200
10. Life-Stage-Based Recovery Dynami cs of M arin e Invertebrates
calculations of instantaneous larval survivorships INST SURV N LARVAE
and INST SURV P LARVAE (Hannon and Ruth 1997).
Juveniles that result from colonizing larvae can grow and mature to become adults. The model doe s not allow these juveniles to enter the adult
pool until the time necessary for maturation is exceeded. Therefore, time
lags LAG NJUV and LAG P JUV are included in the modules of Figures 10.3
and 10.4 to halt the transition of an entire weekly cohort of larva-derived
colonists. During the lag, the mortality of these individuals is compounded
to reflect the number of weeks spent in the juvenile stage. For example, a
cohort of Nep btys juveniles (which all settle from the plankton during the
same week) is allowed to transition into adulthood after an 80-week lag, in
which it exper iences 80 wee ks of maturation and mortality.
Although adult individuals do not transition into a more mature stage,
they will senesce and eventually die of old age. In the model, juveniles becoming adults are assumed to die after exceeding a certain number of
weeks-the adult-stage duration-in the adult pool. Adults that mature
from juveniles are modeled in the same fashion as juveniles that mature
from larvae ; a lag is used to prevent such adults from dying of old age until
the adult-stage duration has been exceeded. These adults experience other
sources of mortality during the lag and this mortality is compo unded to reflect the duration of the adult stage.
10.2.3. Post-Settler Colonist Pool
The rate of post-settler lateral immigration of juvenile and adu lt life-stages
to disturbed patches is calculated using four parameters: 0 ) Lx-the density
of ambient ind ividuals of life-stage x serving as the source of immigrants;
(2) Ax- the prop ortion of individuals found in the ambient popul ation of
life-stage x horizontally advected across the seabed; (3) Px-th e size (radius) of a defau nated patch; and (4)
density of immigrants present in
a given patch at time t (a dynamical variable). The net density flux due to
immigration is calculated using eq uations based on the following general
formula: L AP (i -fII IL I ). The model assumes that immigration exceeds
x x x
x
emigration in empty patches. As densities of juveniles and adults increase
in the previously disturbed patches, however, the immigration and emigration of post-settlers in the patch become more balanced . Thus, the net
influx of juvenile and adult immigrants follows an asymptotic decline
through time.
For simplicity, juveniles in the undisturbed ambient sed iments (like larvae in the overlying water) are modeled with uniform age-distributions.
Young and old juveniles are advected across the seabed in equa l prop ortions, both serving as potent ial immigrants to the patch. Maturation into
adulthoo d of the oldest juvenile colonists is possible immediately following
their arrival in a patch. The flows MATURE N JUV IMM and MATURE P JUV
IMM capture that maturation (Figures 10.3 and 10.4). The pro portion transi-
10. Life-Stage-Based Recovery Dynami cs of M arin e Invertebrates
calculations of instantaneous larval survivorships INST SURV N LARVAE
and INST SURV P LARVAE (Hannon and Ruth 1997).
Juveniles that result from colonizing larvae can grow and mature to become adults. The model doe s not allow these juveniles to enter the adult
pool until the time necessary for maturation is exceeded. Therefore, time
lags LAG NJUV and LAG P JUV are included in the modules of Figures 10.3
and 10.4 to halt the transition of an entire weekly cohort of larva-derived
colonists. During the lag, the mortality of these individuals is compounded
to reflect the number of weeks spent in the juvenile stage. For example, a
cohort of Nep btys juveniles (which all settle from the plankton during the
same week) is allowed to transition into adulthood after an 80-week lag, in
which it exper iences 80 wee ks of maturation and mortality.
Although adult individuals do not transition into a more mature stage,
they will senesce and eventually die of old age. In the model, juveniles becoming adults are assumed to die after exceeding a certain number of
weeks-the adult-stage duration-in the adult pool. Adults that mature
from juveniles are modeled in the same fashion as juveniles that mature
from larvae ; a lag is used to prevent such adults from dying of old age until
the adult-stage duration has been exceeded. These adults experience other
sources of mortality during the lag and this mortality is compo unded to reflect the duration of the adult stage.
10.2.3. Post-Settler Colonist Pool
The rate of post-settler lateral immigration of juvenile and adu lt life-stages
to disturbed patches is calculated using four parameters: 0 ) Lx-the density
of ambient ind ividuals of life-stage x serving as the source of immigrants;
(2) Ax- the prop ortion of individuals found in the ambient popul ation of
life-stage x horizontally advected across the seabed; (3) Px-th e size (radius) of a defau nated patch; and (4)
density of immigrants present in
a given patch at time t (a dynamical variable). The net density flux due to
immigration is calculated using eq uations based on the following general
formula: L AP (i -fII IL I ). The model assumes that immigration exceeds
x x x
x
emigration in empty patches. As densities of juveniles and adults increase
in the previously disturbed patches, however, the immigration and emigration of post-settlers in the patch become more balanced . Thus, the net
influx of juvenile and adult immigrants follows an asymptotic decline
through time.
For simplicity, juveniles in the undisturbed ambient sed iments (like larvae in the overlying water) are modeled with uniform age-distributions.
Young and old juveniles are advected across the seabed in equa l prop ortions, both serving as potent ial immigrants to the patch. Maturation into
adulthoo d of the oldest juvenile colonists is possible immediately following
their arrival in a patch. The flows MATURE N JUV IMM and MATURE P JUV
IMM capture that maturation (Figures 10.3 and 10.4). The pro portion transi-