1
Methods S1: Details – description of the submodels:
2
3
Fire spread
4
During each time step (one year) one randomly selected grid cell is ignited. Fire spreads with
5
probability pspread to that cell’s four nearest neighbours. Fire spread continues from all ignited
6
grid cells in the same way. Grid cells that have been ignited can only burn once in a given
7
fire. This process continues until all grid cells have been burnt or fire spread ceases (i.e. no
8
new cells are ignited). Fire-spread probability, pspread, can either be constant from year-to-
9
year, pc, or can depend on the local time since last fire, t, as a proxy for the available fuel load
10
[23]: pspread = pc × {1 + exp[-d × (t - b)]}, where d determines the steepness of the sigmoidal
11
curve and b parameterizes the point in time when half of the basic fire-spread probability pc is
12
reached. The parameterization is chosen to reflect the fact that fire-spread probability is low
13
when the time since last fire is less than four years (e.g. pspread = 0.12 × pc, for t = 3 years),
14
increases rapidly to about eight years (pspread = 0.95× pc, for t = 8 years) and more slowly
15
thereafter. For the same constant spread probability, pc, the dependency on fuel load results in
16
an increase of the average time since last fire tslf for about 10–20 years (see Fig. S1).
17
18
Seed dispersal and seed production
19
When a grid cell burns, the canopy seed stores for all plants within it are released and all non-
20
sprouters are killed and a fraction of resprouters survive (see fire survival for details). We
21
model seedlings rather than seeds to avoid very large seed numbers. The number of seedlings
22
per adult bi (i indicates the species) that are dispersed after a fire for non-sprouters depends on
23
the time since last fire and for resprouters on the age of the plant and the local time since last
24
fire, based on detailed studies of the demography of large serotinous shrubs at Eneabba [25—
25
27]. In table 1 and 2 at the end of this document we present the number of seedlings per adult
26
bi for non-sprouters and resprouters. New non-sprouters cannot store viable seeds until they
Coexistence niche- or neutral-based
27
reach four years of age. Number of seedlings produced per adult for non-sprouters (bi) reaches
28
its maximum at 20–25 years [25] and then slowly declines, reflecting increased annual
29
interfire mortality as shrubs approach their maximum longevity (Fig. 1b). Thus, bi combines
30
two processes: decreasing overall stand density due to interfire mortality, and seed
31
accumulation over time. The number of seedlings (S) generated by a local population (for
32
resprouters cohort) after a fire is then determined by the product of the local population (for
33
resprouters cohort) size after the last fire (N) and the number of seedlings each adult produces,
34
bi (S = N × bi). For non-sprouters, where all adult shrubs are killed, bi is the potential local
35
population growth rate. However, the realised growth rate depends on the number of sites
36
available for establishment and interspecific competition, and for resprouters on the fire
37
survival of shrubs. Resprouters require longer to attain a positive bi (30 years; [19]). After
38
resprouters have reached reproductive maturity they produce seeds but, on average, fewer
39
than non-sprouters [22]. Although the maximum number of seedlings per adult bi is
40
approximately 0.6 for resprouters their population can grow given a sufficient fire survival of
41
the mature shrubs. A mature resprouter affected by fire recovers and recommences seed
42
production three years after fire. The number of seedlings produced per resprouter increases
43
with time since last fire (reflecting an accumulating canopy seed bank) until time since last
44
fire exceeds 15 years, after which it is constant (Fig. 1b). For resprouters we ignore interfire
45
mortality, which is very low [27], and only model fire mortality (Fig. 1c).
46
Number of seedlings per adult bi can depend on species (correction factor for species i,
47
ai), and on intraspecific density regulation (expressed by the parameter fK that describes the
48
strength of the density regulation). The number of seedlings bi is multiplied by a factor βi
49
(seedling modification factor, reference value that is used in the simulations if not mentioned
50
otherwise βi = 1.8). The parameter βi can also be interpreted as the number of non-sprouter
51
seedlings at age 9 since bi = 1 for time since last fire tslf = 9 years. For resprouters βi is always
2
Coexistence niche- or neutral-based
52
1. Whenever a patch burns all individuals disperse their seeds, and the adjusted number of
53
seedlings per adult bi,adj is given by:
54

