Ecological Archives M076-016-A3

Craig A. Aumann, Lisa A. Eby, and William F. Fagan. 2006. How transient patches affect population dynamics: the case of hypoxia and blue crabs. Ecological Monographs 76:415–438.

Appendix C. A table of model parameters and additional model results.


Next: List of Figures Previous: Altering All Clam Factors


Model Parameters and Additional Results


TABLE C1. Names, units, descriptions, values and references for the list of variables used in the crab model. 

Symbol

Units

Description

Value

References

 

3D Random Fields

# of Mesh Levels

 

Total number of refinements done of the coarse grid

4

Appendix A.3.

$ N_x$

 

Number of discretization points used for generating field in the $ x$ direction

64

Appendix A.3.1

$ N_y$

 

Number of discretization points used for generating field in the $ y$ direction

32

Appendix A.3.1

$ N_t$

 

Number of discretization points used for generating field in the $ t$ direction

256

Appendix A.3.1

$ \eta$

 

Filter used on the Gaussian Random Field

 

Eq. (A.1)

$ \sigma_{x,S}$

m

SD of filter in $ x$ direction used for generating salinity field

1000

Appendix A.3.3

$ \sigma_{y,S}$

m

SD of filter in $ y$ direction used for generating salinity field

800

Appendix A.3.3

$ \sigma_{t,S}$

hr

SD of filter in $ t$ direction used for generating salinity field

48

Appendix A.3.3

$ \sigma_{x, T}$

m

SD of filter in $ x$ direction used for generating temperature field

1000

Appendix A.3.2

$ \sigma_{y,T}$

m

SD of filter in $ y$ direction used for generating temperature field

800

Appendix A.3.2

$ \sigma_{t, T}$

hr

SD of filter in $ t$ direction used for generating temperature field

48

Appendix A.3.2

$ \xi(x, \sigma)$

 

Component of the filter $ \eta$

 

Eq. (A.2)

 

 

Variables Associated with Habitat

$ d(x,y)$

m

Distance from the western most point of the estuary

 

Appendix A.3.2

$ d_$max

m

Maximum distance from the western most point of the estuary

 

Appendix A.3.2

$ d_s$

 

Proportion of distance from the western most point of the estuary

$ d(x, y)/d_$max

Appendix A.3.2

$ D(x,y)$

m

Depth of estuary at location

 

Appendix A.3

$ DO$

mg/L

Concentration of oxygen in bottom water of estuary

Eq. (A.9)

Borsuk et al. (2001b, Eq. 21)

$ DO_u$

mg/L

Concentration of oxygen in upper water column at saturation

Eq. (A.11)

Hyer et al. (1971, Eq. 12)

$ K_d$

1/hr

Rate constant for oxygen demand by sediment Eq. (A.15)

5.75E-3

Based on Borsuk et al. (2001b); Borsuk et al. (2001a)

$ \theta_{d}$

$ x^{-T}$

Constant representing level of temperature dependency. Eq. (A.15)

1.13

Borsuk et al. (2001b, Table 1)

$ k_v$

m/hr$ ^{1/2}$

Constant for vertical oxygen exchange from surface, Eq. (A.12)

0.003

Based on Borsuk et al. (2001b); Schnoor (1996, Table 6.3)

$ K_v$

1/hr

Governs vertical oxygen exchange. Eq. (A.10) and (A.12)

 

Schnoor (1996, Sec 6.3)

$ \theta_v$

$ x^{-T}$

Constant representing level of temperature dependence. Eq. (A.12)

1.0

Borsuk et al. (2001b, Table 1)

$ S_{\text{bot}}$

psu

Bottom salinity

Eq. (A.6)

Appendix A.3.3

$ S_{\text{deep}}$

psu

Maximum salinity

Eq. (A.7)

Appendix A.3.3

$ T$

$ ^\circ$ C

Temperature

Eq. (A.3)

Appendix A.3.2

$ T_$depth

$ ^\circ$ C

Temperature

Eq. (A.5)

Appendix A.3.2

$ T_$mean

$ ^\circ$ C

Temperature

Eq. (A.4)

Appendix A.3.2

$ U$

m/hr

Mean tidal velocity Eq. (A.12)

100

 Luettich Jr. et al. (1999)

 

 

Clam Variables

$ \alpha_{\text{c}}$

g/cm$ ^3$

Scaling parameter relating clam length, $ L_{\text{c}}$, to wet weight, $ w_$c,w. Eq. (A.16)

0.1

Bachelet (1980, Table 2); Gilbert (1973)

$ \beta_{\text{c}}$

 

Power relating clam length $ L_{\text{c}}$, to wet weight, $ w_$c,w. Eq. (A.16)

3.0

Bachelet (1980, Table 2); Gilbert (1973)

$ \beta_{\text{c,grow}}$

$ ^\circ$C$ ^{-1}$

Coeff. of temperature growth. Eq. (A.17)

0.2

Solidoro et al. (2000)

$ \beta_{\text{c,resp}}$

$ ^\circ$C$ ^{-1}$

Coeff. of temperature respiration. Eq. (A.17)

0.17

Solidoro et al. (2000)

$ \Delta t$

hr

Time between updates of clams

24

 

$ f_{c, G}$

 

Temperature dependence of clam growth

Eq. (A.18)

 Solidoro et al. (2000)

$ f_{c, r}$

 

Temperature dependence of clam respiration

Eqs. (A.17)

 Solidoro et al. (2000)

$ G_{\text{c,max}}$

g$ ^{1/3}$/hr

Maximum growth rate for clam on a wet weight basis Eq. (A.17).

