Download Appendix S1. Details of Species Distribution Modeling and

Appendix S1. Details of Species Distribution Modeling and Population
Modelling Methods
Species Distribution Modeling
For both species, we used spatially explicit data on occurrences (“presence”) from the
San Diego Natural History Museum as well as a database of vegetation plots (Hannah
2008). To base the species distribution models on as many presence locations as
possible, we did not set aside a fraction of the data for testing accuracy because our
objective was to create predictive maps, as opposed to explaining the most important
drivers of the species’ distribution.
Model fit was assessed using the area under the curve (AUC) of the receiver operating
characteristic (ROC). The AUC represents the probability that, for a randomly selected
set of observations, the model prediction is higher for a presence observation than an
absence observation. The species distribution model of current habitat for C. verrucosus
had a training accuracy of 0.99, as calculated by the area under the curve (AUC) of the
receiver operating characteristic (ROC). The AUC for C. greggii was 0.93. This
resubstitution accuracy, based on the training data, represents a slightly higher
performance measure than would likely be found with independent assessment data
(Franklin, 2002). Both species showed “ecologically sensible” unimodal responses to
climate variables (Austin, 2002) (Figure S1). Climate variables were among the most
important predictors in both models (Table S1).
Figure S1. Marginal response curve for climate predictors estimated using MaxEnt
Table S1. A heuristic estimate of relative contributions of the climate, soil and
terrain variables used in the Maxent model for each species, presented in the order
of relative importance for C. greggii. In each iteration of the training algorithm, the
increase in regularized gain is added to the contribution of the corresponding
variable (or subtracted from it if the change to the absolute value of regularized gain
is negative) to determine the estimate.
Variable
Source
Absolute minimum January
temperature (averaged over
30 yr)
Annual precipitation
(averaged over 30 yr)
Absolute maximum July
temperature (averaged over
30 yr)
Soil depth (m)
Soil order
Soil available water capacity
(cm/cm)
potential winter solstice
solar insolation (Watt hr /m 2)
Slope angle (degrees)
Topographic moisture index
(unitless)
potential summer solstice
solar insolation (Watt hr /m 2)
Soil pH
PRISM1
Ceanothus
greggii
53.8
Ceanothus
verrucosus
48.7
PRISM1
27.0
3.2
PRISM1
5.1
19.6
STATSGO2
County soil series maps
aggregated to order, 13
categories
STATSGO2
3.3
2.5
0.6
4.5
2.4
1.2
from DEM using Solar
Analyst
USGS 30-m DEM
From USGS 30-m DEM
1.8
0.4
1.5
1.4
6.0
0.8
from DEM using Solar
Analyst
STATSGO2
1.1
0.6
0.3
14.5
1
PRISM: http://www.prism.oregonstate.edu/
2
STATSGO: State Soil Geographic data base for California, U.S. Department of Agriculture
Natural Resources Conservation Service. [WWW document]. URL
http://gis.ca.gov/catalog/BrowseRecord.epl?id=21237.
DEM: Digital Elevation Model; USGS: U.S. Geological Survey; Solar Analyst: an ArcView extension
for modeling solar radiation at landscape scales
Preparing habitat suitability maps for input to population models
For C. greggii, we used a regional vegetation map
(http://www.fs.fed.us/r5/rsl/projects/classification/system.shtml) to select all polygons
classified as vegetation types in which C .greggii is known to occur. We overlaid the C.
greggii presence points on these polygons and selected those that intersected a point to
represent occupied habitat patches.
A threshold discriminates between suitable and unsuitable habitat so that areas
with a predicted probability higher than the threshold value are considered suitable and
those below the value are considered unsuitable. To be consistent for both species, we
used “equal training sensitivity and specificity” as a threshold criterion because it
provided a balance between errors of omission and commission (based on “availability”
data of MaxEnt). This threshold was 0.301 for C. verrucosus and 0.397 for C. greggii.
All areas with probabilities of occurrence lower than the threshold value were assigned a
habitat suitability value of 0. Because this results in some very large patches for C.
greggii, greater than the average size of fires in the regions, we further split large patches
into smaller patches using the incidence of roads to ensure that fires occurred at a realistic
spatial scale.
After applying the thresholds to the habitat maps, we also developed criteria for
distinguishing between which patches were initially occupied for the population models
and which patches represented suitable but unoccupied habitat. For C. verrucosus, we
obtained a map that outlined all areas where the species is currently located (D. Lawson,
personal communication) to designate as occupied in our habitat maps. We assigned an
initial habitat suitability of 1.0 to all occupied habitat patches and maintained a
continuous distribution of predicted probabilities (i.e., between the threshold probability
and 1.0) for unoccupied, suitable patches to serve as indicators of relative habitat quality,
which is related to carrying capacity in the population models. We also filtered out
patches smaller than 25 ha because these would contain few individuals relative to the
entire population and would considerably slow processing time.
For maps of predicted distribution in the future climate scenarios, we applied the same
thresholding and patch size filtering rules.
Population Modelling
We used RAMAS® GIS (Akçakaya et al., 2005) to link the dynamic spatial
distributions, the population model and fire risk functions and to run stochastic
simulations of the resulting population dynamics. All survival rates and fecundities for
C. greggii were particular to the species, whereas early survival rates for C. verrucosus
were based on rates of the congeneric species C. impressus, C. ramulosus, C. cuneatus,
and C. megacarpus and survival rates for older age classes were the same as for C.
greggii. Fecundities for C. verrucosus were scaled from those for C. greggii based on
relative seed size.
