Growth of the Lobster,Homarus Americanus.

Abstract

Among the workers on the growth of the lobster, credit is due to Hadley 1 for giving the best data yet available. The object of the present paper is to analyze Hadley's data mathematically and make some comments upon it.∗

It should be borne in mind that there remains something to be desired in Hadley's data. First of all, the material for the females is relatively poor, not only in deficiency of larger specimens but also in the sense that the growth curve abruptly shows linearity immediately after reaching the sexual maturity, if one assumes his time basis to be correct. And yet it is almost beyond doubt that his record of the males covers all the stages up to the oldest one, although his estimation of the age coupled with actual observation is trust-worthy up to 6 years only.

It should first be noted that it is impossible to get by mathematical analysis any definite idea about the true age of the larger specimens out of the data at our disposal. First, taking all of Hadley's estimates of the age of the males for granted, a logarithmic parabola of the form,

was fitted by least squares. The constants, shifting the origin at −1, were as follows:

where y represents the length of the males in millimeters and x the age of the same in 60-day units. On the other hand, a logarithmic parabola fitted to the observations on the males up to 6 years (i.e., over the period of definite o'bservation as distinguished from estimates of age) gave the following result :

where × and y represent the same variables as in (1) with the origin at −1. The maximum age of the males obtained from the equation (1) is 35.196 years, whereas the largest males, measuring 568 mm. in length, would be less than 15 years old in case their growth followed curve (2) further than 6 years.