4.3E-4

Based on Solidoro et al. (2000, Table 2)

$ g(DO)$

 

Proportion decrease in metabolism due to DO

Eq. (A.19)

 McMahon and Wilson (1981)

$ \gamma_{cB}$

 

Clam biomass factor influencing recruitment

Eq. (A.23)

 

$ \gamma_{c D}$

 

Triangle depth factor influencing recruitment

App A.4.3

 

Initial mass

g

Initial mass of recruited clam

0.001

 

$ L_$c

cm

Length of clam shell

 

Eq. (A.16)

$ \lambda_a$

hr

Parameter Eq. (A.20), CDF of times till death at fixed DO

32.16

 Borsuk et al. (2002)

$ \lambda_b$

L hr/mg

Parameter Eq. (A.20), CDF of times till death at fixed DO

27.36

 Borsuk et al. (2002)

$ \lambda_c$

hr

Parameter Eq. (A.20), CDF of times till death at fixed DO

9.6

 Borsuk et al. (2002)

$ \lambda_{\text{Base}}$

hr$ ^{-1}$

Mortality rate without predation Eq. (A.20)

1.2E-5

 Commito (1982); van der Meer et al. (2001)

$ \lambda_{T_{\text{c,min resp}}}$

hr$ ^{-1}$

Mortality rate for clams in water less than -5 $ \ensuremath{^\circ\text{C }}$. Eq. (A.20)

0.2

 

$ \lambda_{T_{\text{c,max resp}}}$

hr$ ^{-1}$

Mortality rate for clams in water greater than $ T_{\text{c,max resp}}$ $ ^\circ$ C. Eq. (A.20)

1.04E-2

 

$ r_{\text{c,max}}$

1/hr

Maximum respiration rate for clam on a wet weight basis Eq. (A.17)

3.5E-4

Based on Hummel (1985a, Table 1); McMahon and Wilson (1981)

$ \rho_{cB}$

g/m$ ^2$

Grams of clam biomass on a given fine-level triangle

 

Eq. (A.23)

$ \rho_{cB,\text{recruit}}$

g/m$ ^2$

Upper bound on clam biomass on a given fine-level triangle Eq. (A.23)

850

 Hines and Comtois (1985)

$ \rho_{ce}$

#/m$ ^2$

Potential recruitment egg density

 

Appendix A.4.3

$ \rho_$c,tri

#/m$ ^2$

Clam density on a fine-level triangle

 

Eq. (A.24)

$ \rho_{c u}$

#/m$ ^2$

Upper bound on clam density on a given triangle Eq. (A.24)

1300

Holland et al. (1980)

$ T$

$ \ensuremath{^\circ\text{C }}$

Temperature of clam.

 

 

$ T_{\text{c,max grow}}$

$ \ensuremath{^\circ\text{C }}$

Max temperature for growth. Eq. (A.17)

31

 

$ T_{\text{c,max resp}}$

$ \ensuremath{^\circ\text{C }}$

Max. temperature for respiration. Eq. (A.17)

33

Wilson (1981); Kennedy and Mihursky (1971)

$ T_{\text{c,min resp}}$

$ \ensuremath{^\circ\text{C }}$

Min. temperature for respiration. Eq. (A.17)

-5

Bourget (1983)

$ T_{\text{c,opt grow}}$

$ \ensuremath{^\circ\text{C }}$

Optimal temperature for growth. Eq. (A.17)

22

Solidoro et al. (2000)

$ T_{\text{c,opt resp}}$

$ \ensuremath{^\circ\text{C }}$

Optimal temperature for respiration. Eq. (A.17)

20

Bensch et al. (1992)

$ w_{\text{c,w}}$

g

Clam's wet weight.

 

Eq. (A.16) and (A.17)

 

 

Background Food

$ A$

m$ ^2$

Area of fine-level triangle

Eq. (A.25)

 

$ \alpha$

1/hr

Base mortality rate of background

2E-4

 

$ \beta_{\text{b,grow}}$

$ ^\circ$C$ ^{-1}$

Coeff. of temperature growth. Eq. (A.25)

0.2

 

$ f_b(T;\cdot)$

 

Temperature dependence of growth of background food Eq. (A.25)

$ f_c(T;\cdot)$

Eq. (A.18)

$ N$

g

Number of grams of background food on a fine-level triangle

 

Eq. (A.25)

$ \tilde{N}$

g

Average density of background food just on triangle and neighbors

 

Eq. (A.25)

$ K$

g/m$ ^2$

Carrying capacity of background

400

Eq. (A.25)

$ \rho_b$

g/m$ ^2$

Density of background food on triangle

$ N/A$

 

$ r_N$

1/hr

Max growth rate of background

8E-4

Eq. (A.25)

$ \Delta t$

hr

Time between updates of background

24

Eq. (A.25)

$ T_{\text{b,max grow}}$

$ \ensuremath{^\circ\text{C }}$

Max temperature for growth. Eq. (A.25)

35

 

$ T_{\text{b,opt grow}}$

$ \ensuremath{^\circ\text{C }}$

Optimal temperature for growth. Eq. (A.25)

26

 

 

 

Crab Variables

$ \alpha_{\text{egest}}$

$ \frac{\text{cm}^{3-\beta_\text{egest}}}{\text{hr}}$

Parameter in Eq. (A.40).

0.004

 

$ \alpha_{\text{ingest}}$

$ \frac{\text{g}^{1-\beta_{\text{ingest}}}}{\text{hr}}$

Parameter relating size of crab to ingestion rate. Eq. (A.38)

30.0

 

$ \alpha_{\text{G}}$

g/cm $ ^{\beta_{\text{G}}}$

Scale parameter in Eq. (A.36) relating CW to wet weight

0.14

Pullen and Trent (1970); Olmi III and Bishop (1983); Cadman and Weinstein (1985); Newcombe et al. (1949)

$ \alpha_{\text{max move}}$

g $ ^{1 -\beta_\text{move}}$

Scalar governing maximum rate of movement Eq. (A.28)

$ 300^{1-\beta_{\text{move}}}$

 

$ \alpha_{\text{max,met}}$

$ \frac{g^{1-\beta_{\text{met}}}}{\text{hr}}$

Maximum base respiration parameter. Eq. (A.44)

0.00678

 Booth and McMahon (1992, Table 1) and Houlihan et al. (1985, Fig. 1).

$ \alpha_{\text{min,met}}$

$ \frac{\text{g}^{1-\beta_{\text{met}}}}{\text{hr}}$

Minimum base respiration rate. Eq. (A.44)

0.00166

 Booth and McMahon (1992, Table 1)and Houlihan et al. (1985, Fig. 1).