Ni 

bi ,adj tslf , age  ai  i  bi tslf , age  1 f

n

K
K


55
(1)
Values for bi are looked up in tables based on detailed studies of the demography of
56
large serotinous shrubs at Eneabba [21, 25—27]. The modifying factors of the number of
57
seedlings per adult bi are calculated as follows: Species-specific differences in growth rates
58
are parameterized by a maximum relative difference between the lowest and the highest
59
seedling numbers. All other species-specific number of seedlings bi are evenly distributed
60
between the extreme values. Therefore, n evenly spaced species-specific factors ai (0 ≤ ai <
61
∞) subdivide the interval [1 - dR/2,1 + dR/2] symmetrically around 1 (if possible), otherwise
62
the interval [0,dR] is used to avoid negative ai’s, in (n – 1) intervals of equal length. Finally,
63
the adjusted number of seedlings bi,adj can also be influenced by intraspecific competition,
64
expressed by a density-dependent term (1 - Ni/(fK × n × K)), where Ni is the abundance of
65
species i in the patch, fK (0 < fK < ∞) modifies the intraspecific density regulation (and 1/fK is
66
the strength of the intraspecific density regulation), n is the number of grid cells in the patch,
67
and K is the grid cell’s carrying capacity (approximately 65 000 individuals). If the term (1 -
68
Ni/(fK × n × K)) results in negative values we set its value to zero. Interspecific competition is
69
considered in the establishment process, but is not considered in the determination of the
70
number of seedlings (see Establishment).
71
When seedlings are released, a fraction m establishes in the wider metacommunity
72
with the majority of seedlings (1 - m) remaining in the patch. All seedlings that remain in the
73
patch are evenly distributed across the burnt grid cells of the home patch. All seedlings
74
dispersed into the metacommunity are evenly distributed across all burnt grid cells in the
75
landscape. This is a reasonable simplification at the spatial scale we focus on (4 × 4 km)
76
given the frequent long-distance dispersal events of several kilometres reported for this
3
Coexistence niche- or neutral-based
77
system [20]. In the following we often refer to the number of non-sprouter seedlings at age 9
78
years, which is identical to the seedling modification factor βi. If βi = 1 it takes non-sprouters
79
9 years to have a seed store sufficient to replace themselves after fire.
80
81
Fire survival of resprouters
82
Resprouters survive fire with an age-dependent basic survival probability psurvb (Fig. 1c), with
83
survival increasing linearly from 0.1 at an age of one year to a maximum survival probability
84
of 0.99 at an age of 10 years. Survival probability decreases linearly with age from 199 years
85
to zero at age 299 (maximum longevity, [27]). Fire survival can be adjusted by the fire
86
survival modification factor h (0 < h < 1). In the paper we refer to the maximum fire survival
87
probability, that is psurv,max = h × psurvb (for mature resprouters and time since last fire 10 ≤ tslf
88
≤ 199). Fire survival probability may vary in the same way as the number of seedlings per
89
adult bi between species gi. Thus, the basic survival probability psurvb is modified as follows:
90
p surv,i  g i  h  p survb
91
Interspecific variation in survival, gi, is modelled such that species specific maximum survival
92
probabilities psurv,max,i are a sequence of evenly spaced values between (psurv,max - dp/2,psurv,max +
93
dp/2) when (psurv,max + dp) ≤ 1 and the interval (1 - dp,1) otherwise. The modification factor gi
94
is then gi = psurv,max,i/psurv,max. The maximum difference between maximum fire survival
95
probabilities is dp. Fire survival of resprouters is binomially distributed with a probability of
