Lynx and Hares Model Equations
Lynx and Hares Model Equations
Variable Descriptions:
area: land area (constant) in which lynx and hares are confined
Lynx: total number of total number of lynx living at some point in time
Hares: total number of hares living at some point in time
hare_density: number of hares living per unit area at some point in time
hare_natality: annual birth rate for hares
lynx_natality: annual bith rate for lynx
hare_births: number of hares born during a time step
lynx_births: number of lynx born during a time step
hare_kills_per_lynx: the number of hares one lynx kills in one year
hare_mortality: annual death rate for hares (not constant)
lynx_mortality: annual death rate for lynx (not constant)
hare_deaths: number of hares that die during one time step
lynx_deaths: number of lynx that die during one time step
t: time (years)
dt: time step (decimal fraction of one year)
Stella Algorithm (w/ initializations for a sample run)
Initializations:
area = 1E3
INIT Hares = 5E4
hare_natality = 1.25
hare_births = Hares*hare_natality
INIT Lynx = 1250
hare_density = Hares/area
hare_kills_per_lynx = GRAPH(hare_density)
(0.00, 3.89e-318), (50.0, 50.0), (100, 100), (150, 150), (200, 200), (250, 250), (300, 300), (350, 350), (400, 400), (450, 450), (500, 500)
hare_deaths = Lynx*hare_kills_per_lynx
lynx_natality = .25
lynx_births = Lynx*lynx_natality
lynx_mortality = GRAPH(hare_density)
(0.00, 0.5), (10.0, 0.45), (20.0, 0.4), (30.0, 0.35), (40.0, 0.3), (50.0, 0.25), (60.0, 0.2), (70.0, 0.15), (80.0, 0.1), (90.0, 0.05), (100, 0.005)
lynx_deaths = Lynx*lynx_mortality+PULSE(100,2,5e3)
Runtime Equations:
Hares(t) = Hares(t - dt) + (hare_births - hare_deaths) * dt
Lynx(t) = Lynx(t - dt) + (lynx_births - lynx_deaths) * dt
hare_births = Hares*hare_natality
hare_density = Hares/area
hare_kills_per_lynx = GRAPH(hare_density)
(0.00, 3.89e-318), (50.0, 50.0), (100, 100), (150, 150), (200, 200), (250, 250), (300, 300), (350, 350), (400, 400), (450, 450), (500, 500)
hare_deaths = Lynx*hare_kills_per_lynx
lynx_births = Lynx*lynx_natality
lynx_mortality = GRAPH(hare_density)
(0.00, 0.5), (10.0, 0.45), (20.0, 0.4), (30.0, 0.35), (40.0, 0.3), (50.0, 0.25), (60.0, 0.2), (70.0, 0.15), (80.0, 0.1), (90.0, 0.05), (100, 0.005)
lynx_deaths = Lynx*lynx_mortality+PULSE(100,2,5e3)
Run the Lynx and Hares Model
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