$ \alpha_{\text{molt}}$

g/cm $ ^{\beta_{\text{molt}}}$

Scalar relating CW to total grams to molt. Eq. (A.46)

2E-2

 

$ \alpha_{\text{move}}$

$ \frac{\text{g}^{1-\beta_\text{move}}}{\text{m hr}}$

Scalar relating mass and movement rate to energy expenditure. Eq. (A.45)

4E-5

Houlihan et al. (1985, Fig. 1)

$ \alpha_{\text{stom}}$

cm

Scaling parameter for stomach volume in Eq. (A.37)

0.0255

Based on McGaw and Reiber (2000)

$ \beta_$egest

 

Parameter in Eq. (A.40).

2.0

 

$ \beta_{\text{ingest}}$

 

Parameter relating size of crab to ingestion rate. Eq. (A.38)

0.25

 

$ {\beta_{\text{G}}}$

 

Power relating CW to wet weight in Eq. (A.36)

2.7

Pullen and Trent (1970); Olmi III and Bishop (1983); Cadman and Weinstein (1985); Newcombe et al. (1949)

$ \beta_{\text{met}}$

 

How metabolic demand increases with weight. Eq. (A.44)

2/3

Houlihan et al. (1985)

$ \beta_{\text{molt}}$

 

Power relating CW to total grams crab must expend to molt. Eq. (A.46)

2

 

$ \beta_{\text{move}}$

 

Power relating mass to rate of energy usage for movement. Eq. (A.45)

0.33

Houlihan et al. (1985)

$ \beta_{\text{stom}}$

 

Power of CW for computing stomach volume Eq. (A.37)

2.0

See Appendix A.5.6

$ b_1$

 

First parameter of movement distribution. App. A.5.4

1

 

$ b_2$

 

Second parameter of movement distribution. App. A.5.4

40

 

CW

cm

Carapace width

 

 

$ CW_$init, lower

cm

Lower range of CW at 7th instar. Appendix A.5.13

1.05

Newcombe et al. (1949, Table IV)

$ CW_{\text{init, width}}$

cm

Width of CW instantiation range at. Appendix A.5.13

0.6

 

$ d_{\text{max inter}}$

m

Maximum distance between crabs when they may interact

12

Appendix A.5.3

$ \delta t$

hr

Random time interval between a crab's updates

 

Appendix A.5.2

Energy$ _{egg}$

cal

Energy content of a single crab egg.

0.0454

Kannupandi et al. (1999)

$ \eta_i$

#

Number of clams in age class $ i$

Eq. (A.33)

 

$ f_$Temp$ (T;\cdot)$

 

Function governing metabolism on temperature

Eq. (A.39)

 

$ f_{\text{ingest, temp}}$

 

Particular parameterization of $ f_$Temp$ (T;\cdot)$

Eq. (A.38)

 

$ G$

g

Wet weight of crab.

Eq. (A.30)

 

$ G_{\text{egest}}$

g/hr

Grams egested from the crab

Eq. (A.41)

 

$ G_{\text{egest stom}}$

g/hr

Grams egested from the stomach

Eq. (A.40)

 

$ G_{\text{ingest}}$

g/hr

Grams ingested into the crab's stomach.

Eq. (A.38)

 

$ G_{\text{mass next molt}}$

g

Mass when next molting will be triggered. Eq. (A.36)

 

 

$ G_{\text{molt}}$

g/hr

Grams expended molting over $ \delta t$

Eq. (A.47)

 

$ G_{\text{move}}$

g/hr

Grams used solely by crab moving

Eq. (A.45)

 

$ G_{\text{repro}}$

g/hr

Grams put into reproduction

Appendix A.5.12

 

$ G_{\text{resp+excrete}}$

g/hr

Respiration and excretion costs

Eq. (A.44)

 

$ G_{\text{stom}}$

g

Grams of food in stomach

Eq. (A.42)

 

$ G_{\text{total to molt}}$

g

Total grams crab expends to molt

Eq. (A.47)

 

$ G_{\text{total molted}}$

g

Grams expended molting.

Eq. (A.47)

 

$ \gamma_{\text{absorbtion}}$

 

Absorption coefficient. Eq. (A.41)

0.6

 Guerin and Stickle (1992, Tables 2 and 3)

$ \gamma_{\text{clam}}$

 

Change in weighting factor caused by DO $ < 1$ mg/L Eq. (A.34)

 

Appendix A.5.6

$ \gamma_{\text{clam,def}}$

 

Default weighting factor for clam depth refuge Eq. (A.34)

1.0

 

$ \gamma_{\text{c,encounter}}$

m$ ^2$/# clams

Constant in Eq. (A.31)

1/75

 

$ \gamma_{\text{b,encounter}}$

m$ ^2$/#

Governs probability of finding background food

Eq. (A.35)

 

$ \gamma_{\text{excretion}}$

 

Excretion as a proportion of respiration costs

0.05

 Guerin and Stickle (1992, Tables 2 and 3)

$ \gamma_{\text{maturation}}$

 

Constant governing rate crab development in maturation pot. See App. A.5.13

0.55

 

$ \gamma_$mov$ (T)$

 

Gives dependence of rate of movement on temperature.

Eq. (A.27)

 

$ \lambda_$mat

1/hr

Mortality rate for crabs in maturation pot. App. A.5.13

5E-3

 

$ \lambda_{\text{update max}}$

hr$ ^{-1}$

Parameter governing crab's update times

1.0

 

$ m_1$

 

First parameter for crab's lifetime distribution. App. A.5.14

3.0

 

$ m_2$

 

Second parameter for crab's lifetime distribution. App. A.5.14

1.5

 

Max Age

hr

App. A.5.14

70080

 Rugolo et al. (1998)

$ \phi_i$

 

Weighting factor governing crab's foraging ability on clams

Eq. (A.33)

 

$ p_{\text{cw,l}}$

 

Lower bound for proportion increase in CW. Eq. (A.49)

0.24

Tagatz (1968, Table 2)

$ p_{\text{cw, u}}$

 

Upper bound for proportion increase in CW. Eq. (A.49)