The average first-year survival rate for C. greggii range was estimated to be 0.56
(Schmalbach, 2005, Keeley et al., 2006), whereas the average first year survival rate for
C. verrucosus was estimated to be 0.47 (Tyler & D’Antonio, 1995; Thomas & Davis,
1989; Frazer & Davis, 1988; Keeley et al., 2006). Age 1 to 5 survival rates were
considerably higher for both species (Table 1): 0.95 and 0.99 for age 1 and ages 2-5,
respectively, for C. greggii, and 0.707 and 0.718 for ages 1-2 and ages 3-5, respectively,
for C. verrucosus (standard deviations in Table 1). Survivorship data (i.e. the proportion
of individuals surviving germination to specified age) at ages 6, 13, 32, 57, and 82 years
for north- and south-facing slopes from Zammit & Zedler, (1993) were used to calculate
average survival rates of shrubs 6-81 years (Table 1). Standard deviations were assumed
to be the maximum absolute difference between the estimated mean and the highest and
lowest survival rate across north- and south-facing slopes. The survival rate for age
classes 82-97+ years was estimated by assuming a 100 year longevity for 95% of plants
in the age class, with 5% reaching older ages (Keeley et al., 2006). Survival rates were
assumed to be uncorrelated across patches; environmental correlation in survival rates
across space was shown to have negligible effects for C. greggii (Regan et al. 2010).
The seed production function of best fit was the polynomial
f s x   0.3422x 2  33.886x  1030.1 where x ≥ 6 years is the age of mature plants in the
stand. Seed production is highly variable with an estimated coefficient of variation of
200% (Zammit & Zedler 1993, Keeley, 1977). A weighted average (weighted by sample
size) of seed predation rates for C. greggii in Davey (1982) (91% predation) and Zammit
&Zedler (1993) (34% predation) was used to estimate a predation rate of 74.8% and seed
viability was estimated as 50% (Keeley 1977). A weighted average (weighted by sample
size) of seed predation rates for C. greggii in Davey (1982) (91% predation) and Zammit
&Zedler (1993) (34% predation) was used to estimate a predation rates of 74.8%.
Ceanothus has ballistic dispersal and seeds explode out of the pods, dropping and rolling
for 1-3 m, then join the soil seed bank and wait for a fire. There is no long distance
dispersal on time scales of centuries except the slow creep at 1-3 m steps. Dispersers such
as harvester ants do not move the seeds more than a few meters. While sedds have
obviously dispersed on geological time scales, the probability of opportunistic dispersal
via floods, for instance, is thought to be negligible on the century time scale of the
simulations.
Two sets of parameters are required to calculate K across the landscape: the per
hectare maximum density of plants in the largest sized age class and the relative
differences in K across age classes. To estimate per hectare maximum density of plants in
the largest sized age class, a least squares line of best fit was applied to the maximum
observed densities for each stand age, from which the maximum density per meter
squared for C. greggii at age 60+ was estimated. However, these densities relate to a
local scale smaller than 1 ha; in order to scale up to 1 ha plots, this estimate was reduced
by the abundance of Ceanothus across the landscape. C. greggii was observed to be
present in 12% of chaparral plots, with an average cover of 18% (J. Franklin, unpubl.
data), resulting in a carrying capacity of 150 plants per ha for 60+ year old stands. For C.
verrucosus, average cover in southern California is 17% (J. Franklin, unpubl. data) and
we assumed that this applied to all occupied patches (i.e. no further reduction was applied
because the predicted patch sizes for C. verrucosus were small relative to C. greggii
patches). This leads to a carrying capacity estimate of 1,173 per ha for age 60+ shrubs.
While these values may underestimate the actual but theoretical ceiling possible, they
provide a consistent upper bound that can be used across all scenarios for ranking and
comparison of outcomes. Density dependence was implemented by reducing rates of
survival and growth (due to intraspecific competition) such that abundance declined
faster than the self-thinning function, W(x), as plant age increased whenever a population
exceeded the carrying capacity of its habitat patch. This is realistic; if there are more
individuals in the patch than the habitat suitability can accommodate then populations
would be expected to decline faster (or at least as fast) due to intra-specific density
dependence than background survival rates or self-thinning relationships would indicate.
Fires were assumed to be uncorrelated across patches. In the model a fire burns
the size of the relevant patch. For C. greggii this results in a mixture of large and small
fires across the landscape through time. For C. verrucosus, which occurs in smaller
patches across the landscape, this results in small patchy fires. This is realistic because
we do not expect fires to be correlated across C. verrucosus habitat because of
urbanization. This species is already restricted to isolated canyons in urban areas and fires
tend to be highly uncorrelated (because fires in urban areas tend to be effectively
suppressed).
Since our initial populations began with age 16 individuals, the age 60 initial
abundance was multiplied by the age 16 weight, W(16), and thus initial abundance was
set at 207 age 16 individuals/ha for C. greggii and 1,623 age 16 individuals/ha for C.
verrucosus. We calculated expected minimum abundance (EMA) with and without the
first 20 years of the population trajectories to determine if initiating the population as an
even-aged aged cohort versus allowing a burn-in period (which would result in stands of
different ages across the landscape) had any effect on results and determined that it did
not. Therefore, results are reported here with the full time series contributing to EMA
calculations.
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