Agriculture Reference
In-Depth Information
to a common objective. Traditionally, mathe-
matical models have been used to assist the
system manager in making optimal decisions
(DeLorenzo
et al
., 1992; Tozer and Stokes, 2001;
Cabrera, 2010). Models are mathematical repre-
sentations of a system, which characterize the
relationships between system elements and
the producer's objective. In order to represent the
production system fully, elements affecting the
system should be described mathematically,
and the relationships between model variables
should be specified. The structuring of the model
depends on the objective of the producer, on
the knowledge of the system manager and on
the data available. Data and information avail-
able for model development can be obtained
from production unit records and the literature.
Using the data collected and models developed in
previous studies is essential in the integration of
knowledge about different elements of a produc-
tion unit. For example, if the objective is the
development of a model that maximizes dairy
profit, the model requires information about
production costs, milk prices, animal production
and regulatory policies. Environmental policies
can restrict the system operation by imposing
regulatory constraints, as discussed above.
Therefore, the mathematical representation of
regulatory policies relies on the characterization
of environmental impacts from the system and
on the establishment of relationships between
animal production and the impacts generated.
Consequently, examining the effects of the regu-
lation of environmental impacts on the milk
production system requires the establishment of
relationships between dietary composition, milk
production, GHG emissions and mineral and
nitrogen excretion. In order to establish these
relationships, several equations to predict meth-
ane emissions have been developed in the past
two decades (Mills
et al
., 2003; Ellis
et al
., 2007)
and previously existing models have been exten-
sively evaluated (e.g. Wilkerson
et al
., 1995;
Ellis
et al
., 2010). Mineral and nitrogen excre-
tion models have been developed (James
et al
.,
1999; Nennich
et al
., 2005) to predict excreted
amounts and to examine effects of animal and
dietary characteristics related to efficiency of
nutrient utilization.
Furthermore, GHG inventories (IPCC, 2006;
EPA, 2011), mechanistic models (Bannink
et al
.,
2011) and whole farm models have been developed
(Chianese
et al
., 2009) for the simulation and
examination of feeding strategies and man-
agement practices that may reduce methane
emissions. Most of these models can determine
or predict reductions in methane emissions
caused by dietary manipulation. However, with
the exception of the model developed by
Chianese
et al
. (2009), which includes a diet
optimization sub-model, most models are not
suitable for the determination of optimal dietary
changes for a target reduction in methane emis-
sions. Most importantly, most of these models
cannot calculate the marginal costs of environ-
mental impact mitigation under optimal deci-
sions. The reductions in methane emissions with
dietary changes are usually assessed with pre-
determined changes in dietary characteristics.
These predetermined dietary changes are in
essence heuristic and not based on mathemati-
cal techniques that can search a specified feasi-
ble region for the optimal combination of feeds
that meet emission targets. The development of
a diet optimization model, in which feed selec-
tion is sensitive to environmental impacts, can
assist producers in formulating diets that will
contribute to their meeting environmental pol-
icy demands. The marginal costs of mitigation
strategies can be derived under optimal deci-
sions, and producers can use sensitivity analy-
sis when examining possibilities for achieving
regulatory demands. In the optimization frame-
work, policy makers and producers could
a priori
examine the effects of imposing a policy. For
example, the effect of methane mitigation
strategies on the demand for human-edible feeds,
producer's marginal revenues and system sus-
tainability can be examined before a regulatory
policy is implemented.
In this chapter, we will present some of the
optimization modelling techniques that can be
used to reduce the environmental impacts of
livestock and to assess the effects of environ-
mental policies on the production system.
Specifically, this chapter: (i) examines feed man-
agement practices that can reduce methane
emissions and mineral excretion from livestock;
(ii) reviews and describes mathematically the
optimization modelling techniques frequently
used for diet optimization and the minimization
of livestock production environmental impacts;
and (iii) presents an optimization model that can
formulate diets when environmental policies are