0.32

Tagatz (1968, Table 2)

$ Q_$egest

 

Slope for temperature dependence of egestion in Eq. (A.40)

5

 

$ Q_$ingest

 

Slope for temperature dependence of intake in Eq. (A.38)

5

 

$ Q_{\text{met}}$

 

Slope for temperature dependence of metabolism

2.5

 Booth and McMahon (1992)

$ q_{\text{feed}}$

 

Quality of food feeding on

 

 

$ q_{\text{stom}}$

 

Quality of food in stomach

Eq. (A.43)

 

$ \rho_$c$[,]$

#/m$ ^2$

Density of clams within crab's forageable size range

 

Eq. (A.31)

$ \rho_{\text{energy}}$

cal/g wet wt

Energy density of crab

1000

Cummins and Wuycheck (1971, Table 2, p. 25)

$ \rho_f$

g/cm$ ^3$

Density of food in stomach

1.5

 

$ \rho_$c

#/m$ ^2$

Density clams on triangle

 

App. A.4 and A.5.6

$ \rho_b$

g/m$ ^2$

Density of background food on triangle

Eq. (A.35)

 

$ \rho_$max

#/m$ ^2$

Upper bound on the density of crabs in the estuary

0.4

Appendix A.5.13

Scale factor

 

Factor by which the estuary is scaled Appendix A.6

100

 

Sex Ratio

 

Proportion of male crab's instantiated into the estuary.

0.5

 

$ \sigma_{\text{molt}}$

g$ ^{-1/2}$

Parameter governing rate of energy expenditure as molting progresses. Eq. (A.47)

0.15

 

$ \theta_$new

rad

Direction of crab movement, kept between $ [0, 2\pi)$.

 

 

$ T_$max egest

$ \ensuremath{^\circ\text{C }}$

Maximum temperature for crab egestion. Eq. (A.40)

33

 

$ T_$max ingest

$ \ensuremath{^\circ\text{C }}$

Maximum temperature for crab ingestion. Eq. (A.38)

33

 

$ T_{\text{max met}} $

$ ^\circ$C

Maximum temperature for metabolic processes

35

Tagatz (1969, Table 1)

$ T_$max spawn

$ ^\circ$C

Maximum temperature for crab spawning

29

van den Avyle (1984)

$ T_$min spawn

$ ^\circ$C

Minimum temperature for crab spawning

19

van den Avyle (1984)

$ T_{\text{min met}} $

$ ^\circ$C

Minimum temperature for metabolic processes

2

Tagatz (1969, Table 1)

$ T_$opt egest

$ \ensuremath{^\circ\text{C }}$

Optimal temperature for crab egestion. Eq. (A.40)

25

 

$ T_$opt ingest

$ \ensuremath{^\circ\text{C }}$

Optimal temperature for crab ingestion. Eq. (A.38)

25

 

$ T_{\text{opt met}} $

$ \ensuremath{^\circ\text{C }}$

Optimal temperature for metabolic processes

26

 

$ v_{\text{max}}$

m/hr

Maximum rate of crab movement. Eq. (A.28)

720

Houlihan et al. (1985); Clark et al. (1999)

$ v$

m/hr

Actual rate of crab movement.

Eq. (A.28)

 

$ V_{\text{stom}}$

cm$ ^3$

Volume of Crab's Stomach.

Eq. (A.37)

 

$ V_f$

cm$ ^3$

Volume of food in crab's stomach.

$ G_{\text{stom}}/\rho_f$

 

$ X$

 

Gaussian Random Field

 

App. A.3 and A.3.1

$ Z$

 

Random mixing term for DO

 

 Eqs. (A.13) and (A.9)


TABLE C2. Estuary wide summaries of hypoxic extent crossed with duration. Additional variables are given in Table 1. For all variables except Recruit 7, 12 and 18, the mean and (SD) were calculated for the daily model exports for years 30 through 39 between June 1 and September 30 (n=1220). Recruit 7, 12 and 18 were calculated over the entire 10 year period. The variable Max % Hypoxic is the maximum percentage of the estuary hypoxic per year averaged over the 10 years.  

 

Max Extent Hypoxia

 

$ \approx$ 15%

$ \approx$ 30%

$ \approx$ 45%

$ \approx$ 60%

Hypoxic Dur

Short

Long

Fixed

Short

Long

Fixed

Short

Long

Fixed

Short

Long

Fixed

Max % Hypoxic

17.7

18

15.6

28.1

27

32.8

44.9

41.7

45.1

61.9

58.3

58.8

 

(6.5)

(6.5)

(0.1)

(7.2)

(7.4)

(0.1)

(7.2)

(7.7)

(0.1)

(6.2)

(6.4)

(0)

% Hypoxic

5.7

6.9

7.3

10.7

12.5

18.9

20.9

22.9

31.1

36.9

37.8

45.2

 

(5.3)

(5.9)

(5.7)

(7.7)

(8.4)

(9.8)

(11.3)

(11.4)

(12.7)

(13)

(12.6)

(12.7)

DO (mg/L)

5.5

5.4

3.5

5.2

5.1

3.1

4.8

4.8

2.9

4.1

4.1

2.6

 

(0.7)

(0.7)

(0.2)

(0.8)

(0.8)

(0.3)

(0.8)

(0.8)

(0.3)

(0.9)

(0.9)

(0.3)

Hypoxic Edge (10$ ^{-2}$ m/m$ ^2$)

1.12

1.33

1.59

1.82

2.06

2.7

3.04

3.25

3.71

4.13

4.24

4.84

 

(0.85)

(0.91)

(1.08)

(1.07)

(1.11)

(0.97)

(1.28)

(1.27)

(1.04)

(0.94)

(0.91)

(1.02)

Clam Density (#/m$ ^2$)

915

913

882

914

902

821

893

852

802

774

722

696

 

(73)

(92)

(134)

(89)

(115)

(184)

(128)

(159)

(236)

(230)

(244)

(248)

Crab Biomass (g/m$ ^2$)

7.84

7.52

4.7

6.84

6.3

3.33

5.29

4.86

2.69

2.83

2.75

2.01

 

(0.8)

