410 John Woods
passed on exactly the same day ofthe year (and time of day). The plankton populations at each location were the same in successive laps five years apart (Fig. 18.8).
Does this mean that the ecosystem was on its demographic attractor at each location around the circuit? The answer must be "No", because the ecosystem is in a
permanent state of transient response to the changing ambient climate caused by
drifting through the geographical variation in the stationary annual cycle of climate. We know from the numerical experiment at the Azores, that the transient
response to demographic imbalance decays within three years. So, as the water column proceeds around the circuit, its planlcton populations will always be recovering from the different ambient climate experienced as far back as three years
upstream.
The definition of demographic attractor introduced for ecosystems with a stationary annual cycle of environment does not work at geographicallocations where the
annual heat budget is not in balance. So we cannot think of the plankton populations as merely deviating from a formal balance condition because of their
upstream history of ambient climate. Nevertheless, if the pattems of ocean circulation and atmospheric climate both exhibited stationary cycles at every geographical
location, then the VPE does experience a unique annual cycle at each location.
(Remember that this "Eulerian" annual cycle at a fixed location is synthesized from
a set of geographically-lagrangian integrations running down the same track with
different phase lags.) This unique cycle is the consequence oftwo constraints: (1)
the track passing through the target site is fixed, and (2) the history of ambient climate experienced upstream along that track is also fixed.
In reality both the track and the ambient climate history vary with the weather
and inter-annual variation of climate. So the annual cycle of the VPE at the target
location will not be fixed. The magnitude of variation due to inter-annual fluctuations of forcing could be discovered by performing many integrations sampling
upstream histories of ambient climate/weather encountered in ERA data along the
track. The ensemble mean derived from such a set of simulations will provide a
"most probable annual cycle". That is the best description ofwhat to expect when
we observe the plankton ecosystem at that location. The variance of the ensemble
will be used in Ecological Turing testing (18.17).
18.12.3 Extinction and re-population
In this numerical experiment the multi-year nutrient stress in the oligotrophic
(tropical) sector caused the plankton populations to decline, but it was not sufficient to make them go extinct. In the absence of extinction, the VPE is robustly stabIe to quite large environmental stress extending over years. Other geostrophic
tracks keep the water column in the Tropics for so long that zooplankton extinction
does occur, for example along the Azores-Antilles track in Fig. 18.7 (see ecosystem
plots in my website). Note that the conditions ofthe numeric al experiment (barotropic advection) did not allow horizontal emigration and immigration, which
allows the possibility ofrepopulation after extinction in the water column. Repopulation allows the ecosystem to recover from extinctions during passage through the
passed on exactly the same day ofthe year (and time of day). The plankton populations at each location were the same in successive laps five years apart (Fig. 18.8).
Does this mean that the ecosystem was on its demographic attractor at each location around the circuit? The answer must be "No", because the ecosystem is in a
permanent state of transient response to the changing ambient climate caused by
drifting through the geographical variation in the stationary annual cycle of climate. We know from the numerical experiment at the Azores, that the transient
response to demographic imbalance decays within three years. So, as the water column proceeds around the circuit, its planlcton populations will always be recovering from the different ambient climate experienced as far back as three years
upstream.
The definition of demographic attractor introduced for ecosystems with a stationary annual cycle of environment does not work at geographicallocations where the
annual heat budget is not in balance. So we cannot think of the plankton populations as merely deviating from a formal balance condition because of their
upstream history of ambient climate. Nevertheless, if the pattems of ocean circulation and atmospheric climate both exhibited stationary cycles at every geographical
location, then the VPE does experience a unique annual cycle at each location.
(Remember that this "Eulerian" annual cycle at a fixed location is synthesized from
a set of geographically-lagrangian integrations running down the same track with
different phase lags.) This unique cycle is the consequence oftwo constraints: (1)
the track passing through the target site is fixed, and (2) the history of ambient climate experienced upstream along that track is also fixed.
In reality both the track and the ambient climate history vary with the weather
and inter-annual variation of climate. So the annual cycle of the VPE at the target
location will not be fixed. The magnitude of variation due to inter-annual fluctuations of forcing could be discovered by performing many integrations sampling
upstream histories of ambient climate/weather encountered in ERA data along the
track. The ensemble mean derived from such a set of simulations will provide a
"most probable annual cycle". That is the best description ofwhat to expect when
we observe the plankton ecosystem at that location. The variance of the ensemble
will be used in Ecological Turing testing (18.17).
18.12.3 Extinction and re-population
In this numerical experiment the multi-year nutrient stress in the oligotrophic
(tropical) sector caused the plankton populations to decline, but it was not sufficient to make them go extinct. In the absence of extinction, the VPE is robustly stabIe to quite large environmental stress extending over years. Other geostrophic
tracks keep the water column in the Tropics for so long that zooplankton extinction
does occur, for example along the Azores-Antilles track in Fig. 18.7 (see ecosystem
plots in my website). Note that the conditions ofthe numeric al experiment (barotropic advection) did not allow horizontal emigration and immigration, which
allows the possibility ofrepopulation after extinction in the water column. Repopulation allows the ecosystem to recover from extinctions during passage through the