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Supplementary Material 1
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Figure SM 1.1 Boosted regression tree derived relative importance (%) of the top five predictors
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for the abundance of forest at the end of a model realisation and whether or not the model
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realisation ended with less than a combined 30% cover across vegetation classes 1, 2 and 3
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[p(escape)] for (a) all 2000 model runs, (b) final forest cover, split by whether a model realisation
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included invasive species or not and (c) whether final forest cover exceeded 30%, split by whether a
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realisation included invasive species or not. Abbreviations: Fire freq. = fire frequency, Start locn =
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Start location (probability of fire starting in a flammable vegetation state [1,2,3]), Seed prodn 3 / 4
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= seed production by state 3 / 4, Mean LDD = Mean distance of long-distance dispersal.
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Figure SM 1.2 Positive feedbacks between vegetation and fire are evident at multiple scales; in the
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composition of: (a) the ignition cell, (b) the immediate neighbourhood (nhb) of the ignition cell
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(number of the eight cells neighbouring the ignition location in states 1 or 2), and (c) the entire
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landscape (flammability scaled from 0 to 1, with 1 representing the case where the landscape
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comprises only the most flammable vegetation). These interactions differ in strength when invasive
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plants are present, and affect (d) the fire size-frequency distribution (represented here by the
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probability density distribution of fire sizes [proportion of landscape burned]; the dashed black line
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represents the distribution for all fires [(that is, whether with or without invasive plants]). In all
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sub-plots red shading denotes model realisations where invasive plants were present and blue
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denotes model realisations where invasive plants were absent.
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1
2
3
4
5
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Figure SM 1.3 Effect of changes in dispersal limitation on time required for the landscape to (a)
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achieve 95% forest cover, and (b) escape the flammable state (less than 30% in classes 1, 2, or 3).
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In all cases fire frequency is set to zero. Points are median values and the shaded areas 95%
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percentiles; red and blue represent baseline and 50% reduced propagule reduction.
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1
2
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Figure SM 1.4 Median Gini values (a measure of compositional evenness) as a function of fire
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frequency with (red) and without (blue) invasive pyrophyllic plant species. The dashed lines show
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the 95% percentile limits. Note the restricted range of fire frequencies under which a range of
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landscape compositions emerge.
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Table SM 1.1 Model Parameterization, Baseline Values, Range Used in Uncertainty Analysis (all uniform deviates) and Source of
Information and Interpretation
Parameter
Description
Baseline
value
Uncertainty
analysis range
Source
Landscape
Initial abundance
Abundance of five vegetation classes in the landscape (based on satellite {0.05, 0.30,
0.25, 0.20,
data collected over the Austral summer of 2008/9).
0.20}**
LCDB 3.0 database (Land
Information NZ); resolution = one
ha; overall accuracy > 95% See:
http://www.lcdb.scinfo.org.nz/
Minimum time spent in each of the vegetation classes before transition
Field observation, published values
expert opinion (see also Perry and
others 2010)
Vegetation dynamics
Successional rates
See Figure 1
Propagule production Number of 'propagules' produced per cell per year by class 3 vegetation 4 per cell per
class 3
yr
2-8
Approximated from demographic
data in Enright and Watson (1992)
and West (1995). See SM 2 for full
details.
Propagule production Number of 'propagules' produced per cell per year by class 4 vegetation 4 per cell per
class 4
yr
2-8
Approximated from demographic
data in Enright and Watson (1992)
and West (1995). See SM 2 for full
details.
Mean fruit movement Mean distance propagules moved from parent cell by birds (mean of
distance (LDD)
Exponential deviate)
4 cells (80
m)
1-8
After Wotton and Kelly (2012) who
report mean dispersal distances of
95, 98 and 61 m for three fleshyfruited tree species in NZ.
Critical density for
Minimum density of 'saplings' required for transition from class 2 to 3
transition class 2 → 3
10 per cell
(250/ha)
5 - 20
Estimated from field-data
describing stand structure in the
four vegetation states. See SM 2 for
full details.
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Baseline
value
Uncertainty
analysis range
10 per cell
(250/ha)
5 - 20
0.05
0.005 - 0.15
No empirical data.
Invasion risk increase Increase in invasion risk per number of fires in last three decades that a
cell has experienced.
0.10
0.05 - 0.20
No empirical data.
Rate at which transition out of post-fire class (states 0 and 1) is slowed
per number of fires in last three decades that a cell has experienced.
2 yr
1-5
No empirical data.
Fire frequency
Probability of a fire event in any given year
0.10
0.0 – 0.25
Fire start
Probability that a fire will start in a flammable cell (class 0 or class 1) or
a randomly located cell of any vegetation type.
0.50
0.0 – 1.0
Parameter
Description
Critical density for
Minimum density of 'saplings' required for transition from class 3 to 4
transition class 3 → 4
Source
Estimated from field-data
describing stand structure in the
four vegetation states. See SM 2 for
full details.
.
Post-fire invasion
Base invasion postfire
Slow rate
Base probability of invasive species invading a grid cell post-fire
Fire regime
No empirical data but the vast
majority of fires in NZ are
anthropogenic (Anderson and others
2008) and are most likely to start in
flammable areas of the landscape.