(0.77)

(0.58)

(0.87)

(0.68)

(0.52)

(0.77)

(0.57)

(0.4)

(0.42)

(0.39)

(0.31)

Mat Female Mass (g)

239.2

245.2

221.8

242.2

241.7

217.6

234.1

231.7

220.3

223.4

220.2

222.4

 

(5.9)

(6.5)

(8.6)

(8.3)

(8.2)

(9.4)

(6.3)

(9.1)

(9.4)

(8)

(13)

(11.1)

Mat Female CW (cm)

17.4

17.6

17.1

17.5

17.5

17

17.5

17.4

17.1

17.4

17.4

17.3

 

(0.1)

(0.1)

(0.2)

(0.1)

(0.1)

(0.2)

(0.1)

(0.2)

(0.2)

(0.2)

(0.4)

(0.3)

Egg (#/m$ ^2$ hr)

19.04

16.22

6.46

16.67

12

4.41

10.83

6.42

3.83

3.28

2.08

2.26

 

(13.38)

(12.75)

(7.98)

(12.55)

(10.74)

(6.66)

(9.94)

(7.9)

(5.88)

(5.8)

(4.48)

(4.57)

Egg per Mat Fe (#/# hr)

1794

1750

1261

1893

1653

1252

1828

1397

1280

1283.

1007

1195

 

(1250)

(1362)

(1501)

(1418)

(1472)

(1839)

(1655)

(1718)

(1962)

(2289)

(2214)

(2418)

Recruit 7 (10$ ^{-6}$#/m$ ^2$ hr)

133.85

119.82

74.95

131.47

99.6

57.65

95.45

64.61

51.51

38.79

27.2

33.41

 

(456.73)

(388.57)

(275.73)

(468.41)

(343.84)

(215.23)

(325.31)

(240.68)

(188.49)

(162.63)

(121.68)

(139.27)

Recruit 12 (10$ ^{-6}$#/m$ ^2$ hr)

14.28

11.94

12.55

15.92

11.52

10.94

15.33

10.34

9.56

8.51

6

7.67

 

(25.53)

(19.91)

(25.75)

(29.51)

(20.15)

(22.62)

(28.66)

(19.22)

(19.84)

(15.94)

(11.53)

(15.87)

Recruit 18 (10$ ^{-6}$#/m$ ^2$ hr)

2.36

2.13

1.69

2.12

1.91

1.25

1.73

1.55

0.99

1.06

0.93

0.79

 

(3.7)

(3.33)

(2.96)

(3.51)

(3.17)

(2.31)

(3.06)

(2.78)

(1.97)

(2.08)

(1.88)

(1.6)

Gut Fullness 7-12

0.366

0.352

0.382

0.4

0.351

0.379

0.438

0.363

0.365

0.394

0.339

0.36

 

(0.07)

(0.063)

(0.092)

(0.069)

(0.064)

(0.091)

(0.077)

(0.068)

(0.085)

(0.078)

(0.081)

(0.094)

Gut Fullness 13-17

0.445

0.447

0.463

0.459

0.456

0.457

0.478

0.459

0.464

0.464

0.438

0.457

 

(0.032)

(0.031)

(0.039)

(0.033)

(0.034)

(0.045)

(0.03)

(0.039)

(0.046)

(0.039)

(0.058)

(0.051)

Gut Fullness 18+

0.43

0.412

0.434

0.455

0.427

0.453

0.492

0.431

0.443

0.452

0.419

0.442

 

(0.037)

(0.034)

(0.029)

(0.035)

(0.035)

(0.031)

(0.031)

(0.042)

(0.038)

(0.044)

(0.046)

(0.042)

Food Qual 7-12

0.347

0.346

0.346

0.347

0.346

0.345

0.347

0.347

0.346

0.35

0.35

0.343

 

(0.015)

(0.016)

(0.016)

(0.014)

(0.015)

(0.016)

(0.014)

(0.017)

(0.017)

(0.019)

(0.027)

(0.02)

Food Qual 13-17

0.415

0.42

0.405

0.409

0.418

0.405

0.402

0.417

0.407

0.405

0.412

0.4

 

(0.007)

(0.009)

(0.007)

(0.007)

(0.008)

(0.008)

(0.006)

(0.008)

(0.01)

(0.01)

(0.011)

(0.009)

Food Qual 18+

0.402

0.407

0.391

0.396

0.403

0.389

0.385

0.398

0.392

0.386

0.392

0.39

 

(0.008)

(0.008)

(0.006)

(0.008)

(0.007)

(0.007)

(0.006)

(0.01)

(0.008)

(0.009)

(0.01)

(0.009)

Death Aggr 7-12 (10$ ^{-4}$/hr)

6.63

6.1

6.04

7.31

5.78

5.76

7.79

5.57

5.63

5.74

4.01

5.08

 

(4.83)

(4.38)

(4.82)

(5.08)

(4.25)

(5.06)

(5.82)

(4.19)

(4.82)

(5.33)

(4.49)

(5.01)

Death Aggr 13-17 (10$ ^{-4}$/hr)

7.31

7.11

8.05

8.24

7.65

8.9

8.89

8.21

9.67

8.31

7.48

9.14

 

(3.16)

(3.38)

(3.54)

(3.78)

(3.96)

(4.85)

(4.47)

(4.94)

(5.51)

(5.11)

(5.59)

(5.77)

Death Aggr 18+ (10$ ^{-4}$/hr)

2.4

2.12

3.07

2.61

2.4

3.36

2.93

2.55

3.19

3.26

2.8

3.5

 

(1.82)

(1.67)

(2.24)

(2.05)

(1.97)

(2.74)

(2.61)

(2.39)

(2.99)

(3.31)

(3.22)

(3.7)


TABLE C3. Effect of altering the levels of clam and background prey. Additional variables are given in Table 2. The food Limited case corresponds to decreasing the upper bound on clam biomass recruitment to $ \rho_{cB,\text{recruit}}$=425 (g/m$ ^2$) (Default value is $ \rho_{cB, \text{recruit}} = 850$ g/m$ ^2$, Table C1) and background carrying capacity to 200 (g/m$ ^2$) (Default value is $ K=400$ g/m$ ^2$, Table C1). The Default is the same as Short hypoxic duration in Table C2. The food Unlimited case corresponds to turning off all clam and background mortality due to hypoxia. A Short hypoxic duration was used in all scenarios.

