Changes between Version 7 and Version 8 of EwEugMortalityForaPreyIsConsumptionForaPredator


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Timestamp:
2010-11-21 22:21:15 (9 years ago)
Author:
shermanl
Comment:

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  • EwEugMortalityForaPreyIsConsumptionForaPredator

    v7 v8  
    3535This can be written in matrix notation as 
    3636 
    37 ''''[''A'']'',,nm,, . ''[''X'']'',,m,, = ''[''Q'']''m''''' Eq. 7''' 
     37[''A''],,nm,, . [''X''],,m,, = [''Q''],,m,, '''Eq. 7''' 
    3838 
    3939Given the inverse ''A''^''-''1^ of the matrix ''A'', this provides 
    4040 
    41 ''''[''X'']'',,nm,, . ''[''A^-1^'']'',,n,m,, = ''[''Q'']''m ''''' Eq. 8''''''' 
     41[''X''],,nm,, . [''A^-1^''],,n,m,, = [''Q''],,m,, ''' Eq. 8''' 
    4242 
    4343If 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. 
     
    4747Of 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, 
    4848 
    49 M0,,i,, = P,,i,, · ''(''1 – EE,,i,,'')''''''' Eq. 9''''' 
     49''M0,,i,, = P,,i,,'' · ''(''1'' – ''EE,,i,,'')'' ''' Eq. 9''' 
    5050 
    5151where ''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, 
    5252 
    53 '''[[Image(0800000B.png)]] Eq. 10''''' 
     53[[Image(0800000B.png)]] '''Eq. 10''' 
    5454 
    5555where 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''). 
     
    6969The net growth efficiency, ''g,,i,,'', is estimated using 
    7070 
    71 ''cg,,i,,= (P,,i,,/B,,i,,)/(Q,,i,,/B,,i,,) ''''' Eq. 11''' 
     71''cg,,i,,= (P,,i,,/B,,i,,)/(Q,,i,,/B,,i,,)'' ''' Eq. 11''' 
    7272 
    7373while ''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 
    7474 
    75 '''[[Image(0800000C.png)]] Eq. 12''''' 
     75[[Image(0800000C.png)]] '''Eq. 12''' 
    7676 
    7777This 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; 
     
    7979The ''EE'' is estimated from 
    8080 
    81 '''[[Image(0800000D.png)]] Eq. 13''''' 
     81[[Image(0800000D.png)]] '''Eq. 13''' 
    8282 
    8383where the predation mortality ''M2'' is estimated from Eq. 2.2.10.