** Initial vegetation composition was estimated from the LCD 3.0 database. Three LCDB classes account for nearly 90% of landcover
on GBI (the others relate to urban or agricultural land): ‘indigenous forest’, ‘indigenous hardwood forest’, and ‘mānuka and/or
kānuka’. The mānuka shrubland (state 2) and kānuka tall shrubland (state 3) states were allocated at a 60:40 ratio across the LCDB
mānuka/kānuka class (so 35% and 25%) and the young (state 4) and mature (state 5) forest modelled states were allocated at a
50:50 ratio to the two LCDB indigenous forest classes (so 20% and 20%). In model scenarios where the model represented invaded
shrubland 5% of the mānuka shrubland was allocated to that state (1) (giving cover in states 1, 2 and 3 of 5%, 30% and 25%,
respectively).
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Supplementary Material 2 - Dispersal and propagule production
It is computationally expensive to simulate all seeds produced in a landscape and follow the fate of
all individuals produced, especially given the high-levels of mortality in small size-classes for
forest trees. To approximately estimate survival in the smaller size classes of typical mid- to latesuccessional forest tree species we use the fecundity and demographic information provided in
Enright (1992), Enright and Watson (1992) for Rhopalostylis sapida (nikau) in secondary Agathis
australis forest near Auckland and West (1995) for Beilschmiedia tawa (tawa) in tawa-dominated
'virgin' forest at Pureora Forest Park. There is a lack of detailed demographic data available for
long-lived NZ tree species but B. tawa and R. sapida are representative of species occurring in
mature podocarp-hardwood forest in northern NZ. We consider the dynamics of two classes
(‘seedlings’ and ‘saplings’) of individuals and so in, effect, within each grid-cell there is a
transition (Lefkovitch) matrix (Figure SM 2.1). Seedlings are individuals in the size range 30 cm
– 1.5 m height (c 10 years old for tawa) and saplings have height greater than 1.5 m (c. 40 years
old for tawa). Individuals accumulate in the sapling class, which is therefore effectively size
unbounded but does suffer background mortality.
To estimate seedling production:
1. We estimate total viable seed production per grid cell after accounting for seed predation (seed
production data from Enright (1992) and West (1995)
2. From the stage-specific mortality rates presented in the life-tables in Enright and Watson (1992)
and West (1995), we used the methods described in Barot and others (2002) to estimate the typical
age of an individual of seedling size (via the ‘age of residence’ so not assuming a SSD) and hence
the probability of a viable seed surviving to seedling size.
3. Multiplying step 1. by step 2. yields an approximate annual production of seedling-sized
individuals per unit area (in our case 20 × 20 m grid cell).
So, for example, using information in West (1995) from her ‘virgin’ site (her Tables 3 and 4) we
have:
1.2 × 104 seeds per ha per yr × 0.0265 [germination rate] × 0.1013 [survival postgermination to stage class] = 31.8 15 cm seedlings per ha per year [ 2 seedlings per 0.04
ha grid cell]
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We then use the demographic rates provided in Enright and Watson (1992) and West (1995) to
parameterise Lefkovitch models incorporating seedling mortality, transition of seedlings to
saplings and sapling mortality. The values derived from the life-tables and transition matrices are
quite similar for both species and also suggest high levels of spatial and temporal variability in
life-history rates. Thus we used the same rates for the stage 3 and stage 4 juveniles of seedling
survival = 0.9, seedling to sapling transition = 0.05 and sapling survival = 0.99. Input of seedlings
is spatially variable.
To estimate critical transition densities:
Using the point centred quarter (PCQ) data described in Perry and others 2010 we identified stem
densities (stems > 5 cm DBH / ha) in stages 3 and 4 for the ‘species’ of interest, these equated to
340 and 500 stems per ha (noting that these are based on stands that had transitioned to the stage at
some point in the past, whereas we are interested in the point of transition). For both stages we set
a baseline minimal density of 250 stems per ha (10 stems per modelled grid cell) in the larger of
the two matrix size classes for transition to occur.
The representation of the regeneration dynamic described here is simple and the parameterisation
values used are approximate and do not include natural variability (for example, inter-annual seed
production). However, they capture the dynamics of the system and uncertainty analyses (Fig SM
1) suggest that uncertainty in these parameter values is overwhelmed by the dominant variables of
fire frequency and seed predation.
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Figure SM2-1 Schematic overview of transition matrix based representation of within grid cell
regeneration dynamics in the model.
References
Barot S, Gignoux J, Legendre S. 2002. Stage-classified matrix models and age estimates. Oikos
96:56–61.
Enright NJ. 1992. Factors affecting reproductive behaviour in the New Zealand nikau palm,
Rhopalostylis sapida Wendl. et Drude. New Zealand Journal of Botany 30:69–80.
Enright NJ, Watson AD. 1992. Population dynamics of the nikau palm Rhopalostylis sapida in a
temperate rainforest remnant near Auckland, New Zealand. New Zealand Journal of
Botany 30:29–43.
West CJ. 1995. Sustainability of Beilschmiedia tawa-dominated forest in New-Zealand population predictions based on transition matrix model analysis. Australian Journal of
Botany 43:51–71.
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