 

Short Duration, Max Extent Hypoxia

 

$ \approx$ 15%

$ \approx$ 30%

$ \approx$ 45%

$ \approx$ 60%

Food Level

Limit

Def

Unlim

Limit

Def

Unlim

Limit

Def

Unlim

Limit

Def

Unlim

Max % Hypoxic

18.6

17.7

19.4

33.9

28.1

30.9

49.9

44.9

46.8

61.8

61.9

62.9

 

(6.7)

(6.5)

(6.2)

(7.4)

(7.2)

(7)

(6.8)

(7.2)

(6.8)

(6.5)

(6.2)

(6)

% Hypoxic

 

 

 

 

 

 

 

 

 

 

 

 

 

6

5.7

6.8

13.5

10.7

12.6

24.9

20.9

23.3

36.8

36.9

38.3

 

(5.6)

(5.3)

(5.7)

(9.1)

(7.7)

(8.2)

(12)

(11.3)

(11.1)

(12.9)

(13)

(12.7)

DO (mg/L)

5.5

5.5

5.4

5.1

5.2

5.2

4.7

4.8

4.8

4.1

4.1

4

 

(0.7)

(0.7)

(0.7)

(0.8)

(0.8)

(0.8)

(0.9)

(0.8)

(0.9)

(0.9)

(0.9)

(0.9)

Hypoxic Edge (10$ ^{-2}$ m/m$ ^2$)

1.14

1.12

1.26

2.16

1.82

2.05

3.34

3.04

3.29

4.13

4.13

4.18

 

(0.87)

(0.85)

(0.86)

(1.2)

(1.07)

(1.06)

(1.21)

(1.28)

(1.18)

(0.95)

(0.94)

(0.89)

Clam Density (#/m$ ^2$)

448

915

915

441

914

928

436

893

947

384

774

983

 

(39)

(73)

(58)

(51)

(89)

(55)

(83)

(128)

(53)

(111)

(230)

(52)

Crab Biomass (g/m$ ^2$)

4.63

7.84

7.99

3.62

6.84

6.92

2.69

5.29

5.53

1.8

2.83

3.78

 

(0.36)

(0.8)

(0.86)

(0.47)

(0.87)

(0.83)

(0.42)

(0.77)

(0.71)

(0.3)

(0.42)

(0.55)

Mat Female Mass (g)

254.4

239.2

239.4

244.5

242.2

239

240

234.1

238.5

225.5

223.4

240.3

 

(10.1)

(5.9)

(6.4)

(8.6)

(8.3)

(6.5)

(12.4)

(6.3)

(6.8)

(13.6)

(8)

(8.9)

Mat Female CW (cm)

17.7

17.4

17.5

17.6

17.5

17.5

17.6

17.5

17.5

17.5

17.4

17.5

 

(0.1)

(0.1)

(0.1)

(0.1)

(0.1)

(0.1)

(0.2)

(0.1)

(0.1)

(0.3)

(0.2)

(0.2)

Egg (#/m$ ^2$ hr)

8.88

19.04

19.3

6.91

16.67

16.39

3.62

10.83

12.45

1.24

3.28

7.33

 

(9.4)

(13.38)

(14.2)

(7.76)

(12.55)

(12.52)

(5.45)

(9.94)

(10.92)

(3.27)

(5.8)

(8.36)

Egg per Mat Fe (#/# hr)

1451

1794

1832

1442

1893

1918

1008

1828

1961

744

1283

2004

 

(1544)

(1250)

(1319)

(1621)

(1418)

(1467)

(1521)

(1655)

(1704)

(2170)

(2289)

(2285)

Recruit 7 (10$ ^{-6}$#/m$ ^2$ hr)

78.91

133.85

145.21

67.36

131.47

126.12

41.92

95.45

107.33

18.38

38.79

79.41

 

(282.99)

(456.73)

(509.53)

(255.09)

(468.41)

(451.22)

(170.24)

(325.31)

(363.06)

(97.89)

(162.63)

(285.18)

Recruit 12 (10$ ^{-6}$#/m$ ^2$ hr)

5.05

14.28

15.51

5.73

15.92

16.95

4.92

15.33

16.15

3.49

8.51

12.19

 

(8.43)

(25.53)

(27.74)

(9.56)

(29.51)

(31.87)

(8.62)

(28.66)

(30.72)

(6.68)

(15.94)

(22.72)

Recruit 18 (10$ ^{-6}$#/m$ ^2$ hr)

1.2

2.36

2.45

1.13

2.12

2.18

0.85

1.73

1.77

0.62

1.06

1.28

 

(1.91)

(3.7)

(3.89)

(1.87)

(3.51)

(3.69)

(1.61)

(3.06)

(3.14)

(1.32)

(2.08)

(2.45)

Gut Fullness 7-12

0.271

0.366

0.39

0.283

0.4

0.429

0.285

0.438

0.451

0.306

0.394

0.459

 

(0.055)

(0.07)

(0.069)

(0.056)

(0.069)

(0.077)

(0.049)

(0.077)

(0.091)

(0.063)

(0.078)

(0.123)

Gut Fullness 13-17

0.372

0.445

0.452

0.386

0.459

0.47

0.409

0.478

0.485

0.393

0.464

0.497

 

(0.041)

(0.032)

(0.031)

(0.04)

(0.033)

(0.031)

(0.043)

(0.03)

(0.028)

(0.058)

(0.039)

(0.027)

Gut Fullness 18+

0.311

0.43

0.443

0.336

0.455

0.478

0.308

0.492

0.505

0.319

0.452

0.518

 

(0.043)

(0.037)

(0.036)

(0.045)

(0.035)

(0.031)

(0.044)

(0.031)

(0.027)

(0.048)

(0.044)

(0.029)

Food Qual 7-12

0.344

0.347

0.347

0.345

0.347

0.347

0.345

0.347

0.345

0.347

0.35

0.336

 

