(1) Measurements were made of body length, width and the lengths of antennae, head, thorax, pleotelson and parts of the uropod of twenty-six specimens of Asellus californicus ranging in size from 1.5 by 0.3 mm to 11.1 by 1.7 mm in order to obtain a quantitative picture of differential growth in this subterranean isopod. (2) The data obtained were analyzed and found to conform with Huxley's law of heterogonic growth, using body width as the standard of comparison. (3) The differential growth ratio (k) for each structure was not uniform overthe entire range of observation but increased abruptly at the middle of the range, dividing the period of growth studied into two uniform stanzas. The constants in the heterogony formula were calculated separately for each structure for the two stanzas, as well as for the entire range when the change from first to second stanza was slight or not statistically significant. (4) Within the range of body width 0.3 to 1.0 mm, growth in length is practically isogonic for all structures except the pleotelson and the uropod, which is heterogonic, due to the marked heterogony in its basal segment. (5) In the second stanza (body width of 1.0 to 1.7 mm) there is a simultaneous and significant onset of heterogony in all structures, with the possible exception of the thorax, although in some eases the increase in the value of k from first to second stanza is not significant. Extreme heterogony is exhibited by the protopodite and endopodite of the uropod with k values of 3.8 and 3.3, respectively. (6) Heterogony is not exhibited to the same degree in all structures or parts and the visible consequences of differences in the growth coefficient, k, are described in terms of changing proportions of parts with growth. The best example is the uropod, in which, as a result of different degrees of heterogony in the protopodite and endopodite and the practically isogonic growth of the exopodite, the proportionate lengths of protopodite, endopodite and exopodite change from about 4:6:5, respectively, in the smallest specimens to about 6.4.1 in the largest. (7) The growth gradient in the longitudinal axis of the body shows, in the first stanza, a center of differential growth in the protopodite of the ufopod from which the gradient slopes down proximally to the head and distally to the endopodite. In the second stanza, the growth gradient features two terminal centers of high d ifferential growth, the second antenna and again the protopodite which is now an extremely high center. From these two distal centers, the growth gradient slopes down sharply to the middle of the body. The whole gradient in the second stanza is significantly elevated above the level line of isogonic growth. (8) Rate genes affecting the various parts of the body and possibly the body as a whole are suggested as the cause of disproportionate but orderly growth. That the heterogony of the second stanza may be a male secondary sexual or sex-limited character is a strong possibility. Reasons are given to show that functional hypertrophy is an inadequate explanation for the extreme heterogony of the second antennae and uropods. (9) The taxonomic and evolutionary significance of heterogonic elongation is discussed. Relative elongation is shown to have no systematic value in separating the subterranean isopods as a genus (Caecidotea) from the surface forms not only because it is a convergent character but also because it is not even a constant specific character, since relative elongation varies with age in individuals of a species as a result of heterogony. Other reasons for invalidating this unnatural genus are reviewed. The elongation distinguishing subterranean forms from surface species possibly resulted in consequence of parallel mutations of rate genes in the ancestral surface species. If so, the mutant genes express themselves relatively late in our Asellus californicus. The heterogonic elongation of parts in this subterranean isopod results in a recapitulation of ancestral body proportions.
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