Will there be predators tomorrow

Figure 1 Real individuals have to make adaptive decisions all the time, that is, decisions that minimize their risk of starving or being eaten, and maximizing the chance to reproduce. For example, for many fish species vertical migration is a key behavior. Moving up usually means better conditions for feeding, but also higher risk of predation. The very decision made by an individual depends on many internal and external variables, that is, we assume the fish knows, or at least has estimates, of these variables. Modified from Strand E (2003) Adaptive Models of Vertical Migration in Fish. Doctoral thesis, University of Bergen, Bergen, Norway, with permission from Espen Strand.

These three aspects of individual-based ecology are hard to deal with mathematically, for example, using calculus. Therefore IBMs have to be formulated as simulation models that are run on computers. Computers with enough power for running IBMs are generally available since the end of the 1980s, which is the time when individual-based modeling became a declared branch of ecological modeling. Nowadays the IBM approach is widely used in ecology but the term 'individual-based' is used in a very broad sense. Some IBMs include only one individual-based aspect, for example, the discreteness of individuals, or local interactions, but otherwise are very similar to classical mathematical models, whereas other IBMs include detailed descriptions of the individuals' fitness-seeking behavior.

In the following, we first describe the elements of IBMs, which have to be specified by the modeler. Then we explain a general modeling strategy that can be used to optimize the complexity of IBMs and to deal with uncertainty in model structure and parameters (pattern-oriented modeling). Then we describe how IBMs are analyzed, and finally we briefly present three example models and give an outlook on the future of individualbased modeling. The emphasis of the following is thus more on what IBMs are and how they are developed and analyzed than on what so far has been achieved with the individual-based approach.

Note that IBMs are referred to as 'agent-based models' (ABMs) in disciplines that deal with human agents, for example, economics, social sciences, and demography. In these disciplines, the emphasis of ABMs always was on the agent's adaptive decisions, whereas most IBMs in ecology so far focus on individual variability and local interactions. But behavioral decisions are increasingly considered also in ecology, so no distinction between 'individual-based' and 'agent-based' should be made in the future. Likewise, 'multiagent systems' are agent-based models which have their roots in computer science and artificial intelligence, but if they are used to tackle ecological problems, they are not fundamentally different from IBMs or ABMs.

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