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Butterfly Model ODD Description

This file describes the model of PeБЂ™er et al. (2005). The description is taken from Section 3.4 of Railsback and Grimm (2012).

Purpose

(Модель бабочек на возвышенностях) описывает поведение бабочек, которые движутся по ландшафту в поисках возвышенных участков — так называемого hilltopping Она исследует, как взаимодействие поведения бабочек и особенностей ландшафта приводит к появлению виртуальных коридоров — узких путей, по которым проходит большинство бабочек. В модели есть две сущности: бабочки и квадратные участки земли (patch) - пятна. Земля разбита на сетку 150 на 150 пятна, у каждого пятна есть только одно состояние — высота (элевация). Бабочки имеют положение — на каком пятне находятся. Каждое движение бабочек происходит по шагам: на каждом шаге бабочка либо идет на соседнее пятно с наивысшей высотой, либо двигается случайно. Вероятность выбрать направление вверх контролируется параметром q (от 0 до 1). Если сгенерированное случайное число меньше q, бабочка поднимается вверх, иначе — двигается случайно.

Process Overview and Scheduling

There is only one process in the model: movement of the butterflies. On each time step, each butterfly moves once. The order in which the butterflies execute this action is unimportant because there are no interactions among the butterflies.

Design Concepts

The basic principle addressed by this model is the concept of virtual corridorsБЂ”pathways used by many individuals when there is nothing particularly beneficial about the habitat in them. This concept is addressed by seeing when corridors emerge from two parts of the model: the adaptive movement behavior of butterflies and the landscape they move through. This adaptive behavior is modeled via a simple empirical rule that reproduces the behavior observed in real butterflies: moving uphill. This behavior is based on the understanding (not included in the model) that moving uphill leads to mating, which conveys fitness (success at passing on genes, the presumed ultimate objective of organisms). Because the hilltopping behavior is assumed a priori to be the objective of the butterflies, the concepts of Objectives and Prediction are not explicitly considered. There is no learning in the model.

Sensing is important in this model: butterflies are assumed able to identify which of the surrounding patches has the highest elevation, but to use no information about elevation at further distances. (The field studies of PeБЂ™er 2003 addressed this question of how far butterflies sense elevation differences.)

The model does not include interaction among butterflies; in field studies, PeБЂ™er (2003) found that real butterflies do interact (they sometimes stop to visit each other on the way uphill) but decided it is not important to include interaction in a model of virtual corridors.

Stochasticity is used to represent two sources of variability in movement that are too complex to represent mechanistically. Real butterflies do not always move directly uphill, likely because of (1) limits in the ability of the butterflies to sense the highest area in their neighborhood, and (2) factors other than topography (e.g., flowers that need investigation along the way) that influence movement direction. This variability is represented by assuming butterflies do not move uphill every time step; sometimes they move randomly instead. Whether a butterfly moves directly uphill or randomly at any time step is modeled stochastically, using a parameter q that is the probability of an individual moving directly uphillinstead of randomly.

To allow observation of virtual corridors, we will define a specific БЂњcorridor widthБЂќ measure that characterizes the width of a butterflyБЂ™s path from its starting patch to a hilltop.

Initialization

The topography of the landscape (the elevation of each patch) is initialized when the model starts. Two kinds of landscapes are used in different versions of the model: (1) a simple artificial topography, and (2) the topography of a real study site, imported from a file containing elevation values for each patch. The butterflies are initialized by creating five hundred of them and setting their initial location to a single patch or small region.

Input Data

The environment is assumed to be constant, so the model has no input data.

Submodels

The movement submodel defines exactly how butterflies decide whether to move uphill or randomly. First, to БЂњmove uphillБЂќ is defined specifically as moving to the neighbor patch that has the highest elevation; if two patches have the same elevation, one is chosen randomly. БЂњMove randomlyБЂќ is defined as moving to one of the neighboring patches, with equal probability of choosing any patch. БЂњNeighbor patchesБЂќ are the eight patches surrounding the butterflyБЂ™s current patch. The decision of whether to move uphill or randomly is controlled by the parameter q, which ranges from 0.0 to 1.0 (q is a global variable: all butterflies use the same value). On each time step, each butterfly draws a random number from a uniform distribution between 0.0 and 1.0. If this random number is less than q, the butterfly moves uphill; otherwise, the butterfly moves randomly.

CREDITS AND REFERENCES

PeБЂ™er, G., Saltz, D. & Frank, K. 2005. Virtual corridors for conservation management. Conservation Biology, 19, 1997БЂ“2003.

PeБЂ™er, G. 2003. Spatial and behavioral determinants of butterfly movement patterns in topographically complex landscapes. Ph.D. thesis, Ben-Gurion University of the Negev.

Railsback, S. & Grimm, V. 2012. Agent-based and individual-based modeling: A practical introduction. Princeton University Press, Princeton, NJ.

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