework is also given in association with environmental conservation.

References:
[1] Schumpeter, J. A., "Capitalism, Socialism and Democracy", New York: Harper & Row, (1942).
[2] Gardner, M. R. and Ashby, W. R., "Connectance of large dynamic (cybernetic) systems - critical values for stability", Nature 228 (1970) 784.
[3] May, R. M., "Will a large complex system be stable?", Nature 238 (1972) 413-414.
[4] Tokita, K. and Yastuomi, A., "Mass extinction in a dynamical system of evolution with variable dimension", Physical Review E 60 (1999) 842-847.
[5] Chawanya, T. and Tokita, K., "Large-dimensional replicator equations with antisymmetric random interactions", Journal of Physical Society of Japan 71-2 (2002) 429-431.
[6] Tokita, K. and Yastuomi, A., "Emergence of a complex and stable network in a model ecosystem with extinction and mutation", Theoretical Population Biology 63 (2003) 131-146.
[7] Tokita, K., "Species abundance patterns in complex evolutionary dynamics", Physical Review Letters 93 (2004) 178102-1~4.
[8] Preston, F. W., "The canonical distribution of commonness and rarity: Part 1 and 2", Ecology 43 (1962) 185-215 and 410-432.
[9] Corbet, A. S., Fisher, R. A. and Williams, C. B., "The relation between the number of species and the number of individuals in a random sample of an animal population", Journal of Animal Ecology 12 (1943) 42-58.
[10] MacArthur, R. H., "On the relative abundance of species", American Naturalist 94 (1960) 25-36.
[11] Nee, S., Harvey, P. H. and May R. M., "Lifting the veil on abundance patterns", Proc. R. Soc. London B 243 (1991) 161-163.


© Copyright 2013 Kei Tokita, Powered by Pukiwiki.  Last-modified: Sun, 23 Jun 2013 13:50:21 JST (2334d)   リロード   新規 編集 凍結 差分 添付 複製 改名   トップ 一覧 検索 最終更新 バックアップ   ヘルプ   最終更新のRSS