The Natural Computing of Biogeography
By the 1940s Computer Science was engaged in the study of automatic computing. The necessary formalism for computability followed the initial achievements, with emphasis on information processing, Turing machines and computational complexity. Information processing has gained still more evidence in Computer Science lately, considering both natural and artificial processes (Denning P., 2008).
Indeed, information processes have been perceived in the essence of various phenomena in several fields of science. In the book The Invisible Future (Denning P. J., The Invisible Future: The Seamless Integration of Thecnology in Everyday Life, 2001), David Baltimore says “Biology is nowadays an information science”. However, if computing is concerned with the study of information processing, in what sense nature processes information? A consistent definition is given by Seth Lloyd (Lloyd S., 2002): “all physical system registers information and, by evolving in time, operating in its context, changes information, transforms information or, if you prefer, processes information”. Information here is interpreted as a measure of order, organization, a universal measure applicable to any structure, any system (Lloyd, 2006). Understanding nature as an information processing system is the fundamental basis of Natural Computing (de Castro, 2007). Several researchers, in many fields of science, have already studied nature in such context:
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Immune systems (Cohen, Real and artificial immune systems: computing the state of the body, Nature Reviews: Immunology, 2009; de Castro & Timmis, Artificial Immune Systems: A New Computational Intelligence Approach, 2002; Hart & Bersini, 2007);
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Ecosystems (de Aguiar, Barange, Baptestin, Kaufman, & Bar-Yam, 2009; Pasti, de Castro, & Von Zuben, 2011);
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Bees (Lihoreau, Chittka, & Raine, 2010; Maia & de Castro, 2012);
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Ants (Dorigo & Maniezzo, 1996; Pratt, Mallon, & Sumpter, 2002; Vittori, Talbot, & Gautrais, 2006);
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Genes (Holland, 2000; Kaufman & Ochumba, 1993);
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Bacteria (Mehta, Goyal, & Long, 2009; Xavier, Omar, & de Castro, 2011);
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Basic laws of nature (Dowek, 2012);
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All universe (Lloyd, 2006);
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Among many others, including (Brent & Bruck, 2006; Denning P. J., 2007; de Castro, 2007; Schwenk & Padilla, 2009).
Just as with biogeography, the object of study here are ecosystems: individuals, species and the environment. Ecosystems are highly complex and dynamic environments composed of a large number of interdependent variables defined in space and time (Harel, 2003; Jorgensen, Patten, & Stragkraba, 1992; Kauffman, 1996; Milne, 1998; Provata, Sokolov, & Spagnolo, 2008). They are usually studied by focusing on the interaction of their components, used to explain the emergence of behaviors (Cohen, 2000). The composition of ecosystems obeys physical and chemical laws, but there is no set of fundamental laws that explain how they work (Cohen & Harel, 2007). The application of reductionism for the understanding of how living systems work is widely used, but shows clear limitations when the goal is to extract universal laws to explain these systems (Cohen & Harel, 2007). It is possible to identify a scale of emergence going from simple molecules to a complex organism. Biogeography emphasizes the emergence of societies of living organisms (individuals and species), representing the highest level of Figure 1.
Figure 1. Emergence of behaviors and objects in different scales. (Based on the paper “Explaining a complex living system: dynamics, multi-scaling and emergence”, by Irun R. Cohen, 2007.)
Starting from the premise that nature processes information, the main goal of this chapter is to further investigate ecosystem computing under the perspective of biogeography (Pasti, de Castro, & Von Zuben, 2011).
As a first step towards understanding ecosystem computing, (Pasti, de Castro, & Von Zuben, 2011) formalized the concept of a metamodel, that will be adopted here to demonstrate how information in ecosystems may promote causality. By the mathematical formalism of the metamodel, it will be possible to build dynamic models that represent the spatio-temporal evolution of ecosystems in discrete states, including adaptive radiation, in which biogeographic processes are responsible for state changes.
This chapter is organized as follows. Section 2 reviews some elementary concepts for the proposal of Biogeographic Computation and its metamodel. In Section 3, the definition of information in ecosystems is explored and Section 4 briefly revisits and further extends the metamodel. In Section 5, a metamodel application is exemplified by means of nature-inspired biogeographic patterns. After some concluding remarks, Section 6 has a brief discussion on the future perspectives of biogeographic computation.