Valuing Ecosystem Services: Oysters,
Denitrification, and Nutrient Trading Programs
Geret S. DePiper, Douglas W. Lipton, and
Romuald N. Lipcius
May 21, 2015
The opinions expressed in this presentation are solely the authors, and do not represent those of NOAA Fisheries



Analyze the role of denitrification/nitrogen sequestration and harvest in optimal management of natural oyster reefs
Assess NPV of Harris Creek restoration initiative




Nitrogen
Phosphorus
Sediment

Wild stock

Kasperski & Wieland (2010)

Mykoniatis & Ready (2015)
Aquaculture

Miller (2009)




Powell et al. (2006)
Mann & Powell (2007)
Powell & Klinck (2007)

Biological model
Jordan-Cooley et al. (2011)
Three equations governing oyster population dynamics

O = live oyster population


B = oyster shell (reef)
S = sedimentation

Oyster growth =
logistic growth – disease and predation – smothering dO dt
=
O [
1
+ r ( 1
−
O
)
+
K exp(
− h (
O
2
ε
+
−
B
µ
−
S )
− ε
]

Reef growth =
Oyster mortality – Shell degradation dB dt
=
µ − ε
O [
1
+ exp(
− h (
O
2
+
B
−
S )
+ ε
]
− γ
B

Sediment rate =
Deposition rate – erosion dS dt
=
C exp(
− η
( O
+
B )) exp(
−
F
0
O exp( y
0 y
0
−
C exp(
− η
( O
+
B ))
))
− β
S y
0

Value =
Harvest + Denitrification + Sequestration
Harvest
=
( p
H
− c
H
( 1
−
(
O
−
K x
)) x
Denitrific ation
= p
N
λ
( 1
− exp(
−
F
0
O exp( y
0 y
0
−
C exp(
− η
( O
+
B ))
))) y
0
Sequestrat ion
= p
N
α
O (
1
+ r ( 1
−
O
)
K exp(
− h (
O
2
+ ε
+
− µ
B
−
S ))
− ε
)

Deterministic Dynamic programming

CompEcon Toolbox for Matlab



5% discount rate

3%, 7%, 11.8% sensitivity
$28.9 bu -1 harvest price

$18.63, $44.79 sensitivity
$10 lb -1 nitrogen price

$0, $4, $20 sensitivity
Jordan-Cooley et al. (2011)

0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
1 3
Baseline
High Growth Rate
5 7 9
Year
Low Carrying Capacity
High Predation
11 13
Low Growth Rate
15

0.2
0.16
0.12
0.08
0.04
0
1 3
Baseline
5
Low Predation
7 9
Year
High Predation
11 13
Low Carrying Capacity
15

4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
1 3
Baseline
5 7
Year
High Nutrient Credit
9 11
Low Carrying Capacity
13 15



$31.6 million restoration of 377 acre oyster reef
Assumptions:


6 years until “restored”
Value begins to be generated in year 7


50 year time horizon (ensure sustainability assessed)
NPV calculation for each modeled scenario


24 simulations over 50 year time horizon

16 positive NPV (67%)

8 negative NPV (33%)
NPV
Break-Even
Oyster Stock
Metric Mean Median STD Min Max
$ million 19.84 18.55 years 15.25 14
Oysters m -1 380 430
27.2 -21.1 67.3
6.6 -
170 0
34
580

•
•
•
•
Optimal management includes both ecosystem service provisioning and harvest
•
Reef level heterogeneity important
Dynamics more sensitive to biological vs economic parameters
Harris Creek NPV positive for 67% of simulations
Private funding for restoration likely not viable

References

Jordan-Cooley, W. C., R. N. Lipcius, L. B. Shaw, J. Shen, and J. Shi. 2011.

