Biology Reference
In-Depth Information
where A is the asymptotic value for D, K is the rate of approach to the asymptotic value
and t
0
is the age at the onset of development. We can therefore predict the value for D at
any age and also predict the degree of developmental maturity, measured as the propor-
tion of the asymptotic adult value attained at that age. For example, we can predict the
degree of maturity attained by the house mouse and cotton rat at birth, eye-opening,
weaning and sexual maturity. House mice are altricial, being blind, deaf, hairless and
immobile at birth; eye-opening occurs at around 10 days. In contrast, the cotton rat is pre-
cocial, opening its eyes the day it is born, its ears shortly thereafter, being furred and
mobile at birth. The two species differ in gestation length by 12 days (
Zelditch et al.,
2003a
), which could explain their difference in degree of maturity at birth. But the cotton
rat is not consistently 12 days more advanced than the house mouse. The two species
wean and become sexually mature at nearly the same ages. As we can infer from the rates
of shape maturation obtained from the linear model (above), the house mouse develops
more rapidly. But non-linear growth models may give a better estimate of developmental
rate.
Fitting the multiple growth models to the data shows that several models fit well
(
Table 11.12
). The logistic model corresponds to the one that we fit above, by regressing D
on log(age
1); but this yields significant autocorrelated residuals for the house mouse so
1
TABLE 11.12
Evaluating Relative Fit of Growth Models to the Data for Developmental Maturity, Measured
as the Procrustes Distance Between Each Specimen and the Mean for the Youngest Age
Species
Model
%Var
AC
AIC Weight
House mouse
Chapman-Richards
0.88
ns
0.1171
Monomolecular
0.88
ns
0.3077
von Bertalanffy
0.87
*
-
Gompertz
0.86
*
-
German Gompertz
0.87
ns
0.2976
Logistic
0.87
*
-
Quadratic
0.86
ns
0.2776
Linear
0.78
*
-
Cotton rat
Chapman-Richards
0.90
ns
0.0615
Monomolecular
0.90
ns
0.1654
von Bertalanffy
0.90
ns
0.1628
Gompertz
0.88
ns
0.1379
German Gompertz
0.90
ns
0.1611
Logistic
0.89
ns
0.1554
Quadratic
0.89
ns
0.1559
Linear
0.83
*
-
% Var
5
variance explained; AC
5
serial autocorrelation of residuals (statistical significance indicated by *).
