Predator Prey dynamics with a generative ABM

1. Population Dynamics:
The Red Queen Effect and
Attractors in Evolution
Ted Carmichael – SwarmFest – July 11, 2015

2. Outline
• Introducing the General Ecosystem model
• Assumptions of the model
• Demo: Stepped pattern of biomass accrual
• Considerations for field studies
• The Red Queen Hypothesis
• Predators: Effects of Effectiveness
• Impacts on Evolutionary Pressures

3. The Marine Ecosystem Model
Three trophic levels:
• Food
• Prey (Fish)
• Predators
Model assumptions:
• Both predators and prey
reproduce as a function of
how much they eat.
• Completely homogeneous
environment.
• The agents move randomly
and eat once per turn if there
is food available.
• All agents have a limited
“lifetime.”

4. The Marine Ecosystem Model
Validation: Lotka-Volterra, Gause's Law,
Paradox of Enrichment, Stepped
pattern of biomass accrual
• Carmichael & Hadzikadic, Advances in Complex
Systems, 2013

5. The Marine Ecosystem Model
Stepped pattern of biomass accrual
• Oksanen, et. al, 1981
• Mathematical predictions of population changes
based on changes in primary enrichment
Model Assumption: prey have a constant supply of food.
- what happens if the food supply changes?
Demo: increasing the food supply to the prey. What happens? Will:
1) the prey population increase?
2) the predator population increase?
3) both prey and predator increase in population size?

6. Considerations for Field Studies
Average Age is an important attribute
●
Can give us important inferences on existent populations
●
Rarely collected systematically
●
Replacement rate and equilibrium population

7. The Red Queen Hypothesis
“Now, here, you see, it takes all the running you can do, to
keep in the same place.” -Through the Looking Glass
●
“Arms race” between predators and prey
●
Assuming the current state is a “basin of attraction,” and
the arms race reaches a terminus, what accounts for the
trade-offs that prevent further advancements?
●
Diversity among prey – old, young, sick, unlucky
●
Prey sharing … leads to cooperative strategies, which leads
to “free riders,” which limits positive evolution
●
Anything else?

8. The Red Queen Hypothesis
Another piece of the evolutionary puzzle … the effects on
predator and prey populations via two different methods
of reducing predator effectiveness:
●
Decrease the “success rate” of predators: i.e., sometimes
the predators try to eat a prey but “miss” (the prey
escapes)
●
Reduce the “turns per tick” of the predators, from 6 to 4.
Predators will live longer … 600 “turns” across more
“ticks”

9. The Red Queen Hypothesis
“Success rate”
reduced by 1/3rd.
“Turns per tick”
reduced by 1/3rd.

10. Conclusions:
●
There are many non-intuitive results, even in a very
simple model of population dynamics
●
Average age for a population is important, and may
help infer attributes (such as consumption rate)
that cannot easily be gathered
●
Not all efficiency gains produce population-level
benefits, and some may even be detrimental to a
species
●
Some of these non-intuitive results may help
explain evolutionary pressures on a species

11. Conclusions:
Thank you!

12. The Competitive Exclusion Principle
The competitive exclusion principle states that two (or
more) species competing for the same resources, and
sharing the same predators, cannot continually co-
exist if all other ecological factors are constant.