Changes between Version 1 and Version 2 of EwEugAscendancy


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Timestamp:
2010-11-23 01:48:19 (8 years ago)
Author:
shermanl
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  • EwEugAscendancy

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    11== 7.22 Ascendancy == 
    22 
    3 Ascendency is a measure of the average mutual information in a system, scaled by system throughput, and is derived from information theory (see Ulanowicz and Norden, 1990). If one knows the location of a unit of energy the uncertainty about where it will next flow to is reduced by an amount known as the average mutual information, 
     3Ascendency is a measure of the average mutual information in a system, scaled by system throughput, and is derived from information theory (see Ulanowicz and Norden, 1990). If one knows the location of a unit of energy the uncertainty about where it will next flow to is reduced by an amount known as the average mutual information', 
    44 
    55[[Image(wiki:EwEugImages:08000084.png)]] ''' Eq. 37''' 
     
    2121[[Image(wiki:EwEugImages:0800008C.png)]] ''' Eq. 41''' 
    2222 
    23 where, it is ''A'' that is called ‘ascendency’. The ascendency is symmetrical and will have the same value whether calculated from input or output. 
     23where, it is ''A'' that is called 'ascendency'. The ascendency is symmetrical and will have the same value whether calculated from input or output. 
    2424 
    25 There is an upper limit for the size of the ascendency. This upper limit is called the ‘development capacity’ and is estimated from 
     25There is an upper limit for the size of the ascendency. This upper limit is called the 'development capacity' and is estimated from 
    2626 
    2727[[Image(wiki:EwEugImages:0800008D.png)]] ''' Eq. 42''' 
    2828 
    29 where ''H'' is called the ‘statistical entropy’, and is estimated from 
     29where ''H'' is called the 'statistical entropy', and is estimated from 
    3030 
    3131[[Image(wiki:EwEugImages:0800008E.png)]] '''Eq. 43''' 
    3232 
    33 The difference between the capacity and the ascendency is called ‘system overhead’. The overheads provide limits on how much the ascendency can increase and reflect the system's ‘strength in reserve’ from which it can draw to meet unexpected perturbations (Ulanowicz, 1986). As an example, the part of the ascendency that is due to imports, ''A,,0,,'', can increase at the expense of the overheads due to imports, ''Q,,0,,''. This can be done by either diminishing the imports or by importing from a few major sources only. The first solution would imply that the system should starve, while the latter would render the system more dependent on a few sources of imports. The system thus does not benefit from reducing ''Q'',,''0'',, below a certain system-specific critical level (Ulanowicz and Norden, 1990). 
     33The difference between the capacity and the ascendency is called 'system overhead'. The overheads provide limits on how much the ascendency can increase and reflect the system's 'strength in reserve' from which it can draw to meet unexpected perturbations (Ulanowicz, 1986). As an example, the part of the ascendency that is due to imports, ''A,,0,,'', can increase at the expense of the overheads due to imports, ''Q,,0,,''. This can be done by either diminishing the imports or by importing from a few major sources only. The first solution would imply that the system should starve, while the latter would render the system more dependent on a few sources of imports. The system thus does not benefit from reducing ''Q'',,''0'',, below a certain system-specific critical level (Ulanowicz and Norden, 1990). 
    3434 
    3535The ascendency, overheads and capacity can all be split into contributions from imports, internal flow, exports and dissipation (respiration). These contributions are additive. 
    3636 
    37 The unit for these measures is ‘flowbits’, or the product of flow (e.g., t/km^2^/year) and bits. Here the ‘bit’ is an information unit, corresponding to the amount of uncertainty associated with a single binary decision. 
     37The unit for these measures is 'flowbits', or the product of flow (e.g., t/km^2^/year) and bits. Here the 'bit' is an information unit, corresponding to the amount of uncertainty associated with a single binary decision. 
    3838 
    39 The overheads on imports and internal flows (redundancy) may be seen as a measure of system stability ''sensu'' Odum, and the ascendency / system throughput ratio as a measure of information, as included in Odums attributes of ecosystem maturity.  For a study of ecosystem maturity using Ecopath see Christensen (1995a). 
     39The overheads on imports and internal flows (redundancy) may be seen as a measure of system stability ''sensu'' Odum, and the ascendency / system throughput ratio as a measure of information, as included in Odum's attributes of ecosystem maturity.  For a study of ecosystem maturity using Ecopath see Christensen (1995a). 
    4040 
    4141Ecopath calculates ascendency, overheads and capacity for the whole system (Total form) and by group (By group form).