On the use of response functions in energy balance analysis

doi:10.1016/S0022-5193(89)80031-1

Journal of Theoretical Biology

Volume 140, Issue 1, 11 September 1989, Pages 83-99

https://doi.org/10.1016/S0022-5193(89)80031-1 Get rights and content

Mathematical and theoretical aspects of applying the Richards plant growth function, the generalized saturation kinetics function and the rational polynomial in the analysis of energy balance studies with farm livestock are examined. These functions are compared and contrasted with the piecewise linear and Mitscherlich. Practical aspects of fitting the functions to experimental data are also given consideration.

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Cited by (15)

A sinusoidal function and the Nelder-Mead simplex algorithm applied to growth data from broiler chickens
2018, Poultry Science
Citation Excerpt :
Traditionally, mathematical equations called growth functions have been used to relate body weight (BW) to age of the bird or cumulative dietary feed intake (McCance, 1960; Lister et al., 1966; Fitzhugh, 1976; Darmani Kuhi et al., 2003, 2004; Faridi et al., 2014, 2015). They can also be used to determine the efficiency of nutrient utilization, which is the derivative of the relationship between BW and dietary nutrient intake and as response functions to predict daily energy, protein, and amino acids requirements for maintenance and growth (France et al., 1989; Darmani Kuhi et al., 2009, 2011, 2012). Such applications have been reported in animal science for nearly a century (for review see Dumas et al., 2008; Darmani Kuhi et al., 2010).
There has been much recent interest in mathematical developments for the analysis of growth in poultry. In this paper, we present a sinusoidal function to describe the evolution of growth as a function of time based on real life experiments. The function was evaluated with regard to its ability to describe the relationship between body weight and age in broilers and was compared to 4 standard growth functions: Gompertz, logistic, Lopez, and Richards. In order to estimate the model parameters, we adopted a global optimization method based on a direct search method instead of using gradient-based techniques. The results of this study show that both the sinusoidal function and the direct search method precisely describe the growth dynamics of broiler chickens. Fitting the growth functions to different data profiles nearly always led to the same or less maximized log-likelihood values for the sinusoidal equation, which is an indication of its superiority in describing growth data from broiler chickens.
Simulation and quantification of pasture condition and animal performance on boreal grasslands in Alberta
2007, Agricultural Systems
We developed a computer model (PASTURE) to simulate both condition of pastures grazed by farmed wildlife and animal performance as dual measures of system performance. For representative habitat types (e.g., aspen forest and open grasslands), the model simulates herbage growth, maturation and senescence, habitat and diet selection, and nutrient intake of several wild ruminant species. The model generated seasonal patterns of pasture productivity and animal behavior expected for Bromus-Poa pastures in aspen boreal ecosystems. Model calibration was conducted using data collected from studies conducted within the aspen boreal ecosystems at the Ministik Research Station in 1997 and 1998, and Elk Island National Park and the University of Alberta greenhouse in 1999 and parameters adjusted until the predicted and observed results were visibly close. Evaluation of the model was conducted using statistical criteria of calculating average error, root mean square, root mean square error, coefficient of residual mass and modeling efficiency and comparing these statistics against optimal values. Statistical tests indicated a good fit between predicted and observed values for cumulative phytomass, herbage use and animal performance.
Alternatives to linear analysis of energy balance data from lactating dairy cows
2003, Journal of Dairy Science
The current energy requirements system used in the United Kingdom for lactating dairy cows utilizes key parameters such as metabolizable energy intake (MEI) at maintenance (ME_m), the efficiency of utilization of MEI for 1) maintenance, 2) milk production (k_l), 3) growth (k_g), and the efficiency of utilization of body stores for milk production (k_t). Traditionally, these have been determined using linear regression methods to analyze energy balance data from calorimetry experiments. Many studies have highlighted a number of concerns over current energy feeding systems particularly in relation to these key parameters, and the linear models used for analyzing. Therefore, a database containing 652 dairy cow observations was assembled from calorimetry studies in the United Kingdom. Five functions for analyzing energy balance data were considered: straight line, two diminishing returns functions, (the Mitscherlich and the rectangular hyperbola), and two sigmoidal functions (the logistic and the Gompertz). Meta-analysis of the data was conducted to estimate k_g and k_t. Values of 0.83 to 0.86 and 0.66 to 0.69 were obtained for k_g and k_t using all the functions (with standard errors of 0.028 and 0.027), respectively, which were considerably different from previous reports of 0.60 to 0.75 for k_g and 0.82 to 0.84 for k_t. Using the estimated values of k_g and k_t, the data were corrected to allow for body tissue changes. Based on the definition of k_l as the derivative of the ratio of milk energy derived from MEI to MEI directed towards milk production, ME_m and k_l were determined. Meta-analysis of the pooled data showed that the average k_l ranged from 0.50 to 0.58 and ME_m ranged between 0.34 and 0.64 MJ/kg of BW^0.75 per day. Although the constrained Mitscherlich fitted the data as good as the straight line, more observations at high energy intakes (above 2.4 MJ/kg of BW^0.75 per day) are required to determine conclusively whether milk energy is related to MEI linearly or not.
Application of the law of diminishing returns for partitioning metabolizable energy and crude protein intake between maintenance and growth in growing male and female broiler breeder pullets
2011, Journal of Agricultural Science
A review of mathematical functions for the analysis of growth in poultry
2010, World's Poultry Science Journal
Mathematical modelling in animal nutrition: A centenary review
2008, Journal of Agricultural Science

