Spatial Bioinvasion Externalities with Heterogeneous Landowner Preferences: A Two-Agent Bioeconomic Model

Shady S. Atallah

doi:10.3368/le.101.2.112024-0209

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Figure 1
Short-Distance Dispersal (SDD) and Long-Distance Dispersal (LDD1 and LDD2)
Note: Shaded cells represent invaded cells on the grid. Lightning bolts represent random long-distance dispersal events that are exogenous to the model (LDD1).
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Figure 2
Optimal Bioinvasion Control in Forestlands G_A and G_B with Market Ecosystem Service Preferences: left, Bioinvasion Starts on G_A, Landowner A Moves First; right, Bioinvasion Starts on G_B, Landowner B Moves First
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Figure 3
Optimal Bioinvasion Control with Nonmarket Ecosystem Service Preferences for Landowner A and Market Ecosystem Service Preferences for Landowner B: (a) Bioinvasion Starts on G_A, A Moves First; (b) Bioinvasion Starts on G_B, B Moves First

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Table 1

Model Parameters

Parameter	Description	Value	Unit
Panel A. Objective Function Parameters
a₀	Intercept of the consumer surplus (CS) function	−2.97^a	$/day
b₀	Intercept of the user days (UD) function	9.32^a	Days/year
a₁	Linear parameter of the CS function	0.24^a	$/day/healthy tree
b₁	Linear parameter of the UD function	0.24^a	Days/healthy tree
_a₂	Quadratic parameter of CS function	−0.00017^a	Unitless
b₂	Quadratic parameter of UD function	−0.0002^a	Unitless
p	Timber prices for young and mature trees	0.11, 0.13^b	$/board feet (BF)
y_m,n,t	Timber yields for mature trees	297^c	BF/tree
c_A, c_B	Bioinvasion treatment cost	4^d	$/invaded tree
ρ	Discount factor	0.961538	Year⁻¹
T	Forward-looking years (> 5 stages)	5, 10,…, 25^e	Years
Panel B. Spatial-Dynamic Externality Parameters
α	Short distance H to E_u transition rate	0.69	Year⁻¹
N_i,j,t	Number of contiguous I_m or I_h neighbors	0,…,8	Cells
γ	Long-distance power-law parameter	3	Unitless
L₁	Average waiting time between invaded-undetectable and invaded-detectable^f	1	Years
L₂	Average waiting time between invaded-detectable to invaded-moderate^g	1	Years
L₃	Average waiting time between invaded-moderate to invaded-high^h	2	Years
τ_young	Years between juvenile and young if tree and its immediate neighbors are healthy	10	Years
τ_mature	Years between young and mature	10	Years
I×J	Grid G_A dimensions	49 × 16 = 784	Rows × columns
M×N	Grid G_B dimensions	49 × 16 = 784	(Trees per acre)

↵^a Values are from Rosenberger et al. (2013), adjusting for tree density per acre in the case of a₁ and b₁.
↵^b New Hampshire Department of Revenue Administration (2016).
↵^c Hepp et al. (2015); Smalley et al. (2016).
↵^d Ending the analysis at 25 years is consistent with landowner demographics and plans (most private forest landowners are above 65 years of age and plan to sell or transfer their land; U.S. Forest Service 2015).
↵^e Lee (2017). This assumes repeated cutting in the spring, summer, and fall to avoid regrowth.
↵^f .
↵^g .
↵^h .

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Table 2

Landowners’ Payoffs and Optimal Amount of Control: Nonmarket Ecosystem Service Preferences Case

	DM		CP		Social Cost of Externality
	Payoffs	Control	Payoff	Control	DM with Respect to CP
	$/Acre	Treatments	$/2 Acres	Treatments	$/2 Acres	%
First mover	841 (77)	0	2,203 (82)	783 (28)	n/a	n/a
Second mover	1,591 (123)	0	2,509 (64)	682 (25)	n/a	n/a
Total	2,432 (145)	0	4,712 (104)	1,465 (38)	−2,280^***	−48

Note: Standard deviations are in parentheses. CP = central planner; DM = decentralized management.
↵^*** p < 0.01.

