Agriculture Reference
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exhibited the largest proportional increase in
nitrogen intake. The identification of the animal
categories, within a herd, that are more sensitive
to environmental policies and the ones for which
mitigation strategies can be implemented in a less
costly manner was possible because model deci-
sion variables were indexed by animal category.
Nutrient composition of diets was substantially
altered when methane emissions were restricted.
The neutral detergent fibre, crude protein and
metabolizable energy dietary contents for the
seven animal categories are presented in Fig. 6.1.
Dietary fibre was substantially reduced and die-
tary protein and energetic density were increased
when methane emissions were restricted. The
reduction of methane emissions was achieved by
the reduction in dry matter intake and by the
reduction of the proportion of fibre in the diet,
consequently forcing the model to select feeds
with higher energy, protein and mineral contents.
Mineral and nitrogen intake and excretion were
altered with reductions in methane emissions,
suggesting that, for our hypothetical herd, reduc-
ing methane emissions through dietary manipu-
lation, especially through the reduction of dietary
fibre, can alter and possibly increase nitrogen and
mineral intake and excretion. Shadow prices were
generated in the methane restriction constraint
and used to represent the marginal costs of miti-
gating methane emissions. When plotted against
the respective reductions in methane emissions
(Fig. 6.2), shadow prices increased monotoni-
cally, suggesting that the cost of reducing the unit
of methane emissions increases with larger
reductions in methane emissions. The shadow
prices generated by the model structure can be
used in a cap and trade policy scheme, in which
total methane emissions are capped but partici-
pants are allowed to trade residual emissions. The
shadow price is the inputted cost attributed to the
residual methane emission when a reduction is
enforced; therefore, it can be used to input a trad-
ing value for those residual emissions. Emissions
could then be traded between policy participants,
for example in a carbon credit market. The mar-
ginal costs of reducing methane emissions were
extremely high in all scenarios, which were con-
sistent with the results from TAXM, where carbon
market current prices did not reduce methane
emissions through taxation.
This modelling framework is very flexible;
the feed composition matrix, animal nutrient
requirements, feed prices, environmental impacts
and herd structure are easily changed to accom-
modate different production systems. The deter-
ministic nature of the model and the limited
data for which the model was solved limit the
extrapolation of these results to the larger condi-
tion of dairies. However, this limitation is related
to model inputs, and the model structure can be
easily incorporated into whole-farm models,
which can simulate different production systems
with different input levels. Moreover, a more
robust analysis can be performed using this
modelling structure, with the incorporation of
uncertainty in model inputs without compro-
mising model linearity, for example through a
Monte Carlo simulation study.
Final Considerations
Substantial progress has been made in the devel-
opment of diet optimization techniques in recent
years. Several extensions of the linear program-
ming diet formulation model have been devel-
oped and implemented to optimize various diet
formulation objectives. The incorporation of
uncertainty in feed composition, feed costs and
nutrient requirements have extended the deter-
ministic approach of diet optimization. The
development of multi-criteria programming
models extended the application range of math-
ematical programming, enabling the derivation
of efficient solutions for multiple objective func-
tions. Concomitantly, a better understanding of
feed nutrient availability has been achieved
through the development of feeding systems in
which nutrients are divided according to feed
digestibility and animal production levels.
Precision feeding strategies have brought a new
perspective to the feeding of animals at the
requirement level. The incorporation of animal
variability in the determination of nutrient
requirements has extended the concept of for-
mulating diets for the average animal. Moreover,
several mathematical and statistical models
have been developed to determine environmen-
tal impacts of livestock production. In this con-
text, the incorporation of animal characteristics,
feed information and environmental impacts in
a diet optimization model enables the joint mini-
mization of diet costs and the environmental
impacts from livestock production. These models
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