= 1000 or all? turtles [finished?] = 0 [stop]
end ; of go
to move ; The butterfly move procedure, in turtle context
; Decide whether to the highest
; surrounding patch with probability q
ifelse random-float 1 < q
[
uphill elevation ; Move uphill
set color red
]
[
move-to one-of neighbors ; Otherwise move randomly
set color blue
]
set visited? true
; ask turtles with [ chosen? ] [ set label precision elevation 0 ]
end ; of move procedure
to build-hills
ask patches
[
; Patch elevation decreases linearly with distance from the center
; of hills. Hills are at (30, 30) and (120, 100). The first hill is
; 100 units high. The second hill is 50 units high.
let elev1 100 - distancexy 30 30
let elev2 50 - distancexy 120 100
ifelse elev1 > elev2
[set elevation elev1]
[set elevation elev2]
]
end
to input-elevation
file-open "ElevationData.txt"
while [not file-at-end?]
[
let next-x file-read
let next-y file-read
let next-elevation file-read
ask patch next-x next-y [set elevation next-elevation]
]
file-close
end
to color-patches
ifelse patch-coloring = "elevation"
[
let max-elevation max [elevation] of patches
let min-elevation min [elevation] of patches
ask patches [ set pcolor scale-color green elevation min-elevation max-elevation]
]
[
let max-turtles max [count turtles-here] of patches
let min-turtles 0
ask patches [ set pcolor scale-color cyan (count turtles-here) min-turtles max-turtles]
]
end
to update-display
color-patches
ifelse show-butterflies?
[ ask turtles [show-turtle]]
[ ask turtles [hide-turtle]]
ifelse show-labels?
[ ask turtles with [chosen?] [set label elevation] ]
[ ask turtles with [chosen?] [set label ""] ]
end
; Corridor width is the number of patches visited by butterflies
; divided by the average distance a butterfly is from its initial position
;
; If a butterfly moves in a straight line, the number of patches visited
; equals the distance from its initial patch, so corridor-width = 1
; The more a butterfly wanders off a straight line, the more patches
; it will visit, so the wider the corridor will be.
;
to-report corridor-width
let pcount count patches with [visited?]
let dist mean [distance initial-patch] of turtles
ifelse dist = 0
[report 1]
[report pcount / dist]
end
to-report fraction-crowded
let crowd-count sum [count turtles-here] of patches with [count turtles-here >= 4]
report crowd-count / num-butterflies
end]]>corridor-widthmean [elevation] of turtlesmean [count turtles-here] of patches with [any? turtles-here]fraction-crowdedhistogram [count turtles-here] of patchesplot 100 * fraction-crowdedplot mean [elevation] of turtles2. Simulations last for 1000 time steps; the length of one time step is not specified but should be about the time it takes a butterfly to move 25--35 m (the distance from one cell to one of its neighbor cells).
## 3. 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.
## 4. Design Concepts
The _basic principle_ addressed by this model is the concept of virtual corridors---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 Pe'er 2003 addressed this question of how far butterflies sense elevation differences.)
The model does not include _interaction_ among butterflies; in field studies, Pe'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.
_Collectives_ are not represented in this model.
To allow _observation_ of the two patterns used to define the model's usefulness, we use graphical display of topography and butterfly locations. Observing virtual corridors requires a specific "corridor width" measure that characterizes the width of butterfly paths from their starting patches to hilltops.
## 5. 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 dispersing them throughout the landscape: each butterfly's initial location is set to a patch selected randomly from among all patches.
## 6. Input Data
The environment is assumed to be constant, so the model has no input data.
## 7. Submodels
The movement submodel defines exactly how butterflies decide whether to move uphill or randomly. First, to "move uphill" 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. "Move randomly" is defined as moving to one of the neighboring patches, with equal probability of choosing any patch. "Neighbor patches" are the eight patches surrounding the butterfly'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
Pe'er, G., Saltz, D. & Frank, K. 2005. Virtual corridors for conservation management. _Conservation Biology_, 19, 1997--2003.
Pe'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. 2018. _Agent-based and individual-based modeling: A practical introduction, Second edition_. Princeton University Press, Princeton, NJ.]]>setup repeat 75 [ go ]setupgocorridor-widthsetupgocorridor-widthsetupgocorridor-widthmean [elevation] of turtlesmean [count turtles-here] of patches with [any? turtles-here]fraction-crowded