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ZenthWolf / EvoSim

Evolution Simulator written in Python
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Population Dynamics - Pred/Prey model #6

Open ZenthWolf opened 4 years ago

ZenthWolf commented 4 years ago

Beast/Food simulations should be able to mirror Pred/Prey (Feast/Famine) population models with right parameterization. Currently, population seems to converge to carrying capacity.

ZenthWolf commented 4 years ago

For discussion of analytic model, use following convention from http://www.tiem.utk.edu/~gross/bioed/bealsmodules/predator-prey.html :

P : Predator (beast) population

N : Prey (food) population

t : time

r : Prey growth rate

a': search/attack efficiency

q : Predator mortality rate

c : Predator to Prey conversion efficiency

ZenthWolf commented 4 years ago

Considerations:

Population model is an instantaneous calculation, but simulation uses discrete generations - probably mock up discretized formula in Mathematica at some point

Discretization also at odds with countable populations (no atto-beasts), so modelling will look very different, but is useful basis.

ZenthWolf commented 4 years ago

Predator mortality rate:

dP/dt = -qP

Analytic reading: At all times, a set percentage of predators can be assumed to be dying, regardless of circumstance.

Current Simulation implementation: All predators are dying until proven otherwise- this ties death, life, and reproduction in one go.

Possible development: A set percentage of beasts could be culled (or a die roll per beast). Could also justify reverse- some beasts may be spared death similarly

ZenthWolf commented 4 years ago

Predator birth rate:

dP/dt = ca'PN

Analytic reading: Predators grow proportion to their population and prey population. Here, only "a' %" of prey is used, at a trophic efficiency, c.

Current Simulation: Predator growth is proportional to either predator population or prey population, but not both. Trophic efficiency is seen by needing multiple food to birth, but a' is uncontrolled (very nearly 1 in current setup at late stages - almost all food is exploited)

Possible development: May introduce a' by making a percent of food not available each gen. Proportionality to PN is unclear.

ZenthWolf commented 4 years ago

Prey growth rate:

dN/dt = rN

Analytic reading: Prey grows exponentially.

Current Simulation: Each starting food has a chance to reproduce, leading to exponential growth.

Development: Only turning r remains.

ZenthWolf commented 4 years ago

Prey mortality rate:

dN/dt = -a'PN

Analytic reading: Prey dies proportional to predator growth (see details about predator growth).

Current simulation: Analytic reading is spot on, but all the problems with predator/beast growth remain.

ZenthWolf commented 4 years ago

Above lines may be updated with progress.