Changes between Version 6 and Version 7 of EwEugSpatialOptimizationProcedures
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 20100131 16:12:11 (14 years ago)
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EwEugSpatialOptimizationProcedures
v6 v7 12 12 '''__Methodology__''' 13 13 14 ''' Objective function'''14 '''''Objective function''''' 15 15 16 16 We 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; ArreguinSanchez et al., 2008) uses a nonlinear 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) … … 50 50 [[Image(wiki:EwEugImages:0300001C.png)]] 51 51 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)]])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)]]) 53 53 54 54 [[Image(wiki:EwEugImages:03000021.png)]] 55 55 56 We truncate the index in the extreme and unlikely case that ../Resources/Images/03000022.pngwould 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.56 We 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. 57 57 58 The final element in the objective function represents spatial connectivity, expressed through the boundary weight factor, ../Resources/Images/03000023.png58 The final element in the objective function represents spatial connectivity, expressed through the boundary weight factor, [[Image(wiki:EwEugImages:03000023.png)]] 59 59 60 ../Resources/Images/image001.png 60 [[Image(wiki:EwEugImages:image001.png)]] 61 61 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.62 where 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. 63 63 64 With the elements of the objective function being defined, we can now obtain the overall objective function measure ( ../Resources/Images/03000029.png) from64 With the elements of the objective function being defined, we can now obtain the overall objective function measure ([[Image(wiki:EwEugImages:03000029.png)]]) from 65 65 66 ../Resources/Images/0300002A.png Equation 2 66 [[Image(wiki:EwEugImages:0300002A.png)]] '''Equation 2''' 67 67 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.68 Where 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. 69 69 70 === Seed cell selection procedure === 70 '''''Seed cell selection procedure''''' 71 71 72 This 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 ecosystemlevel 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). 72 73