Supplementary Material
Scenario Generation
In this document we describe the structure of the stock-and-flow model used to generate the
scenarios presented in Figure 5. The model was built using the Stella™ software. The model
equations are listed below in Table A1. The variables are defined in Table A2. Because this
is a conceptual model intended for qualitative scenario generation, its stocks (state variables)
are normalised to have values that lie in the range from 0 to 1. In Table A3, we give the
parameter settings used to generate the three scenarios.
Table A1. Model Equations
1
2
3
4
5
Aa(t) = Aa(t - dt) + (Restore - Protect - Develop) * dt
INIT Aa = 0.96
Restore = (1/Tr)*PGmr*Aa*Ad
Protect = 0.001 + (PGp/Tp)*Aa*Ap
Develop = (1/Td)*(PGd - PGmr)*Aa*Ad
6
7
8
9
Ad(t) = Ad(t - dt) + (Develop - Restore) * dt
INIT Ad = 0.04
Develop = (1/Td)*(PGd - PGmr)*Aa*Ad
Restore = (1/Tr)*PGmr*Aa*Ad
10
11
12
Ap(t) = Ap(t - dt) + (Protect) * dt
INIT Ap = 0.00
Protect = 0.001 + (PGp/Tp)*Aa*Ap
13
14
15
16
CB(t) = CB(t - dt) + (Bchange - Bcollapse) * dt
INIT CB = 0.98
Bchange = (1/Tb)*gap
Bcollapse = (1/Tc)*CB*THRb^Nb/(CB^Nb + THRb^Nb)
17
18
19
PGd(t) = PGd(t - dt) + (PF1) * dt
INIT PGd = 0.60
PF1 = (1/TPF1)*(PGd*PGmr - (2 + 4*RSP)*PBD)
20
21
22
23
PGmr(t) = PGmr(t - dt) + (- PF2 - PF1) * dt
INIT PGmr = 0.39
PF2 = (1/TPF2)*(PGmr*PGp + (2 - 4*RSP)* PBD)
PF1 = (1/TPF1)*(PGd*PGmr - (2 + 4*RSP)*PBD)
24
25
26
PGp(t) = PGp(t - dt) + (PF2) * dt
INIT PGp = 0.01
IPF2 = (1/TPF2)*(PGmr*PGp + (2 - 4*RSP)* PBD)
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
EB = IF(CB - 1.0*THA^0.9 > 0) THEN 1.0*THA^0.9 ELSE CB
{Note: EB = 1.0*THA^0.9 in the case of Scenario 3}
gap = EB - CB
Nb = 10
Npbd = 15
PBD = THRpbd^Npbd/(THRpbd^Npbd + CB^Npbd)
RSP = 0 {set to 0 for S1 and S2, set to 1 for S3}
Tb = 30
Tc = 10
Td = 30
THA = Aa + Ap
THRb = 0.4
THRpbd = 0.0 {set to 0.0 for S1, set to 0.6 for S2 and S3}
Tp = 5
TPF1 = 20
TPF2 = 20
Tr = 20/max(PBD,0.01)
1
Table A2. Conceptual Model Variables
Name
Aa(t)
Ad(t)
Ap(t)
Description [dimensions are given in square brackets]
Stock: Land area available for development or protection [fraction] = [area available/total area].
Stock: Land area developed [fraction] = [area developed /total area].
Stock: Land area protected [fraction] = [area protected /total area].
Constraint on these three stocks: Aa + Ad + Ap = total area = 1.
CB(t)
Stock: Current biodiversity [fraction] = [number of extant species/number of species in original
undisturbed landscape]. This dimension referred to as [biodiversity fraction] below.
PGd(t)
PGmr(t)
PGp(t)
Stock: Power of governance regimes that develop [fraction] = [power held/total power].
Stock: Power of governance regimes that maintain & restore [fraction] = [power held/total power].
Stock: Power of governance regimes that protect [fraction] = [power held/total power].
Constraint on these three stocks: PGd + PGmr + PGp = total power = 1.
Restore
Protect
Develop
Bchange
Flow: Process that transforms developed land into available land [area fraction/year].
Flow: Process that transforms available land into protected land [area fraction/year].
Flow: Process that transforms available land into developed land [area fraction/year].
Flow: Process of growth or shrinkage of current biodiversity CB(t) as it tracks equilibrium
biodiversity EB. Process rate driven by the gap between EB and CB.
Flow: Process of collapse of biodiversity when CB(t) falls below biodiversity threshold. Process
rate described by a Hill function with exponent Nb and threshold THRb [biodiversity fraction/year].
Flow: Process of power transfer between governance regimes that develop and those that
maintain & restore [power fraction/year]
Flow: Process of power transfer between governance regimes that maintain & restore and those
that protect [power fraction/year]
Bcollapse
PF1
PF2
EB
gap
RSP
Nb
Npbd
PBD
Tb
Tc
Td
THA
THRb
THRpbd
Tp
TPF1
TPF2
Tr
Equilibrium biodiversity. Calculated using species-area curve with exponent set to z = 1 to
simulate global aggregation of many species. [biodiversity fraction] = [number of species at
equilibrium/number of species in original undisturbed landscape].
A measure of the magnitude and sign of the time-rate-of-change of CB.
gap = EB – CB.
Scenario switch: Ratio of stewardship to protection [number].
Exponent in biodiversity collapse Hill function [number].
Exponent in public biodiversity discourse Hill function [number].
Extent of public biodiversity discourse, 0 < PBD < 1. Hill function with independent variable CB(t),
threshold THRpbd, and exponent Npbd [number].
Characteristic (e-folding) time for biodiversity change process [years].
Characteristic time for biodiversity collapse process [years].
Characteristic time for Develop process [years].
Total habitat area. Sum of Aa(t) and Ap(t). 0 < THA < 1 [fraction].
Hill-function threshold for biodiversity collapse process [biodiversity fraction].
Hill-function threshold for public biodiversity discourse [biodiversity fraction].
Characteristic time for Protect process [years].
Characteristic time for Power Shift 1 process [years].
Characteristic time for Power Shift 2 process [years].
Characteristic time for Restore process [years].
Table A3. Parameter Settings for Scenario Generation
Scenario
1
2
3
Figure
5.a
5.b
5.c
Description
Business as Usual
Enhanced Protection
Enhanced Maintenance and Restoration
2
THRpbd
0.0
0.6
0.6
RSP
0
0
1