Changes between Version 5 and Version 6 of EwEugMortalityForaPreyIsConsumptionForaPredator
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 20101118 01:57:37 (9 years ago)
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EwEugMortalityForaPreyIsConsumptionForaPredator
v5 v6 11 11 ''P'',,''i '',,''= Y'',,''i'',,'' + B'',,''i'',,''.M2'',,''i'',,'' + E'',,''i'',,'' + BA'',,''i'',,'' + P'',,''i'',,''(''1''  EE'',,''i'',,'')''''' Eq. 2''' 12 12 13 where ''P'',,''i'',, is the total production rate of (''i''), Y''''i'''' is the total fishery catch rate of (''i''), M2''i'' is the total predation rate for group (''i''), ''B'',,i,, the biomass of the group, E''i'' the net migration rate (emigration – immigration), ''BA'',,''i'',, is the biomass accumulation rate for (''i''), while ''M0'',,''i'',,'' = P'',,''i'',, · (1EE''i'') is the ‘other mortality’rate for (''i'').13 where ''P'',,''i'',, is the total production rate of (''i''), Y''''i'''' is the total fishery catch rate of (''i''), M2''i'' is the total predation rate for group (''i''), ''B'',,i,, the biomass of the group, E''i'' the net migration rate (emigration – immigration), ''BA'',,''i'',, is the biomass accumulation rate for (''i''), while ''M0'',,''i'',,'' = P'',,''i'',, · (1EE''i'') is the 'other mortality' rate for (''i''). 14 14 15 15 This formulation incorporates most of the production (or mortality) components in common use, perhaps with the exception of gonadal products. Gonadal products however nearly always end up being eaten by other groups, and can be included in either predation or other mortality. … … 27 27 Based on Eq. 2.3, for a system with ''n'' groups, ''n'' linear equations can be given, in explicit terms, 28 28 29 ..[[Image(08000007.png)]]^''''''^''' Eq. 5'''^''''''^ 29 '''[[Image(08000007.png)]] Eq. 5''' 30 30 31 31 This system of simultaneous linear equations can be reexpressed … … 47 47 If the set of equations is overdetermined (more equations than unknowns), and the equations are not consistent with each other, the generalized inverse method provides least squares estimates, which minimizes the discrepancies. If, on the other hand, the system is underdetermined (more unknowns than equations), an answer that is consistent with the data will still be output. However, it will not be a unique answer. 48 48 49 Of the terms in Eq. 2.3, the production rate, ''P,,i,,'', is calculated as the product of ''B,,i,,'', the biomass of (''i'') and ''P,,i,,/B,,i,,'', the production/biomass ratio for group (''i''). The ''P,,i,,/B,,i,,'' rate under most conditions corresponds to the total mortality rate, ''Z'', see Allen (1971), commonly estimated as part of fishery stock assessments. The ‘other mortality’is a catchall term including all mortality not elsewhere included, e.g., mortality due to diseases or old age, and is internally computed from,49 Of the terms in Eq. 2.3, the production rate, ''P,,i,,'', is calculated as the product of ''B,,i,,'', the biomass of (''i'') and ''P,,i,,/B,,i,,'', the production/biomass ratio for group (''i''). The ''P,,i,,/B,,i,,'' rate under most conditions corresponds to the total mortality rate, ''Z'', see Allen (1971), commonly estimated as part of fishery stock assessments. The 'other mortality' is a catchall term including all mortality not elsewhere included, e.g., mortality due to diseases or old age, and is internally computed from, 50 50 51 51 M0,,i,, = P,,i,, · ''(''1 – EE,,i,,'')''''''' Eq. 9''''' 52 52 53 where ''EE,,i,,'' is called the ‘ecotrophic efficiency’of (''i''), and can be described as the proportion of the production that is utilized in the system. The production term describing predation mortality, ''M2'', serves to link predators and prey as,53 where ''EE,,i,,'' is called the 'ecotrophic efficiency' of (''i''), and can be described as the proportion of the production that is utilized in the system. The production term describing predation mortality, ''M2'', serves to link predators and prey as, 54 54 55 55 ../Resources/Images/0800000B.png^''''''^''' Eq. 10'''^''''''^ 56 56 57 where the summation is over all (''n'') predator groups (''j'') feeding on group (''i''), ''Q,,j,,'' is the total consumption rate for group (''j''), and ''DCji'' is the fraction of predator (''j'') ’s diet contributed by prey (''i''). ''Qj'' is calculated as the product of ''Bj'', the biomass of group (''j'') and ''Qj/Bj'', the consumption/biomass ratio for group (''j'').57 where the summation is over all (''n'') predator groups (''j'') feeding on group (''i''), ''Q,,j,,'' is the total consumption rate for group (''j''), and ''DCji'' is the fraction of predator (''j'')'s diet contributed by prey (''i''). ''Qj'' is calculated as the product of ''Bj'', the biomass of group (''j'') and ''Qj / Bj'', the consumption/biomass ratio for group (''j''). 