Ask the Chicken Philosopher

by Olivia DeLane

Dear Olivia,

It’s typical when hunting gazelle for us lions to target the sick and wounded, and the young and elderly. We’ve done this since the dawn of time. Personally, I have no objections to killing the wounded. (Let’s face it, all the gazelle I eat are wounded. Between the time I first get my paws on their tight little haunches to when I sink my fangs into their sweet, juicy necks, there’s some hardcore wounding goin’ on.) And, as a guy with an expected lifespan of 10 years, I have no problems at all offing a 15-year-old Tommie.

But I have to confess I’ve never felt good about taking down a yearling and, for the past few months, I’ve been unable to bring myself to kill a kid at all. When no one’s looking, I won’t even give chase. And when other members of the pride are around, I’ll catch one, but then just let it go and say the little bugger slipped away.

Olivia, I’m writing to you because this can’t go on much longer. There are only so many times I can use the ‘That punk pronked like he had a gun’ line before the pride will start thinking I’m some sort of bleeding heart.

I’d like to try to convince everyone my way is better, but don’t know how. Tell me, would it be better for all lions to give up killing young gazelle, or should I just bite the bovidae (so to speak) and once again chow down on chinkaras?

Sincerely,
“Leo the Lyin’-Hearted”
near Robanda, Tanzania

~~~~~~~~~~~~~~~~~~

Dear Leo,

I am not much of a hunter myself (I’m more of a salad-and-chardonnay type of girl, actually) but since I do enjoy scratching and pecking around the ant hill on occasion, I can sympathize with the “carnivore’s dilemma” that you face. One approach to confronting deep questions of ethics is to engage in meditation and introspection, but another, equally valid approach is to resort to the cold, hard logic of mathematics.

It is easy to extend the famous ‘Lotka-Volterra model‘ of predator-prey dynamics to the case where there is a third population group (Kids) who are exempt from being eaten by lions. Say that the change in the population of Kids (K), Adult gazelle (A) and Lions (L) are represented by these coupled differential equations:

The first line says that the rate of change of Kids (dK/dt) depends on the number of adult gazelle (A) times the number of kids born per adult per month, r. Some fraction of the kids are eaten by lions each month (according to the rate ‘aLK’), and some fraction (t) of kids mature to become Adults (according to the rate ‘tK’). The second line says that the rate of change of Adults (dA/dt) depends on the number of Kids that mature each month (tK) and the fraction of Adults who are eaten by lions (according to the rate ‘aLA’). And the last line says that the rate of change of Lions (dL/dt) depends on the number of Adult gazelle consumed by lions each month (according to ‘bLA’) and the number of Kids consumed (according to ‘bLK’). Additionally, some fraction of lions die each month (according to ‘mL’) from natural causes, like catching a nasty virus.

We can approximate a solution to these equations by numerical integration using the 2nd-order Runge-Kutta method (4th-order RK integration would also work, but there is significant error introduced if we resort to Euler’s Method). For the case where the initial numbers of Kids, Adults, and Lions is 25, 60 and 10, the changes in Gazelle (Kids plus Adults) and Lions are shown in the graph below:

(The case where Lions eat both Adult and Kid gazelle)

This is classic predator-prey dynamics: the number of gazelle increase, causing an abundance of food for lions (whose own population booms). The increase in the number of lions causes the gazelle population to crash which, in turn, causes a severe shortage in the food supply for lions, whose population then crashes, causing the cycle to repeat. (The parameters I’ve used here are r and t = 0.1, a=0.005, b=0.001 and m=0.02. These values have the cycle take about 240 months, or 20 years. Different values can change the frequency and height of the peaks, but the dynamics are conceptually unchanged.)

We can examine the case where Lions do not eat Kids by simply deleting those terms from our set of equations to get:

In this case, you can see that the number of Kids only decreases by Kids maturing into Adult gazelle and Lions only eat Adult gazelle, not Kids. For that case, the dynamics are very different:

(The case where Lions eat only Adult gazelle)

In this case, the populations of Lions and Gazelle still undergo the ‘boom-and-bust’ cycle I described previously, but now each peak is less extreme than the previous one. Thus, the populations continuously approach stable levels and, interestingly, the numbers of both Lions and Gazelle are higher, on average, than the case where Lions would eat Kids.

So, the short answer to your question is probably Yes – it seems from this analysis that both lions and gazelle would be better off if lions would refrain from eating young gazelle. However, this is a very simple model and it would not be wise to implement major policy changes to the behavior of lions that, by your own admission, have been going on for many millennia.

In fact, the cases where only a fraction of the lions choose to not eat kids are more complex than you might imagine from the graphs above. I’d love to share my findings, but will have to save them for another day, since all this talk has made me hungry and I think I’ll head over the ant hill now to see what I can find.

Love always,
Olivia DeLane, Chicken Philosopher

~~~~~~~~~~~~~~~~~~~~~~~

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 extended pamphlet “What Would Jesus Stew? A Cooking Guide to 11 Delicious Animals That Are Not Chicken” is available in many fine churches and public libraries across this bountiful land.

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  1. 1 The Geometry of Behavior « The Brothers Dreyzen

    […] 1: Predator-prey dynamics over 20 years. (1) View source for an excellent piece on this […]




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