Changes between Version 7 and Version 8 of EwEugMortalityForaPreyIsConsumptionForaPredator

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Timestamp:
2010-11-21 22:21:15 (10 years ago)
Comment:

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• EwEugMortalityForaPreyIsConsumptionForaPredator

 v7 This can be written in matrix notation as ''''[''A'']'',,nm,, . ''[''X'']'',,m,, = ''[''Q'']''m''''' Eq. 7''' [''A''],,nm,, . [''X''],,m,, = [''Q''],,m,, '''Eq. 7''' Given the inverse ''A''^''-''1^ of the matrix ''A'', this provides ''''[''X'']'',,nm,, . ''[''A^-1^'']'',,n,m,, = ''[''Q'']''m ''''' Eq. 8''''''' [''X''],,nm,, . [''A^-1^''],,n,m,, = [''Q''],,m,, ''' Eq. 8''' If the determinant of a matrix is zero, or if the matrix is not square, it has no ordinary inverse. However, a generalized inverse can be found in most cases (Mackay, 1981). In the Ecopath model, the approach of Mackay (1981) is used to estimate the generalized inverse. 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 catch-all term including all mortality not elsewhere included, e.g., mortality due to diseases or old age, and is internally computed from, M0,,i,, = P,,i,, · ''(''1 – EE,,i,,'')''''''' Eq. 9''''' ''M0,,i,, = P,,i,,'' · ''(''1'' – ''EE,,i,,'')'' ''' Eq. 9''' 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, '''[[Image(0800000B.png)]] Eq. 10''''' [[Image(0800000B.png)]] '''Eq. 10''' 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''). The net growth efficiency, ''g,,i,,'', is estimated using ''cg,,i,,= (P,,i,,/B,,i,,)/(Q,,i,,/B,,i,,) ''''' Eq. 11''' ''cg,,i,,= (P,,i,,/B,,i,,)/(Q,,i,,/B,,i,,)'' ''' Eq. 11''' while ''P,,i,,/B,,i,,'' and ''Q,,i,,/B,,i,,''are attempted solved by inverting the same equation. The'' P/B'' ratio is then estimated (if possible) from '''[[Image(0800000C.png)]] Eq. 12''''' [[Image(0800000C.png)]] '''Eq. 12''' 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; The ''EE'' is estimated from '''[[Image(0800000D.png)]] Eq. 13''''' [[Image(0800000D.png)]] '''Eq. 13''' where the predation mortality ''M2'' is estimated from Eq. 2.2.10.