Changes between Version 6 and Version 7 of EwEugSpatialOptimizationProcedures


Ignore:
Timestamp:
2010-01-31 16:12:11 (10 years ago)
Author:
varunr
Comment:

--

Legend:

Unmodified
Added
Removed
Modified
  • EwEugSpatialOptimizationProcedures

    v6 v7  
    1212'''__Methodology__''' 
    1313 
    14 '''Objective function''' 
     14'''''Objective function''''' 
    1515 
    1616We employ an objective function for the optimizations, which corresponds to the objective function used in the policy optimization module of EwE. This module, which has been applied to a number of case studies, (e.g., Christensen and Walters, 2004; Araújo et al., 2008; Arreguin-Sanchez et al., 2008) uses a non-linear search routine to find a combination of effort by fishing fleets that will maximize the objective function. The objective function in turn includes ecological, economical and social indicators, even legal constraints if pertinent, through considering profit, number of jobs, stock rebuilding, and two ecological measures. For the spatial optimizations we add a further indicator in form of a boundary weight factor (See Table 1) 
     
    5050[[Image(wiki:EwEugImages:0300001C.png)]] 
    5151 
    52 here .[[Image(wiki:EwEugImages:0300001D.png)]] is the number of functional groups, and [[Image(wiki:EwEugImages:0300001E.png)]] is the biomass of the ([[Image(wiki:EwEugImages:0300001F.png)]])^th^ most common group, using a weighted average of the two closest group if ([[Image(wiki:EwEugImages:0300001F.png)]]) is not an integer. The biomass diversity index describes the slope of a cumulative group abundance curve. As a sample with high diversity (evenness) will have a low slope, we reverse the index and express it relative to index value from the Ecopath base run ([[Image(wiki:EwEugImages:03000020.png)]]) 
     52here .[[Image(wiki:EwEugImages:0300001D.png)]] is the number of functional groups, and [[Image(wiki:EwEugImages:0300001E.png)]] is the biomass of the ([[Image(wiki:EwEugImages:0300001F.png)]])th most common group, using a weighted average of the two closest group if ([[Image(wiki:EwEugImages:0300001F.png)]]) is not an integer. The biomass diversity index describes the slope of a cumulative group abundance curve. As a sample with high diversity (evenness) will have a low slope, we reverse the index and express it relative to index value from the Ecopath base run ([[Image(wiki:EwEugImages:03000020.png)]]) 
    5353 
    5454[[Image(wiki:EwEugImages:03000021.png)]] 
    5555 
    56 We truncate the index in the extreme and unlikely case that ../Resources/Images/03000022.png would more than double from the base run. We only include higher trophic level groups (TL>3) in the calculation of the biomass diversity index – should this, for models with only few functional groups, lead to less than 10 groups being included in the calculations, we, however, base the calculations on all living groups. As for the other ecological indicators we do not discount future index values. 
     56We truncate the index in the extreme and unlikely case that [[Image(wiki:EwEugImages:03000022.png)]] would more than double from the base run. We only include higher trophic level groups (TL>3) in the calculation of the biomass diversity index – should this, for models with only few functional groups, lead to less than 10 groups being included in the calculations, we, however, base the calculations on all living groups. As for the other ecological indicators we do not discount future index values. 
    5757 
    58 The final element in the objective function represents spatial connectivity, expressed through the boundary weight factor, ../Resources/Images/03000023.png 
     58The final element in the objective function represents spatial connectivity, expressed through the boundary weight factor, [[Image(wiki:EwEugImages:03000023.png)]] 
    5959 
    60 ../Resources/Images/image001.png 
     60[[Image(wiki:EwEugImages:image001.png)]] 
    6161 
    62 where the total protected area size (../Resources/Images/03000025.png, km2) is summed over spatial cells (../Resources/Images/03000026.png), and the boundary length is estimated by summing over all protected cell (../Resources/Images/03000027.png) the side lengths (../Resources/Images/03000028.png, km) that do not border another protected cell or land. 
     62where the total protected area size ([[Image(wiki:EwEugImages:03000025.png)]], km^2^) is summed over spatial cells ([[Image(wiki:EwEugImages:03000026.png)]]), and the boundary length is estimated by summing over all protected cell ([[Image(wiki:EwEugImages:03000027.png)]]) the side lengths ([[Image(wiki:EwEugImages:03000028.png)]], km) that do not border another protected cell or land. 
    6363 
    64 With the elements of the objective function being defined, we can now obtain the overall objective function measure (../Resources/Images/03000029.png) from 
     64With the elements of the objective function being defined, we can now obtain the overall objective function measure ([[Image(wiki:EwEugImages:03000029.png)]]) from 
    6565 
    66 ../Resources/Images/0300002A.png  Equation 2 
     66[[Image(wiki:EwEugImages:0300002A.png)]]  '''Equation 2''' 
    6767 
    68 Where each of the objective weighting factors, (../Resources/Images/0300002B.png), can assume any value, including zero, which is used for measures that are ignored in a given optimization. We use the objective function measure for both of the optimization methods described below. 
     68Where each of the objective weighting factors, ([[Image(wiki:EwEugImages:0300002B.png)]]), can assume any value, including zero, which is used for measures that are ignored in a given optimization. We use the objective function measure for both of the optimization methods described below. 
    6969 
    70 === Seed cell selection procedure === 
     70'''''Seed cell selection procedure''''' 
     71 
    7172This optimization method is based on a previous study (Beattie 2001; Beattie et al. 2002), in which a very simple optimization scheme was used to evaluate tradeoff between proportion of area protected and the ecosystem-level objective function. We have modified the previous approach by securing a better program flow, and notably by changing the objective function from considering only profit from fishing and existence value of biomass groups to the more detailed function described above (Equation 2). 
    7273