Growth curve

Fitzguh, 1976 mentioned that mathematical growth models provide good way of condensing the information contained in such data into a few parameters with biological meaning.

De Torre, 1992 mentioned 3 non linear function for weight-age data of 50 cows.

  • Von Bertalanffy; W=A (1-B*EXP(-kt)³)
  • Brody; W=A (1-B*EXP(-kt))
  • Richards; W=A (1-B*EXP(-kt)m

Where;

  • W= observed weight at age t
  • A=asymptotic limit of the weight when age (t) approaches infinity. This does not imply that A is the heaviest weight attained by the individual, but it indicates the average weight of the mature cow, independent of short term fluctuations in weight due to temporary environmental effects of climate, feed availability, or pregnancy/lactation status.
  • B=indicates the proportion of the asymptotic mature weight to be gained after birth, established by the initial values of W and t. This parameter adjusts for the situation in which W (initial weight) or t(time of origin) not equal to 0.
  • m/b=point of inflection, which occurs where the estimated growth rate changes from an increasing to a decreasing function. Rate of change in weight is maximum at the point of inflection because, by definition, these equations have zero gradient at point of inflection.
  • k= function of the ratio of maximum growth rate to mature size, normally referred to as maturing rate. It is related to postnatal rate of maturing and serves both as a measure of growth rate and of rate rate of change in growth animal. Large k values indicate early maturing animals and vice versa.

Koenen and Groen, 1996 used the two phase logistic growth function to fit with the data from Dutch Black and white heifer bodyweight. The fitted data have to be noted as average growth taking into account all diseases occur.

Yt=                a1                              +                    a2      

               1 + EXP(-km(t-b1)               1+EXP(-km(t-b2)



Where;

  • Yt=BW(kg) at age t (day)
  • a1=asymptotic BW during the first phase (kilogram)
  • b1=age at the first inflection point (day)
  • km=maturation rate
  • a2=asymptotic BW during the second phase (kilogram), and
  • b2=age at the second inflection point (d)

Mean BW of heifers fitted by the two phase logistic function based on unadjusted means

 

Means

σр

Range

a1

309

41.9

166-480

b1

161

29.5

65-404

km

0.01128

0.00157

0.00572-0.0155

a2

237

48.2

32-583

b2

550

81.1

130-941




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