154
Systematic conservation planning: past, present and future
(which we will refer to henceforth as the year). These actions will alter the dynamics of a variety of
state variables, y ijt . , such as the size of the population of a species in a site, or the amount of an
ecosystem service in a site. Mathematically this means that our control, or decision, variable is a jkt ,
the amount of money we spend on action k in place j in year t . A fairly general formulation of the
conservation resource allocation problem is to:
max
(
)
,
f y ijt
t
T
1
1
=
∑
subject to a budgetary constraint each year
a
b
t
jkt
k
P
j
N
t
=
=
∑
∑
≤
1
1
for all ,
and contingent on the dynamics of the state variables, that is, how key system states move from
year to year in response to actions or forces we do not control:
y
g a y x
i j
t
ijt
t
t
t
.
. .
. .
. .
(
, ,)
,
,
1 ⋅
for all
and
where f is a function that turns our state variables into a reward function that we are trying to maximize (this could be highly non - linear), g is a function that determines how the state variables, yijt,
evolve in space and time as a consequence of actions and forces we do not control, xijt. In this
formulation, N is the number of different places and P is the number of different sorts of actions.
This mathematical formulation of a problem that considers expenditure of money on different
conservation actions in space and time is a fairly general formulation of all resource allocation
problems. It is called a resource allocation problem because there is a fi xed annual budget.
Evaluating actions based on their cost - effectiveness (Joseph et al ., 2009 ) provides one algorithm
that can often provide rough solutions to this very complex optimization problem.
seven - step decision theory framework which has been
articulated by a number of authors for systematic conservation planning (Table 6.2 ; Possingham et al .,
2001 ; K.A. Wilson et al ., 2009 ).
There is now a large amount of literature on optimal
protected area design based on this decision theory
framework (summarized in Moilanen et al ., 2009 ). The
problems generated using this framework can be
expressed mathematically and then solved by one of a
number of methods. There are two classic problem
defi nitions commonly used in conservation planning,
the minimum set and maximal coverage conservation
prioritization problem (Box 6.4 ).
The minimum set problem minimizes the resources
expended while meeting the conservation objectives.
For this problem, the objective is to minimize cost and
the constraint is the conservation objectives.
The maximal coverage conservation prioritization
problem maximizes the objectives (e.g. target level
achievement) given a fi xed amount of resources. Here,
the problem is reversed: the constraint is the budget
and the objective is to maximize conservation
objectives.
Methods for solving systematic conservation planning problems fall into several classes: local heuristic
algorithms, which select sites in a stepwise manner
(Pressey et al ., 1993; 1994 ); global heuristic algorithms, which select sites in sets (e.g. simulated annealing, Ball & Possingham 2000 ); and optimization
algorithms (Cocks & Baird, 1989 ). These methods are
dealing with increasingly large and more complex
problems (see section 6.7 ), which includes having multiple and confl icting objectives and multiple types of
management actions.
It must be noted that decision problems can be quite
complex, and there are now several software packages
that can support systematic conservation planning
(e.g. Marxan , C - Plan , Zonation , ConsNet ; see Moilanen
et al . (2009) for a thorough review of each platform).
However, as Bottrill & Pressey (2009) point out, these
Systematic conservation planning: past, present and future
(which we will refer to henceforth as the year). These actions will alter the dynamics of a variety of
state variables, y ijt . , such as the size of the population of a species in a site, or the amount of an
ecosystem service in a site. Mathematically this means that our control, or decision, variable is a jkt ,
the amount of money we spend on action k in place j in year t . A fairly general formulation of the
conservation resource allocation problem is to:
max
(
)
,
f y ijt
t
T
1
1
=
∑
subject to a budgetary constraint each year
a
b
t
jkt
k
P
j
N
t
=
=
∑
∑
≤
1
1
for all ,
and contingent on the dynamics of the state variables, that is, how key system states move from
year to year in response to actions or forces we do not control:
y
g a y x
i j
t
ijt
t
t
t
.
. .
. .
. .
(
, ,)
,
,
1 ⋅
for all
and
where f is a function that turns our state variables into a reward function that we are trying to maximize (this could be highly non - linear), g is a function that determines how the state variables, yijt,
evolve in space and time as a consequence of actions and forces we do not control, xijt. In this
formulation, N is the number of different places and P is the number of different sorts of actions.
This mathematical formulation of a problem that considers expenditure of money on different
conservation actions in space and time is a fairly general formulation of all resource allocation
problems. It is called a resource allocation problem because there is a fi xed annual budget.
Evaluating actions based on their cost - effectiveness (Joseph et al ., 2009 ) provides one algorithm
that can often provide rough solutions to this very complex optimization problem.
seven - step decision theory framework which has been
articulated by a number of authors for systematic conservation planning (Table 6.2 ; Possingham et al .,
2001 ; K.A. Wilson et al ., 2009 ).
There is now a large amount of literature on optimal
protected area design based on this decision theory
framework (summarized in Moilanen et al ., 2009 ). The
problems generated using this framework can be
expressed mathematically and then solved by one of a
number of methods. There are two classic problem
defi nitions commonly used in conservation planning,
the minimum set and maximal coverage conservation
prioritization problem (Box 6.4 ).
The minimum set problem minimizes the resources
expended while meeting the conservation objectives.
For this problem, the objective is to minimize cost and
the constraint is the conservation objectives.
The maximal coverage conservation prioritization
problem maximizes the objectives (e.g. target level
achievement) given a fi xed amount of resources. Here,
the problem is reversed: the constraint is the budget
and the objective is to maximize conservation
objectives.
Methods for solving systematic conservation planning problems fall into several classes: local heuristic
algorithms, which select sites in a stepwise manner
(Pressey et al ., 1993; 1994 ); global heuristic algorithms, which select sites in sets (e.g. simulated annealing, Ball & Possingham 2000 ); and optimization
algorithms (Cocks & Baird, 1989 ). These methods are
dealing with increasingly large and more complex
problems (see section 6.7 ), which includes having multiple and confl icting objectives and multiple types of
management actions.
It must be noted that decision problems can be quite
complex, and there are now several software packages
that can support systematic conservation planning
(e.g. Marxan , C - Plan , Zonation , ConsNet ; see Moilanen
et al . (2009) for a thorough review of each platform).
However, as Bottrill & Pressey (2009) point out, these