Changes

==='''Proportional and disproportional development'''===

==='''Proportional and disproportional development'''===

Isometry is a particular case of allometry (Gr. allos, other; metron, measure).  Both terms relate to the measurement of the proportions of two components, or a component and the whole, during the development of an organism.  Isometry refers to proportionate development, and allometry to disproportionate development.  Development may be within a species, describing growth patterns (ontogenic allometry), or between species, describing evolutionary patterns (phylogenic allometry).  Partly because body dimensions bear power functional relationships and partly because growth is a multiplicative process, it is convenient to study developmental patterns on logarithmic scales.  When a double logarithmic linear relationship has a slope b=1, two weight components develop isometrically:  when b < 1 or b > 1, they develop allometrically (Fig. 7.4).

Isometry is a particular case of allometry (Gr. allos, other; metron, measure).  Both terms relate to the measurement of the proportions of two components, or a component and the whole, during the development of an organism.  Isometry refers to proportionate development, and allometry to disproportionate development.  Development may be within a species, describing growth patterns (ontogenic allometry), or between species, describing evolutionary patterns (phylogenic allometry).  Partly because body dimensions bear power functional relationships and partly because growth is a multiplicative process, it is convenient to study developmental patterns on logarithmic scales.  When a double logarithmic linear relationship has a slope b=1, two weight components develop isometrically:  when b < 1 or b > 1, they develop allometrically (Fig. 7.4).

:::::'''Fig 7.4 Relative growth of tissues in a beef carcass'''  

 

:::::'''Fig 7.4 Relative growth of tissues in a beef carcass'''  

:::::Total carcass muscle weight grows isometrically with body weight, since the slope of the regression on logarithmic scales, b, equals 1.  For bone and fat, however, the slopes of the regressions lines are not equal to 1; bone grows slower and fat faster than the body as a whole.   

:::::Total carcass muscle weight grows isometrically with body weight, since the slope of the regression on logarithmic scales, b, equals 1.  For bone and fat, however, the slopes of the regressions lines are not equal to 1; bone grows slower and fat faster than the body as a whole.   

:::::The values are for female Jersey cattle.   

:::::The values are for female Jersey cattle.   

:::::'''Fig 7.5 Allometry of bones according to Galileo'''  

 

:::::'''Fig 7.5 Allometry of bones according to Galileo'''  

:::::"To give a short example of what I mean, I once drew the shape of a bone, lengthened only three times, and then thickened in such proportion that it could function in its large animal relatively as the smaller bone serves the smaller animal; here are the pictures. You see how disproportionate the shape becomes in the enlarged bone.  From this it is manifest that if one wished to maintain in an enormous giant those proportions of members that exist in an ordinary man, it would be necessary to find either much harder and more resistant material to form his bones, or else to allow his robustness to be proportionately weaker than in men of average stature; otherwise, growing to unreasonable height, he would be seen crushed by his own weight and fallen".   

:::::"To give a short example of what I mean, I once drew the shape of a bone, lengthened only three times, and then thickened in such proportion that it could function in its large animal relatively as the smaller bone serves the smaller animal; here are the pictures. You see how disproportionate the shape becomes in the enlarged bone.  From this it is manifest that if one wished to maintain in an enormous giant those proportions of members that exist in an ordinary man, it would be necessary to find either much harder and more resistant material to form his bones, or else to allow his robustness to be proportionately weaker than in men of average stature; otherwise, growing to unreasonable height, he would be seen crushed by his own weight and fallen".