Bistability in a Differential Equation Model of Oyster Reef Height and
Sediment Accumulation. Journal of Theoretical Biology 289: 1 – 11.
Kasperski, S., and R. Wieland. 2010. When is it Optimal to Delay Harvesting?
The Role of Ecological Services in the Northern Chesapeake Bay Oyster





Fishery. Marine Resource Economics 24: 361 – 85.
Mann, R., and E. N. Powell. 2007. Why Oyster Restoration Goals in the
Chesapeake Bay Are Not and Probably Cannot be Achieved. Journal of
Shellfish Research 26(4): 905-17.
Miller, A. L. 2009. An Economic Evaluation of the Nutrient Assimilation
Potential for Commercial Oyster Aquaculture in the Chesapeake Bay. M.S.
Thesis. Blacksburg: Virginia Polytechnic Institute and State University.
Mykoniatis, N., and R. Ready. 2015. Spatial Harvest Regimes for a Sedentary
Fishery. Environmental and Resource Economics: 1 - 31.
Powell, E. N., J. N. Kraeuter & K. A. Ashton-Alcox. 2006. How long does oyster shell last on an oyster reef? Estuar. Coast. Shelf Sci. 69:531–542
Powell, E. N., and J. M. Klinck. 2007. Is Oyster Shell a Sustainable Estuarine
Resource? Journal of Shellfish Research, 26(1): 181-94.

Model
Baseline
100% Cull mortality
Shell degradation = 0.9
Shell degradation = 0.5
Nitrogen price/lb = $0
Nitrogen price/lb = $4
Nitrogen price/lb = $20
Harvest cost = $9
Harvest cost = $3
Oyster price = $12.15
Oyster price = $8.55
Discount rate = 0.03
Discount rate = 0.07
Discount rate = 0.118
Natural Mortality = 0.2
Natural Mortality = 0.6
Carrying Capacity = 0.1
Intrinsic growth = 0.7
Intrinsic growth = 1.3
Sediment deposition = 0.08
Sediment Decay Rate = 0.04
Burial Scaling factor = 30
Burial Scaling factor = 10
No harvest
Total $/m 2 Harvest $/m 2 Denitrification $/m 2 Sequestration $/m 2 NPV ($Million) Break-even Year
51.28
43.46
17.72
12.32
25.31
25.31
8.25
5.83
26.3
20.1
15
18
46.60
56.69
71.27
39.66
25.95
87.49
26.07
9.23
16.76
84.76
17.83
52.80
60.60
22.78
27.56
18.40
31.83
83.97
42.35
72.27
61.48
42.98
14.41
21.50
18.40
18.24
17.35
9.50
37.92
27.39
9.89
24.63
13.60
8.62
44.42
0.60
3.67
0
41.23
6.43
18.64
24.25
0
0
25.31
25.31
0
10.12
50.62
25.31
25.31
25.31
25.31
35.35
19.29
12.64
25.31
25.30
7.79
18.58
25.31
9.93
25.31
25.31
23.87
25.31
6.88
9.88
0
3.46
16.00
7.54
9.05
8.77
7.79
10.69
6.77
4.69
17.76
0.17
-2.23
-1.83
18.22
1.47
8.86
11.05
-1.09
2.25
21.1
32.5
-10.8
4.4
63.3
16.3
50.1
37.9
17.0
58.5
8.2
-12.1
67.3
-2.1
-21.1
-12.7
64.2
-11.4
28.1
36.9
-5.9
-0.05
17
13
-
9
-
15
12
22
-
8
-
-
12
-
-
-
34
8
20
10
12
19

State Variables
Live Oysters
Dead Oyster
Sediment 0.25
0.2
0.15
0.1
0.05
0
0 5 10 15 20 25
Year
30 35 40 45 50




Collocation Policy iteration (Newton’s method)
Linear spline approximation for state space

Oyster population = 90 nodes


Reef growth = 7 nodes
Siltation = 4 nodes
Tolerance set to square root of machine precision

~1.49e-8

0
-2
-4
4
2
6 x 10
-5
-6
0
-8
0.1
yster Stock
0.2
-0.5
0 0.5
Reef Height
1 1.5
2

0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
0.5
Reef Height
0.05
0.1
0.15
Oyster Stock
0.2
0.25
0.3
0.35




29.89 acres of reef restored to high relief (HRR) in
2004

(25 – 45 cm)
Less than 2 oysters m -2 density pre-restoration
Persistent 1000 oysters m -2 density on HRR after restoration (sampled in 2007 & 2009)

Shellfish Aquaculture: Ecosystem Effects,
Benthic–Pelagic Coupling and Potential for Nutrient Trading
Roger I. E. Newell
Roger Mann
A Report Prepared for the Secretary of Natural
Resources,
Commonwealth of Virginia.
June 21, 2012

Crassostrea virginica: Denitrification and
Nitrogen Sequestration



Newell et al. (2005)
Kellogg et al. (2013)
STAC (2013)