### Chicken Dynamics

Feisty turns one month old this Friday. (Here’s a photo at one day old and a post about the weight gain in the first week.) Oh, they grow up so fast. The photo below is Feisty (at center) and a couple of friends earlier today. They’re not at the ‘buck-buck’ing stage yet – they can still only say ‘cheep-cheep’.

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I’ve been weighing Feisty each day (with a couple of exceptions), as close to 6:00pm as possible. The graph below shows the measured weight each day, with the earlier days being accurate to 0.5 grams, but later days only to about the nearest 5 grams.

(click to enlarge)

The growth curve looks exponential, but I’m guessing that it conforms to Gompertz’s equation.

Benjamin Gompertz (1779-1865) was a self-taught British mathematician most famous for his work on the natural increase of populations. (I say ‘self-taught’ because as a Jew he was not Anglican and therefore prohibited from enrolling in university). He derived an expression for a type of S-shaped growth where the early period and the later approach to an asymptotic limit are asymmetric. (I’ve written about asymptotes previously, too.)

His work was first used to estimate mortality rates for pricing life insurance policies and later, in the 1960s, for modeling tumor growth. But it seems to work well so far for chickens, too.

The specific form of Gompertz’s function that I’ve used here is:

where b is a constant, t* is the day where the growth is the largest (in grams per day), and the value a is the asymptotic weight limit. Guessing from the early measurements, it looks like Feisty will hit peak growth rate early this week and approach an ultimate weight of about 2250 grams (just about 5 pounds) by mid-September.