Ecological Archives A020-057-A2

J. Wilson White, Louis W. Botsford, Elizabeth A. Moffitt, and Douglas T. Fischer. 2010. Decision analysis for designing marine protected areas for multiple species with uncertain fishery status. Ecological Applications 20:1523–1541.

Appendix B. Life history parameters for California North Central Coast species.
Contents

Introduction

Species Notes

Literature Cited




Introduction

In order to model the dynamics of commercially important species in California’s North Central Coast, we compiled literature estimates of larval dispersal distances, juvenile and adult home range sizes, and other life history parameters.  In this text and the tables that follow, we provide both reported estimates of each parameter and, for those parameters with different estimates or a range of values, we indicate the value we have chosen to use in our models.  Unless otherwise noted, all distances are in km, all organism lengths are in cm, and all masses are in kg.

We obtained information on larval dispersal distances from a variety of sources, including (1) genetic relatedness over space, (2) artificial or natural elemental tags in fish otoliths, (3) biophysical models of ocean circulation, and (4) estimates of the pelagic larval duration (PLD). In many cases, PLD was the only information available, and we assumed that larval dispersal distance will generally be longer for species with greater PLD (Shanks et al. 2003), or that at least species with longer PLDs have a greater opportunity to disperse long distances.  We report larval dispersal in terms of the standard deviation of a larval dispersal kernel (a probability distribution of settlement locations).  Because our models assume there is no net advection, this dispersal distance is equivalent to the mean of one side of the kernel, and we sometimes refer to this as the mean dispersal distance (in one direction).

The species we modeled either have very little adult movement or move within a specified home range.  In general, we report home range size in terms of diameter, which facilitates implementation in a one-dimensional model.  Home range diameter estimates are derived from studies using a variety of tagging methods, but we note that there is greater confidence in estimates derived from acoustic tagging studies than from simple tag-recapture studies (Zeller 1999, Lowe et al. 2003). 

We model the adult demography of all species by assuming that they have asymptotic von Bertalanffy growth and that both weight and per capita fecundity are allometric functions of length, although there is some variety in the precise functional form that is appropriate for each species.  We modeled mortality as an instantaneous rate that consists of two components, fishing mortality and natural mortality.  The size ranges that are available to be caught by the fishery are either specified by regulation or estimated from fishery or other data.




Red abalone (Haliotis rufescens)

Parameter values were estimated from studies on red abalone and its congeners in California and elsewhere. Based on information from red abalone and other abalone species, it is doubtful that red abalone larvae disperse more than several kilometers, and some disperse considerably less than that (see review by Morgan and Shepherd 2006).  The larval duration in Table 1 is for H. rubra from Tasmania, and is mentioned in Hobday and Tegner (2002).  A study using a circulation model indicated that in normal calm conditions most larvae of H. iris (New Zealand) settled within 200 m of their parents, and the maximum distance traveled was 4 km (Stephens et al. 2006).

We did not use the most recent estimate of natural mortality rate (Leaf et al. 2007) because with those mortality rates and published ages of maturity and first capture, virtually no individuals survive to fishable age.  Instead we used a natural mortality rate of 0.15/y, which was used by Tegner et al. (1989), and comes from Fournier and Breen (1983) who estimated natural mortality of Haliotis sp. in British Columbia.  We assumed that the age of first capture in the fishery was 8 y, at which age individuals only 20 mm (13%) larger than the mean length could be harvested legally.



TABLE B1.  Red abalone parameters.
Parameter
Literature estimate
Value used in model
Source
Pelagic larval duration (d)
4–7
-
a
Mean larval dispersal distance (km)
0–10
1
b, c
Home range diameter (km)
0–1
<1
d
Length-at-age (cm)
L(t) = Linf{1-exp[-k(t-t0)]}


e
Linf (cm)
19.24
19.24
k (y-1)
0.217
0.217
t0 (y)
0
0
Weight-at-length (kg)
W = qLp


f
q
1.69 × 10-4
1.69 × 10-4
p
3.02
3.02
Maximum age (y)
30–40
30
g
Age at maturity (y)
3
3
h
Fecundity-at-length (eggs)
E = gLh


i
g
15.32
15.32
h
4.518
4.518
Natural mortality rate (y-1)
0.65 (L < 10 cm)
0.34–0.75 (10 ≤ L < 17.8 cm)
0.05 (L ≥ 17.8 cm)
0.15
i,j
0.15
k
Available to fishery
17.8 cm
8 y
l

Sources:





Red sea urchin (Strongylocentrotus franciscanus)

There are several references for the duration of the larval stage of red sea urchin, so we used the consensus value reported by Leet et al. (2001), then estimated dispersal distance based on the approach of Shanks et al. (2003).  No direct measurements of home range size have been made, but so we estimated a value based on consistent observations that red sea urchins move very little after settlement (less than 10 m; Rogers-Bennett et al. 1995).

