Remarks on the article of Packard: Julian Huxley, Uca pugnax and the allometric method.
نویسنده
چکیده
restudied Huxley's measurements of Uca pugnax and presented not only a two-parameter power function but also a three-parameter power function; this three-parameter model 'is better than the two-parameter model for describing the observations'. The two-parameter model has a biological meaning, as explained by Huxley (Huxley, 1924); the three-parameter model has no biological meaning. I have shown (Geraert, 2004) that there is a constant change in the relationship (and not a constant relationship) between a small amount of growth of body part y compared with that of body part x; mathematically speaking, the 'second difference' is constant. This second difference is the growth rate and is present in the quadratic factor of a quadratic equation; the other factors in the equation have no biological meaning but are necessary to position the quadratic curve in a diagram. In my study (Geraert, 2004), growth is followed from the newborn stage to the adult; in Huxley's study on the fiddler crab, a comparison is made among adult males; as these adults show a very large variation in the development of the claw, Huxley (Huxley, 1924; Huxley, 1932) interpreted this also as 'growth'. An attempt is made to see whether a quadratic parabola can also be used to describe variation in adults, called here 'comparative' growth. The quadratic equation calculated for the males of Uca pugnax is as follows: Y = 0.097X 2 + 0.42X – 0.045 , (1) in which Y is the mean mass (in g) of the large chela and X is the mean mass (in g) of the rest of the body after removal of large chela (Huxley, 1932). The calculated values for Y are very near to the observed ones, except for the smallest bodies where a slightly different Y-value is calculated; the overall similarity is obvious in Fig. 1; it is also obvious by the very small value of the sum of (Y measured – Y calculated) 2 being only 4.5 mg. The quadratic factor in the above equation is the growth factor; multiplied by 2, it gives the second difference in the growth of the claw relative to the growth of the rest of the body; e.g. for every additional growth of the body with 100 mg, the differences in the growth of the claw show a constant increase of 1.94 mg (=2×0.97). In the case of Uca pugnax, a quadratic curve describes the comparative growth in males …
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Julian Huxley, Uca pugnax and the allometric method.
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عنوان ژورنال:
- The Journal of experimental biology
دوره 216 Pt 3 شماره
صفحات -
تاریخ انتشار 2013