10.2 Life-Stage-Based Invertebrate Model
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life-stages horizontally along the seabed, (2) the relative importance of juvenile versus adult life-stages as post-settlement colonists , (3) the role of
species' life-history traits (primarily reproductive strategies and maturation
times of post-set life-stages) in affecting the rate of recovery, and (4) the effects of spatial scale (i.e. disturbed patch size) on the recovery process. The
general structure of the model is laid out first, before we address in more
detail assumptions about larval and post-settler colonist pools .
Two polychaete worm specie s (Nephtys incisa and Polydora cornuta) are
used to illustrate recovery dynamics because of their contrasting life-history
strategies, and because demographic data such as stage-specific survivorship, fecundity, maturation time, and lifespan are available for use in
model parameterization (Zajac 1991; Zajac and Whitlatch 1989) . Polydora is
characteristic of an "early stage " colonist, whereas Nepbtys is normally
viewed as a "late stage" successional spe cies (e.g. Pearson and Rosenberg
1978; Rhoads et al. 1978). For simplicity, both species' life-histories (Figure
10.1 and 10.2) are modeled as three distinct life-stages: larvae, juveniles and
adults using as a general framework the three-stage insect model described
in Hannon and Ruth (997).
Adult worm densitie s are used to assess recovery time in disturbed
patches of habitat. Recovery time-measured in weeks-is operationally
defined as the time by which the density of adults in disturbed patches
reaches 90% of the density of adults in undisturbed areas of the habitat. We
choose the 90% threshold value for two reasons . First, normal spatial and
temporal variability of natural population densities (often exceeding 10%)
would prevent disturbed and undisturbed populations from being distinguished when they differ in the field at this level. Second , as discussed in
more detail below, recovery time in the model is asymptotic, and as a consequence, disturbed patch densities occasionally remain between 90 and
100% for extended periods before reaching a threshold of 100%.
Disturbed (completely defaunated) patches are assumed to be circular
with radius r and surrounded by undisturbed sediments. Although patches
are devoid of fauna at time 0, larvae produced by worms in the undisturbed
area are assumed to reside in the water column above patches and postsettled life-stages (i.e. juveniles and adults) are assumed to occupy surrounding sediments. Even the largest patch (r = 200 m) is extremely small
relative to the undisturbed ambient area (100 km/). Therefore, ambient densities of juvenile and adult life-stages are fixed in our model (i.e. we assume
they would be unaffected by the dynamics of patch recovery) . Those fixed
densities are , respectively , denoted NEPH ]lNENILES, NEPH ADULTS,
POLY]lNENILES and POLY ADULTS in the model (Figure 10.3 to 10.6).
With information about the individual life-stages, calculated in Figures
10.1 through 10.6, we can calculate total Nephtys and Polydora populations
as shown in Figures 10.7 and 10.8Larval and post-settler life stages represent two independent colonist pools.
Larvae in the water column rain down from above a patch and-assuming
193
life-stages horizontally along the seabed, (2) the relative importance of juvenile versus adult life-stages as post-settlement colonists , (3) the role of
species' life-history traits (primarily reproductive strategies and maturation
times of post-set life-stages) in affecting the rate of recovery, and (4) the effects of spatial scale (i.e. disturbed patch size) on the recovery process. The
general structure of the model is laid out first, before we address in more
detail assumptions about larval and post-settler colonist pools .
Two polychaete worm specie s (Nephtys incisa and Polydora cornuta) are
used to illustrate recovery dynamics because of their contrasting life-history
strategies, and because demographic data such as stage-specific survivorship, fecundity, maturation time, and lifespan are available for use in
model parameterization (Zajac 1991; Zajac and Whitlatch 1989) . Polydora is
characteristic of an "early stage " colonist, whereas Nepbtys is normally
viewed as a "late stage" successional spe cies (e.g. Pearson and Rosenberg
1978; Rhoads et al. 1978). For simplicity, both species' life-histories (Figure
10.1 and 10.2) are modeled as three distinct life-stages: larvae, juveniles and
adults using as a general framework the three-stage insect model described
in Hannon and Ruth (997).
Adult worm densitie s are used to assess recovery time in disturbed
patches of habitat. Recovery time-measured in weeks-is operationally
defined as the time by which the density of adults in disturbed patches
reaches 90% of the density of adults in undisturbed areas of the habitat. We
choose the 90% threshold value for two reasons . First, normal spatial and
temporal variability of natural population densities (often exceeding 10%)
would prevent disturbed and undisturbed populations from being distinguished when they differ in the field at this level. Second , as discussed in
more detail below, recovery time in the model is asymptotic, and as a consequence, disturbed patch densities occasionally remain between 90 and
100% for extended periods before reaching a threshold of 100%.
Disturbed (completely defaunated) patches are assumed to be circular
with radius r and surrounded by undisturbed sediments. Although patches
are devoid of fauna at time 0, larvae produced by worms in the undisturbed
area are assumed to reside in the water column above patches and postsettled life-stages (i.e. juveniles and adults) are assumed to occupy surrounding sediments. Even the largest patch (r = 200 m) is extremely small
relative to the undisturbed ambient area (100 km/). Therefore, ambient densities of juvenile and adult life-stages are fixed in our model (i.e. we assume
they would be unaffected by the dynamics of patch recovery) . Those fixed
densities are , respectively , denoted NEPH ]lNENILES, NEPH ADULTS,
POLY]lNENILES and POLY ADULTS in the model (Figure 10.3 to 10.6).
With information about the individual life-stages, calculated in Figures
10.1 through 10.6, we can calculate total Nephtys and Polydora populations
as shown in Figures 10.7 and 10.8Larval and post-settler life stages represent two independent colonist pools.
Larvae in the water column rain down from above a patch and-assuming