(0.018)

(0.015)

(0.015)

(0.018)

(0.014)

(0.014)

(0.022)

(0.014)

(0.031)

(0.025)

(0.019)

(0.063)

Food Qual 13-17

0.426

0.415

0.411

0.42

0.409

0.404

0.414

0.402

0.4

0.419

0.405

0.4

 

(0.009)

(0.007)

(0.007)

(0.008)

(0.007)

(0.006)

(0.009)

(0.006)

(0.006)

(0.011)

(0.01)

(0.008)

Food Qual 18+

0.424

0.402

0.397

0.418

0.396

0.389

0.422

0.385

0.386

0.41

0.386

0.385

 

(0.01)

(0.008)

(0.008)

(0.01)

(0.008)

(0.007)

(0.012)

(0.006)

(0.005)

(0.013)

(0.009)

(0.007)

Death Aggr 7-12 (10$ ^{-4}$/hr)

3.84

6.63

7.2

4.11

7.31

7.81

3.46

7.79

8.87

3.28

5.74

8.7

 

(2.96)

(4.83)

(5.09)

(2.83)

(5.08)

(5.58)

(2.59)

(5.82)

(14.06)

(3.43)

(5.33)

(10.36)

Death Aggr 13-17 (10$ ^{-4}$/hr)

4.82

7.31

7.39

5.87

8.24

8.34

6.67

8.89

9.12

6.38

8.31

9.09

 

(3.02)

(3.16)

(3.22)

(3.61)

(3.78)

(3.79)

(4.43)

(4.47)

(4.57)

(4.86)

(5.11)

(5.2)

Death Aggr 18+ (10$ ^{-4}$/hr)

1.85

2.4

2.44

2.43

2.61

2.6

2.53

2.93

2.75

2.99

3.26

3.01

 

(1.8)

(1.82)

(1.76)

(2.36)

(2.05)

(2.08)

(2.78)

(2.61)

(2.41)

(3.86)

(3.31)

(2.91)


TABLE C4. Estuary wide summaries for altering cannibalism potential via maximum interaction distance (Section A.5.3). Additional variables are given in Table 3. The Default interaction distance corresponds to the value used in previous simulations, Small to decreasing this distance by a factor of 4 and Large represents doubling it. All simulations done using Short hypoxic duration (Table C2).  

 

Short Duration, Max Extent Hypoxia

 

$ \approx$ 15%

$ \approx$ 30%

$ \approx$ 45%

$ \approx$ 60%

Interact Dist

Small

Default

Large

Small

Default

Large

Small

Default

Large

Small

Default

Large

Max % Hypoxic

15.4

17.7

19

25.8

28.1

29.2

43.2

44.9

45.7

61.4

61.9

62.3

 

(6)

(6.5)

(6.3)

(7.2)

(7.2)

(7)

(7.3)

(7.2)

(7.2)

(6.3)

(6.2)

(6.3)

% Hypoxic

4.7

5.7

6.3

9.5

10.7

11.4

19.7

20.9

21.5

36.4

36.9

37.1

 

(4.7)

(5.3)

(5.6)

(7.3)

(7.7)

(8)

(11)

(11.3)

(11.4)

(12.9)

(13)

(13)

DO (mg/L)

5.5

5.5

5.4

5.3

5.2

5.2

4.9

4.8

4.8

4.1

4.1

4.1

 

(0.7)

(0.7)

(0.7)

(0.8)

(0.8)

(0.8)

(0.8)

(0.8)

(0.8)

(0.9)

(0.9)

(0.9)

Hypoxic Edge (10$ ^{-2}$ m/m$ ^2$)

0.98

1.12

1.18

1.66

1.82

1.91

2.9

3.04

3.1

4.11

4.13

4.14

 

(0.82)

(0.85)

(0.86)

(1.03)

(1.07)

(1.1)

(1.27)

(1.28)

(1.28)

(0.95)

(0.94)

(0.94)

Clam Density (#/m$ ^2$)

878

915

952

888

914

951

864

893

923

758

774

789

 

(85)

(73)

(64)

(95)

(89)

(80)

(132)

(128)

(122)

(234)

(230)

(218)

Crab Biomass (g/m$ ^2$)

12.1

7.84

4.67

9.93

6.84

3.62

8.29

5.29

2.63

4.43

2.83

1.65

 

(0.85)

(0.8)

(0.38)

(1.43)

(0.87)

(0.32)

(0.89)

(0.77)

(0.29)

(0.78)

(0.42)

(0.23)

Mat Female Mass (g)

252

239.2

243

260.4

242.2

236.6

246.2

234.1

229.8

218.8

223.4

218.6

 

(8.7)

(5.9)

(8.6)

(8.6)

(8.3)

(9.1)

(8.1)

(6.3)

(8.5)

(12)

(8)

(11.9)

Mat Female CW (cm)

17.8

17.4

17.3

17.7

17.5

17.1

17.7

17.5

17.2

17.6

17.4

17.1

 

(0.1)

(0.1)

(0.1)

(0.1)

(0.1)

(0.2)

(0.1)

(0.1)

(0.2)

(0.1)

(0.2)

(0.3)

Egg (#/m$ ^2$ hr)

16.45

19.04

14.28

15.08

16.67

9.89

8.45

10.83

6.79

2.19

3.28

3.01

 

(12.75)

(13.38)

(11.18)

(12.9)

(12.55)

(9.55)

(9.46)

(9.94)

(7.68)

(4.64)

(5.8)

(5.14)

Egg per Mat Fe (#/# hr)

971

1794

2203

1036

1893

2131

704

1828

2092

387

1283

1919

 

(749)

(1250)

(1732)

(878)

(1418)

(2061)

(784)

(1655)

(2365)

(828)

(2289)

(3372)

Recruit 7 (10$ ^{-6}$#/m$ ^2$ hr)

121.11

133.85

119.67

116.8

131.47

91.53

84.46

95.45

70.87

27.41

38.79

37.4

 

(472.82)

(456.73)

(414.75)

(451.65)

(468.41)

(326.21)

(329.71)

(325.31)