Growth and mortality rates have been estimated from size distributions collected along the coast of northern California (Morgan, et al. 1997, 2000).   We could not obtain a length–weight relationship so assumed a cubic function.



TABLE B2.  Red sea urchin parameters.
Parameter Literature estimate
Value used in model
Source
Pelagic larval duration (wk) 7–19
-
a
Mean larval dispersal distance (km)
50
b
Home range diameter (km) 0.001
< 1
c
Length-at-age (cm)
L(t) = Linf{1-exp[-k(t-t0)]}


d
Linf (cm) 11.8
11.8
k (y-1) 0.22
0.22
t0 (y) 0
0
Weight-at-length (kg)
W = qLp


-
q -
1
p
-
3
Maximum age (y) 30
30
d
Age at maturity (y) 3
3
d
Size at maturity (test diameter, cm)
6
6
d
Fecundity-at-length (eggs)
E = gLh


d
g 5.47 × 10-6
5.47 × 10-6
h
3.45
3.45
Natural mortality rate (y-1) 0.08
0.08
d
Available to fishery 8.9 cm ( 5 yr)
8.9 cm ( 5 yr) d

Sources:





Black rockfish (Sebastes melanops)

Our estimate of the one-sided mean dispersal distance was based on empirical information from otolith geochemical studies in Oregon and Washington (Miller and Shanks 2004; J. Miller, unpublished data).  The empirical data can be approximated by a mean dispersal distance of approximately 73 km using a Gaussian dispersal distribution (J. W. White, unpublished data).

The range of home range diameters estimated for this species was 9–14 km, but we favor Starr and Green’s (2007) estimate of 9 km because their study was done at Duxbury Reef in the North Central Coast study region.  This was the distance from the release point within which 95% of recaptures were obtained.
   
Black rockfish stock assessments commonly report both lower and upper length limits for fishery selectivity.  The lower limit is due to CDFG regulations, while upper limit may be due to larger fish moving offshore and out of the fishery altogether.  For now we have included only the statutory lower bound in Table B3.



TABLE B3.  Black rockfish parameters.
Parameter Literature estimate Value used in model Source
Pelagic larval duration (d) 4–6
-
a
Mean larval dispersal distance (km) 73
73 b, c
Home range diameter (km) 9–16
9
d, e, f
Length-at-age (cm)
L(t) = Linf{1-exp[-k(t-t0)]}


g
Linf (cm) 44.2
44.2
k (y-1) 0.33
0.33
t0 (y) 0.075
0075
Weight-at-length (kg)
W = qLp


h
q
1.68 × 10-5 1.68 × 10-5
p
3
3

Maximum age (y) 50
50
a
Age at maturity (y) 7
7
g
Fecundity-at-length (eggs)
E = (d + eW)W


h
d 2.89 × 105 2.89 × 105
e 1.0 × 105 1.0 × 105
Natural mortality rate (y-1) 0.14 0.14 h, i
Available to fishery 32 cm (live fishery)
27 cm (recreational)
29 cm (4 y)
i

Sources:





Cabezon (Scorpaenichthys marmorata)

Our estimate of the mean larval dispersal distance is larger for cabezon than for rockfish with similar pelagic larval durations.  Unlike rockfish, which have a pelagic juvenile stage, cabezon remain in a larval form throughout the pelagic period.  We assume that this is associated with less advanced swimming abilities and thus less larval retention and greater overall dispersal.

The home range diameter for cabezon was based on an acoustic tagging study which found that cabezon were found within this diameter 95% of the time (C. Merelis, R. Nakamura, D. Wendt, unpublished manuscript).



TABLE B4.  Cabezon parameters.
Parameter Literature estimate Value used in model Source
Pelagic larval duration (d) 3–4
-
a
Mean larval dispersal distance (km) ≤ 1000
100
b
Home range diameter (km) 0.06
< 1
c
Length-at-age (cm)
L(t) = Linf{1-exp[-k(t-t0)]}


a
Linf (cm) 62.12
62.12
k (y-1) 0.18
0.18
t0 (y) -1.06
-1.06
Weight-at-length (kg)
W = qL


a
q
9.2 × 10-6
9.2 × 10-6
p
3.187
3.187
Maximum age (y) > 13
15
a, d
Age at maturity (y) 3
3
a
Fecundity-at-length (eggs)
E = gLh


a
g
1.4 × 10-7 1.4 × 10-7
h
3.187
3.187
Natural mortality rate (y-1) 0.25
0.25
a
Available to fishery 38.1 cm
38 cm (4 y)
e