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^*: The work formed part of a Commission from the Ministry of Agriculture, Fisheries and Food.

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Journal of Theoretical Biology

References (24)

Allosteric and related phenomena: an analysis of sigmoid and non-hyperbolic functions

J. theor. Biol.

New methods for comparing the biological efficiency of alternative nutrient sources

J. Nutr.

The quantitative analysis of growth

The Nutrient Requirements of Ruminant Livestock

Sigmoid curves, non-linear double-reciprocal plots and allosterism

Biochem. J.

The effect of date of cut and barley substitution on gain and on the efficiency of utilization of grass silage by growing cattle. 2. Nutrient supply and energy partition

Br. J. Nutr.

The estimation of the nutritive value of feeds as energy sources for ruminants and the derivation of feeding systems

J. Agric. Sci.

The utilization of food by sheep and cattle

J. Agric. Sci.

The efficiency of energy utilization in growing cattle consuming fresh perennial ryegrass (Lolium perenne cv. Melle) or white clover (Trifolium repens cv. Blanca)

Br. J. Nutr.

Mathematical Models in Agriculture

Simulation of the metabolism of absorbed energy-yielding nutrients in young sheep

Br. J. Nutr.

Energy feeding standards: a methodological problem

Cited by (15)

A sinusoidal function and the Nelder-Mead simplex algorithm applied to growth data from broiler chickens

Simulation and quantification of pasture condition and animal performance on boreal grasslands in Alberta

Alternatives to linear analysis of energy balance data from lactating dairy cows

Application of the law of diminishing returns for partitioning metabolizable energy and crude protein intake between maintenance and growth in growing male and female broiler breeder pullets

A review of mathematical functions for the analysis of growth in poultry

Mathematical modelling in animal nutrition: A centenary review

On the use of response functions in energy balance analysis*

J. theor. Biol.

J. Nutr.

The Nutrient Requirements of Ruminant Livestock

Sigmoid curves, non-linear double-reciprocal plots and allosterism

Biochem. J.

The effect of date of cut and barley substitution on gain and on the efficiency of utilization of grass silage by growing cattle. 2. Nutrient supply and energy partition

Br. J. Nutr.

The estimation of the nutritive value of feeds as energy sources for ruminants and the derivation of feeding systems

J. Agric. Sci.

The utilization of food by sheep and cattle

J. Agric. Sci.

The efficiency of energy utilization in growing cattle consuming fresh perennial ryegrass (Lolium perenne cv. Melle) or white clover (Trifolium repens cv. Blanca)

Br. J. Nutr.

Mathematical Models in Agriculture

Simulation of the metabolism of absorbed energy-yielding nutrients in young sheep

Br. J. Nutr.

Energy feeding standards: a methodological problem