(257.33)

(144.76)

(162.63)

(158.16)

Recruit 12 (10$ ^{-6}$#/m$ ^2$ hr)

5.29

14.28

11.27

4.69

15.92

10.2

5.15

15.33

9.04

2.83

8.51

6.05

 

(9.98)

(25.53)

(22.15)

(8.92)

(29.51)

(19.52)

(9.15)

(28.66)

(17.51)

(5.82)

(15.94)

(11.35)

Recruit 18 (10$ ^{-6}$#/m$ ^2$ hr)

2.05

2.36

1.24

1.65

2.12

1.03

1.58

1.73

0.83

1

1.06

0.56

 

(2.79)

(3.7)

(2.47)

(2.28)

(3.51)

(2.11)

(2.3)

(3.06)

(1.85)

(1.83)

(2.08)

(1.36)

Gut Fullness 7-12

0.201

0.366

0.421

0.195

0.4

0.395

0.205

0.438

0.391

0.195

0.394

0.371

 

(0.038)

(0.07)

(0.186)

(0.044)

(0.069)

(0.203)

(0.042)

(0.077)

(0.199)

(0.057)

(0.078)

(0.21)

Gut Fullness 13-17

0.232

0.445

0.504

0.248

0.459

0.503

0.282

0.478

0.502

0.294

0.464

0.503

 

(0.047)

(0.032)

(0.028)

(0.048)

(0.033)

(0.032)

(0.047)

(0.03)

(0.039)

(0.062)

(0.039)

(0.049)

Gut Fullness 18+

0.189

0.43

0.532

0.187

0.455

0.534

0.181

0.492

0.533

0.19

0.452

0.529

 

(0.038)

(0.037)

(0.019)

(0.046)

(0.035)

(0.022)

(0.035)

(0.031)

(0.026)

(0.035)

(0.044)

(0.035)

Food Qual 7-12

0.343

0.347

0.299

0.343

0.347

0.282

0.344

0.347

0.283

0.35

0.35

0.271

 

(0.027)

(0.015)

(0.119)

(0.032)

(0.014)

(0.134)

(0.033)

(0.014)

(0.135)

(0.042)

(0.019)

(0.144)

Food Qual 13-17

0.433

0.415

0.414

0.425

0.409

0.415

0.42

0.402

0.416

0.437

0.405

0.413

 

(0.02)

(0.007)

(0.01)

(0.022)

(0.007)

(0.01)

(0.019)

(0.006)

(0.011)

(0.019)

(0.01)

(0.017)

Food Qual 18+

0.444

0.402

0.39

0.452

0.396

0.391

0.445

0.385

0.39

0.437

0.386

0.382

 

(0.013)

(0.008)

(0.005)

(0.012)

(0.008)

(0.006)

(0.014)

(0.006)

(0.007)

(0.018)

(0.009)

(0.008)

Death Aggr 7-12 (10$ ^{-4}$/hr)

1.42

6.63

12.11

1.21

7.31

11.65

1.24

7.79

11.24

0.64

5.74

8.38

 

(1.18)

(4.83)

(19.65)

(1.17)

(5.08)

(22.6)

(1.13)

(5.82)

(22.35)

(1.38)

(5.33)

(13.92)

Death Aggr 13-17 (10$ ^{-4}$/hr)

1.74

7.31

9.3

2.2

8.24

9.9

2.95

8.89

10.29

2.91

8.31

10.49

 

(1.37)

(3.16)

(5.13)

(1.62)

(3.78)

(6.55)

(2.04)

(4.47)

(7.96)

(2.88)

(5.11)

(15.52)

Death Aggr 18+ (10$ ^{-4}$/hr)

0.61

2.4

2.06

0.85

2.61

2.29

1.03

2.93

2.76

1.26

3.26

2.93

 

(0.61)

(1.82)

(1.83)

(0.81)

(2.05)

(2.21)

(1.04)

(2.61)

(3.08)

(1.44)

(3.31)

(3.97)


\begin{figure}\begin{center}\epsfig{file=plots/assessment/results/results/dist_crab_bio_w_avg_do.eps, width=7in}\end{center}\end{figure}

   FIG. C1. Proportion of total crab biomass shallower than 3 m vs the average DO in the estuary from the beginning of year 30 to the end of year 39 under the different hypoxic extents and durations.


\begin{figure}\begin{center}\epsfig{file=plots/assessment/results/appendix/estuary_ratemortalbydensity1317.eps,width=7in}\end{center}\end{figure}

   FIG. C2. Rate of mortality (#.m$ ^{-2}$.hr$ ^{-1}$) from all causes of 13 to 17 instar crabs relative to the density (#/m$ ^2$) of 13 to 17 instar crabs in the estuary for the different hypoxic durations considered. Solid line generated using a Loess smoother.


\begin{figure}\begin{center}\epsfig{file=plots/assessment/results/appendix/estuary_ratemortalbydensity18.eps,width=7in}\end{center}\end{figure}

   FIG. C3. Rate of mortality (#.m$ ^{-2}$.hr$ ^{-1}$) from all causes of 18+ instar crabs relative to the density (#/m$ ^2$) of 18+ instar crabs in the estuary for the different hypoxic durations considered.


\begin{figure}\epsfig{file=plots/assessment/results/results/surv_durationXextent.eps, width=7in, height=3in}\end{figure}

   FIG. C4. Crab survival function under three hypoxic durations and four hypoxic extents.



\begin{figure}\epsfig{file=plots/assessment/results/results/extdur_timetill_18.eps, width=6in, height=7in}\end{figure}

   FIG. C5. Empirical cumulative distribution function for the time it takes crabs under different hypoxic extents and durations to reach the 18th instar from the 7th.


\begin{figure}\epsfig{file=plots/assessment/results/results/surv_interdist.eps, width=7in}\end{figure}

   FIG. C6. Effect of altering the maximum interaction distance in Scenario III on crab survival. Default corresponds to the default interaction distance used, Small to decreasing this distance by a factor of 4 and Large represents doubling it. All simulations done using Short hypoxic duration. Compare to Figs. C4 and Fig. 9 in the paper.


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