### Ask the Chicken Philosopher

by Olivia DeLane

What seems like a lifetime ago (actually, for a chicken it was about a lifetime ago) I started looking at a simple model of predator-prey dynamics and found that it might be better for Lions to stop eating Gazelle kids.

Just as people tend to throw back young fish, perhaps excluding young Gazelle from the food supply would be better for both Lions and Gazelle.

The basic model looked like below, where K is the number of Kids, A is Adults, L is Lions and the rest are parameters.

The two values of the s-parameter that I looked at were the case where Lions eat Kids (s=1) and where Lions refrain from eating Kids (s=0).

I noticed that the ratio of Adults-to-Kids tends to converge on the Golden Ratio (approximately 1.618) when s=1 and that this ratio (A/K) tends to go to 1 when s=0. I am curious about other values of s, so that only a portion of Lions eat Kids.

What has made me curious about this is the idea that these equations might not be just a model of Lions and Gazelle, but also of the rate at which new companies are formed. Every venture starts small (like a Kid Gazelle) and then might either die out or grow to be a mature enterprise. These established companies (like Adult Gazelle) help to spawn new small enterprises, through intentional spin-offs (like when Microsoft spun-off Expedia) or by serving as a meeting place where entrepreneurs then strike out on their own (like the famous Traitorous Eight who started Fairchild).

The ‘predators’ in this example would be investors and the general business environment, which seek to tear apart companies when the number of Lions is high and are relatively weaker in power when their numbers are low. Likewise, conditions are best for established firms when s is high and best for startups when it is low.

Apparently, I am not the only one who has thought of this analogy, since I received this message via Twitter:

The graph below shows the ratio of Adult (or, Established firms) to Kids (Startups), for differing values of the s-parameter. For values of s up to about 0.25, the ratio of Adults to Kids remains constant, being a little over 1. When s = 1, as I mentioned before, the A/K ratio also tends toward a constant, the Golden Ratio.

(click image to enlarge)

But for intermediate s values, the A/K ratio steadily oscillates between two different values. My thinking is that since we tend to see times that favor established firms and times that favor startups (similar in concept to the ‘business cycle’), then this simple model of predator-prey dynamics might be useful for studying startup dynamics in the economy as a whole, or perhaps in just one industry, especially if the value of s itself varies over time.

At this point, I don’t know if this model is actually useful, or if it just an analogy, but I hope to be able to put a little more time into studying it before this lifetime is over.

Best,

Olivia

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Olivia DeLane has a Master’s certificate in normative ethology from Gallus College, a non-accredited online institution. Her writings are for entertainment purposes only and should not be misconstrued as being for any other use. Olivia’s new book “50 Simple Tips to Turn Your Chicken Shack into a Hen House” will soon be available.