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Table 3

Landowners’ Payoff and Optimal Amount of Control: Market Ecosystem Service Preferences Case

	DM		CP		Social Cost of Externality
	Payoffs	Control	Payoff	Control	DM with Respect to CP
	$/Acre	Treatments	$/2 Acres	Treatments	$/2 Acres	%
First mover	12,491 (2,885)	1,203 (12)	15,467 (3,346)	944 (33)	n/a	n/a
Second mover	15,318 (3,114)	962 (13)	15,847 (3,318)	744 (28)	n/a	n/a
Total	27,808 (4,245)	2,165 (18)	31,314 (4,712)	1,688 (43)	−3,506^***	−11

Note: Standard deviations are in parentheses. CP = central planner; DM = decentralized management.
↵^*** p < 0.01.

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Table 4

Landowners’ Payoffs ($) and Optimal Amount of Control (Treatments) under Decentralized Management (DM) and Central Planner (CP) Cases for Landowner A and Landowner B

	DM		CP		Social Cost of Externality
	Payoffs	Control	Payoff	Control	DM with Respect to CP
	$/Acre	Treatments	$/2 Acres	Treatments	$/2 Acres	%
Panel A. G_A* and G_B Ecologically Isolated (No Long-Distance Dispersal)*
G_A (NMES)	2,999 (42)	498 (7)	n/a	498 (7)	n/a	n/a
G_B (MES)	16,731 (3,384)	497 (9)	n/a	497 (9)	n/a	n/a
G_A + G_B	19,731 (3,384)	995 (11)	19,731 (3,384)	995 (11)	0	0
Panel B. Bioinvasion Starts on G_A, Landowner A (NMES) Moves First
G_A (NMES)	831 (73)	0 (0)	2,187 (152)	836 (32)	n/a	n/a
G_B (MES)	10,432 (2,453)	1,543 (12)	16,667 (3,367)	700 (29)	n/a	n/a
G_A + G_B	11,263 (2,453)	1,543 (12)	18,854 (3,370)	1,536 (43)	−7,591^***	−40
Panel C. Bioinvasion Starts on G_B, Landowner B (MES) Moves First
G_A (NMES)	1,569 (123)	0 (0)	2,119 (72)	812 (26)	n/a	n/a
G_B (MES)	10,490 (2,121)	785 (0)	15,127 (3,357)	1,025 (33)	n/a	n/a
G_A + G_B	12,060 (2,125)	785 (0)	17,246 (3,358)	1,837 (42)	−5,187^***	−30

Note: Landowner A = nonmarket ecosystem service preferences (NMES); landowner B = market ecosystem service preferences (MES). Standard deviations are in parentheses.
↵^*** p < 0.01.

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Table 5

Net Aggregate Payoffs ($) for Different Levels of Uniform and Nonuniform Subsidies for Landowner A and Landowner B

Cost (c_A, c_B)	Subsidy (P_A, P_B)	Control in G_A	Control in G_B	Aggregate Control	Aggregate Payoffs	Total Subsidy Cost^a	Net Aggregate Payoffs^a^,^b	Change Relative to Baseline
$/Treatment		Treatments			$/2 Acres			Change Relative to Baseline
Panel A. Bioinvasion Starts on G_A, Landowner A (NMES) Moves First
(4, 4)	(0, 0)	0	1,543	1,543	11,263	0	11,263	0%
(1, 1)	(3, 3)	1,358	1,180	2,537	20,992	4,653	16,339	45%
(2, 2)	(2, 2)	1,041	865	1,905	19,547	2,532	17,015	51%
(1, 4)	(3, 0)	1,042	603	1,644	19,546	2,016	17,529	56%
Panel B. Bioinvasion Starts on G_B, Landowner B (MES) Moves First
(4, 4)	(0, 0)	0	785	785	12,060	0	12,060	0%
(2, 2)	(2, 2)	1,390	1,649	3,038	17,751	3,765	13,986	16%
(1, 1)	(3, 3)	1,225	1,673	2,898	19,802	5,562	14,240	18%
(1, 4)	(3, 0)	1,480	1,207	2,686	17,547	2,921	14,626	21%

Note: Landowner A = nonmarket ecosystem service preferences (NMES); landowner B = market ecosystem service preferences (MES). Standard deviations are not shown.
↵^a In present value terms (25 years, 4% annual discount rate).
↵^b This is defined as aggregate payoffs minus total subsidy.