96
psurv,i. If the product of the number of individuals n and the fire survival probability, psurv,i, is ≥
97
5.5 and [n × (1 - psurv,i)] ≤ 5.5, the demographic variability can be neglected and the number
98
of survivors approximated by the mean of the respective binomial distribution (µ = n × psurv,i).
(2)
99
100
Establishment
101
When a grid cell is burnt all non-sprouters and a fraction of resprouters, depending on the fire
102
survival probability, die. These empty spaces can be colonized by the seedlings of burnt
4
Coexistence niche- or neutral-based
103
(killed and resprouting) plants originating either from the patch itself or from other burnt
104
patches within the metacommunity (see Seed dispersal and seed production section). If the
105
number of seedlings is less than or equal to the number of available sites in a grid cell then all
106
the seedlings establish. To represent demographic variation at the grid cell level the number
107
of new recruits is determined by drawing, for each species i, a random number from a Poisson
108
distribution, where the mean equals the number of seedlings for species i. If the number of
109
seedlings exceeds the number of available sites in a grid cell (Kgridcell minus surviving
110
resprouters), the successful individuals are determined by lottery competition, i.e. are drawn
111
from a multinomial distribution using the relative abundances as probabilities.
112
113
114
115
116
117
Table 1: basic number of seedlings per adult bi for non-sprouters. The age of non-sprouters is
118
always the same as the time since last fire. The table is also visualized in Figure 1b).
119
Time since last fire
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Basic number of seedlings per adult bi
0.00E+00
0.00E+00
0.00E+00
2.32E-01
3.04E-01
4.06E-01
5.45E-01
7.35E-01
1.00E+00
1.35E+00
1.78E+00
2.32E+00
2.94E+00
3.62E+00
4.32E+00
5.00E+00
5
Coexistence niche- or neutral-based
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
5.60E+00
6.09E+00
6.46E+00
6.71E+00
6.86E+00
6.93E+00
6.93E+00
6.88E+00
6.81E+00
6.64E+00
6.39E+00
6.07E+00
5.71E+00
5.30E+00
4.87E+00
4.42E+00
3.97E+00
3.52E+00
3.09E+00
2.68E+00
2.30E+00
1.94E+00
1.63E+00
1.35E+00
1.10E+00
8.88E-01
7.07E-01
5.57E-01
4.33E-01
3.32E-01
2.51E-01
1.88E-01
1.38E-01
1.01E-01
7.21E-02
5.10E-02
3.55E-02
2.44E-02
1.65E-02
1.10E-02
7.24E-03
4.68E-03
2.98E-03
1.87E-03
1.15E-03
7.01E-04
4.18E-04
6
Coexistence niche- or neutral-based
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
>100
2.46E-04
1.42E-04
8.03E-05
4.47E-05
2.45E-05
1.31E-05
6.93E-06
3.58E-06
1.82E-06
9.02E-07
4.39E-07
2.10E-07
9.79E-08
4.47E-08
2.00E-08
8.74E-09
3.73E-09
1.56E-09
6.33E-10
2.51E-10
9.73E-11
3.67E-11
1.35E-11
4.81E-12
1.67E-12
5.62E-13
1.84E-13
5.83E-14
1.79E-14
5.31E-15
1.52E-15
4.22E-16
1.13E-16
2.90E-17
7.16E-18
1.70E-18
3.85E-19
0.00E+00
120
121
122
Table 2: basic number of seedlings per adult bi for resprouters. If resprouters are younger than
123
30 years they do not produce any seeds. If they are older than 30 years their basic number of
124
seedlings per adult bi depends on the time since last fire. If the onset of maturity started within
7
Coexistence niche- or neutral-based
125
the last inter fire interval the time since last fire has to be corrected accordingly, i.e. for
126
example if a plant is 35 years of age and the last fire has happened 10 years before the value
127
for time since last fire = 5 is chosen. The table is also visualized in Fig. 1b.
Time since last fire
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
>15
Basic number of seedlings per adult bi
0.00
0.00
0.02
0.07
0.13
0.20
0.28
0.35
0.41
0.46
0.50
0.54
0.57
0.59
0.61
0.61
128
129
130
8