When put together in the petri dish, prey and predator show a characteristic cyclic dynamic: when prey population explodes, predator follows it after a short time; that increases the predation rate so prey population starts to fall, which makes predators start to starve and die and so on, the cycles continues (see graphics below).

That behavior is described by a simple model of differential equations: the Lotka-Volterra model. It has two parameters for each specie population: one for intrinsic exponential growing or decreasing in absence of the other species, and one for the response to the interaction with the other species.

As I said, the prey population dynamic has two parameters:

**r**(the proportional growing rate of prey in absence of predator) and

**d**(the decreasing of that value due to hunting). Since the simulation has a discrete logging interval of 1 h,

**dX/dt**can be assumed as

**ΔX/Δt**. Thus,

**d**and

**r**are the slope and intercept of the following inear equation respectively:

**ΔX/(Δt.X)= r-dY**

**ΔX**=increment in prey number from one hour to next

**Δt**=1 h

**X**=prey number at the time considered

**Y**=predator number at the time considered

Similarly, the predator population parameters,

**m**and

**b**, can be calculated analyzing the intercept and slope of the following equation respectively:

**ΔY/(Δt.Y)=-m+ bX**

I tried to estimate the four parameters using the log file data of a series of 6 simulations. I assigned red color to the predator larvae and adult cells and green color to the prey adult cells so I could track their populations. The conditions of the simulations were: dish-diameter=3.0, nutrient rate= 15(max.), max_cell_count=6000, logging_interval=1 h.

(Cycles: red = predator, green = prey

Scatterplots: each color corresponds to a different simulation)

Finally, in order to check if the estimation of the parameters was appropriate, I computed the prey and predator number values at an hypothetical equilibrium as a gross indicator. This can be easily done by replacing the obtained parameters in the equations above and equalizing these to zero (i.e. looking what values X and Y do take in the virtual case in which prey and predator changing rate,

**dx/dt**and

**dy/dt**respectively, are zero). That gives an

**Xo**and

**Yo**equilibrium values corresponding to

**1394**prey and

**1779**predator individuals respectively. Those numbers coincide, at least by eye, with the values at which the populations oscillate around. That coherence could be checked more precisely with some statistic tests and confidence intervals. May be in a future.