# Theory of growth

Attempts have been made in the past to produce an accurate theory of growth, and thereby differentiate between genotypes.

*Wilson (1977)* suggested that more could be learned of the differences in genotype between broilers by the use of growth curves than by measuring growth rates to one or possibly two ages. However, he realised that growth curves per se fail to incorporate an explicit statement of the inputs required to generate that growth.

*Parks (1982)* addressed this problem by integrating information regarding growth, feed intake and time into a prediction equation.

*Emmans and Fisher (1986)* addressed the problem in a different way: they assumed that each growing bird had an inherent potential growth rate that could be measured in an ideal or non-limiting environment. They suggested that the bird has a ‘purpose’, namely, to achieve it’s potential and therefore to reach maturity in the shortest possible time. Using this theory it is possible to describe the potential growth rate and hence determine the nutrient requirements for potential growth of different genotypes. But it is possible, in addition, to determine to what extent the bird will be successful in achieving it’s potential when kept in a limiting environment and when given an imbalanced food.

## Potential growth rate

The chemical and physical composition of the body changes systematically during growth, so a single growth function would not be sufficient to describe the changes in composition as growth proceeds. By predicting the growth of protein in the body by means of a growth function and then relating the growth of water, ash and lipid to this, it is possible to determine the rate of growth of the whole body. There are strict relationships between the weights of the components in potential growth *(Emmans and Fisher, 1986; Emmans, 1988; 1989)* that can be used for this purpose. The first step in describing a genotype, then, is to determine the potential rate of protein gain, which can be accomplished by means of a *Gompertz (1852)* growth curve.

The Gompertz growth equation has the following form:

Wt = A . exp ( -exp ( -B ( t – t*)))

where the weight of the bird at time **t**, (**W**), is expressed in terms of **A**, the weight at which the growth rate becomes zero, i.e. the mature weight of the bird; **B**, the rate parameter, or rate of maturing; **t***, the time at which the growth rate is at its maximum. An advantage of this equation is that the parameters of the equation can be interpreted in terms of the biology of the bird.

The growth rate of the bird at time **t** can be calculated from the derivative of the above equation, namely:

dW/dt = B . W . ln (A/W)

The Gompertz function predicts that the relative growth rate will decline linearly to zero as the logarithm of weight increases to that of **A**, and that the absolute growth rate will increase to a maximum when weight is 0.368 of **A** and then decline to zero as **W** approaches **A**. That this equation is capable of accurately predicting the growth rate of broilers is illustrated in Figure 1. in which the function has been used to describe the growth of male and female broilers of a single strain *(Hancock et al., 1995)*. The parameter values used for the males and females respectively were: **A** = 5.8 and 4.4 kg, **B** = 0.0352 and 0.0363 /day and **t*** = 45 and 42 days. Different values for these parameters were measured among the six different breeds evaluated in this study, indicating that potential growth rates and hence nutrient requirements would differ between these commercial broiler breeds.

Accurate predictions of the growth of body protein can be obtained in the same way as described above, from measurements of protein growth under non-limiting conditions, using the Gompertz equation. Estimates of the growth of the other chemical components of the body can be predicted from the protein component using the allometric relationships that exist between the different components of the body.

## Growth of the chemical components of the body

As the empty body consists of water, lipid and the remainder (lipid-free dry matter), a separate equation could be fitted to each component in turn. There is good evidence to suggest that the lipid-free dry matter (protein plus ash) is of constant composition *(Doornenbal, 1971; 1972)* and that the growth rate parameters (**B**) for each component are the same for a given genotype *(Emmans, 1988)*. This means that the ash component of the carcass can be predicted directly from the protein content, using the isometric relationship that exists between them, and that water and lipid weights, which are related to the lipid-free dry matter weight of the carcass by a simple power function, can be predicted from the protein weight, under non-limiting conditions, by allometry. In order to calculate the allometric relationship between the protein and lipid, which will differ between individuals and between genotypes, estimates of the lipid to protein ratio at maturity and the allometric parameter for lipid are required, which have to be determined under non-limiting conditions.

**FIGURE 1**

Observed and predicted growth rates of males and females of the same broiler strain (Hancock, 1990)

Given the growth rate of the remainder (protein plus ash) and the allometric relationship between both water and lipid and the remainder, the growth rate of the empty body can be seen as the sum of the growth rates of the components which can be estimated with a high degree of accuracy for birds kept under non-limiting conditions. The growth rate of protein, water and ash calculated in this way represents the maximum possible growth rate of those components of the bird, which could occur only under non-limiting conditions. The rate of growth of lipid, however, would exceed the ‘desired’ lipid content under certain feeding and environmental conditions.

Feathers make up a substantial proportion of the total body protein, and because the amino acid composition of feathers differs markedly from that of non-feather protein *(Emmans, 1989)* it is necessary to predict the growth of both feather protein and of non-feather protein so that the nutrients required for the production of these components can be calculated. In the model of broiler growth used in the present exercise, feather weight in potential growth is made a Gompertz function of time, the rate of maturing of feathers being related to the value of B for body protein and the rate of feathering parameter. Mature feather weight is calculated from the mature body protein weight and the time constant is made the same as that for body protein. The protein content of feathers is roughly proportional to the degree of maturity of the feathers due to the apparent loss of moisture with age, and this is taken into account in determining the composition and the growth rate of feathers at a time.