58 58 59 59 An important implication of the equation above is that information about predator consumption rates and diets concerning a given prey can be used to estimate the predation mortality term for the group, or, alternatively, that if the predation mortality for a given prey is known the equation can be used to estimate the consumption rates for one or more predators instead. … … 67 67 Catch rate;Net migration rate;Biomass accumulation rate;Assimilation rate; andDiet compositions. 68 68 69 It was indicated above that Ecopath does not rely on solving a full set of linear equations, i.e., there may be less equations than there are groups in the system. This is due to a number of algorithms included in the parameterization routine that will try to estimate iteratively as many ‘missing’parameters as possible before setting up the set of linear equations. The following loop is carried out until no additional parameters can be estimated.69 It was indicated above that Ecopath does not rely on solving a full set of linear equations, i.e., there may be less equations than there are groups in the system. This is due to a number of algorithms included in the parameterization routine that will try to estimate iteratively as many 'missing' parameters as possible before setting up the set of linear equations. The following loop is carried out until no additional parameters can be estimated. 70 70 71 71 The net growth efficiency, ''g,,i,,'', is estimated using … … 77 77 ../Resources/Images/0800000C.png^''''''^''' Eq. 12'''^''''''^ 78 78 79 This expression can be solved if both the catch, biomass and ecotrophic efficiency of group ''i'', and the biomasses and consumption rates of all predators on group i are known (including group ''i'' if a zero order cycle, i.e., ‘cannibalism’exists). The catch, net migration and biomass accumulation rates are required input, and hence always known;79 This expression can be solved if both the catch, biomass and ecotrophic efficiency of group ''i'', and the biomasses and consumption rates of all predators on group i are known (including group ''i'' if a zero order cycle, i.e., 'cannibalism' exists). The catch, net migration and biomass accumulation rates are required input, and hence always known; 80 80 81 81 The ''EE'' is estimated from … … 93 93 In cases where for a given prey the P/B, B, EE are known and where the only unknown predation is due to one predator whose ''B'' or ''Q/B'' is unknown, it may be possible to estimate the B or Q/B of the prey in question. 94 94 95 After the loop no longer results in estimate of any ‘missing’ parameters a set of linear equations is set up including the groups for which parameters are still ‘missing’. The set of linear equations is then solved using a generalized inverse method for matrix inversion described by Mackay (1981). It is usually possible to estimate ''P/B'' and ''EE'' values for groups without resorting to including such groups in the set of linear equations.95 After the loop no longer results in estimate of any 'missing' parameters a set of linear equations is set up including the groups for which parameters are still 'missing'. The set of linear equations is then solved using a generalized inverse method for matrix inversion described by Mackay (1981). It is usually possible to estimate ''P/B'' and ''EE'' values for groups without resorting to including such groups in the set of linear equations. 96 96 97 97 The loop above serves to minimize the computations associated with establishing massbalance in Ecopath. The desired situation is, however, that the biomasses, production/biomass and consumption/biomass ratios are entered for all groups and that only the ecotrophic efficiency is estimated, given that no procedure exists for its field estimation.