Sources:

a. Cope and Punt (2005)
b. Shanks et al. (2003)
c. C. Merelis, R. Nakamura, and D. Wendt, unpublished manuscript.
d. Love (1996)
e. CDFG (2008)





Canary rockfish (Sebastes pinniger)

Preliminary results suggest that larval dispersal patterns for canary rockfish are potentially variable over time and reflect a high degree of mixing in the plankton (J. Miller, personal communication).  At present there are insufficient data to obtain a reliable estimate of the larval dispersal distance, so in the interest of parsimony we used the same value as the congener, black rockfish.

The home range estimate for canary rockfish is 9 km, based on seven recaptures of tagged fish at Duxbury Reef in the North Central Coast study region (Starr and Green 2007) as well as tagging studies in central California and Oregon (DeMott 1983, Lea et al. 1999).

The estimate of size at which canary rockfish become available to the fishery applies to the commercial trawl fishery, and does not include size selectivity of bycatch mortality from the nearshore recreational fishery, which is currently closed to this species.



TABLE B5. Canary rockfish parameters.
Parameter
Literature estimate
Value used in model
Source
Pelagic larval duration (d) 3–4
-
a
Mean larval dispersal distance (km) 70
70
b
Home range diameter (km) 9
9
c, d, e
Length-at-age (cm)
L(t) = Linf{1-exp[-k(t-t0)]}


f
Linf (cm) 58.9 (female)
52.3 (male)
58.9
k (y-1) 0.146 (female)
0.189 (male)
0.146
t0 (y) -0.84 (female)
-0.5 (male)
-0.84
Weight-at-length (kg)
W = qLp


f
q 2.45 × 10-4 (female)
2.818 × 10-4 (both sexes)
2.45 × 10-4
p 2.91 (female)
2.28 (both sexes)
2.91
Maximum age (y) > 84
85
a
Age at maturity (y) 7
7
f
Fecundity-at-length (eggs)
E = gLh


f
g
4.24 × 10-5 4.24 × 10-5
h
5.95
5.95
Natural mortality rate (y-1) 0.06 (males, young females)
0.09 (females > 15 y old)
0.06
f
Available to fishery 40 cm
40 cm (7 y)
f

Sources:





Lingcod (Ophiodon elongatus)
   
There are several tagging studies of adult lingcod movement (references within Starr et al. 2004, Starr and Green 2007) which indicate a high percentage of fish are caught within 8–17 km of their origin.  We chose 9 km because the higher values were from the Pacific Northwest, whereas a study at Duxbury Reef, just north of San Francisco (Starr and Green 2007) reported lower values.
   
Larval dispersal parameters for lingcod are difficult to discern.  A 3 month PLD suggests a dispersal distance on the order of 1000 km (Shanks et al. 2003) and a recent genetic study using mitochondrial DNA found no significant genetic structure along the Pacific coast as measured by FST (Marko et al. 2007).  However, a Markov chain – Monte Carlo analysis of gene flow in the same study suggested little connectivity (< 63 migrants per generation) between two California sites separated by 100 km (Marko et al. 2007).  Given the latter result, we chose the relatively conservative dispersal distance of 35 km.



TABLE B6.  Lingcod parameters.
Parameter
Literature estimate
Value used in model
Source
Pelagic larval duration (d) 2–3
-
a, b
Mean larval dispersal distance (km) ≤ 1000
35
c
Home range diameter (km) 8–17
9
d–l
Length-at-age (cm)
L(t) = Linf +(L1- Linf)exp[k(1 - t)]


m
Linf (cm) 112.8
112.8
k (y-1) 0.145
0.145
L1 (cm) 35.1
35.1
Weight-at-length (kg)
W = qLp


m
q
1.76 × 10-6
1.76 × 10-6
p
3.398
3.398
Maximum age (y) 20
20
m
Age at maturity (y) 4
4
m
Fecundity-at-length (eggs)
E = gLh


m
g
2.82 × 10-4
2.82 × 10-4
h
3.00
3.00
Natural mortality rate (y-1) 0.18
0.18
m
Available to fishery 61 cm, 3–4 y (recreational)
2–3 y (commercial)
3 y
m, o

Sources:





LITERATURE CITED

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Culver, B. N. 1987 Results from tagging Black Rockfish (Sebastes melanops) off the Washington and Northern Oregon coast. Alaska Sea Grant Report 87:231–239.

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