Appendix S1: Extended description of methods
Generating Climate Projections
To explore future climatic trends relevant to abalone population abundance, we generated
annual climate forecasts for August and March SST according to two global emission
scenarios: a no-climate-policy reference (no stabilization) scenario (MiniCAM Ref.) and a
corresponding policy (stabilization) scenario (MiniCAM, Level 1) designed to stabilize at an
equivalent CO2 concentration of 450 ppm (Clarke et al., 2007, Wigley et al., 2009).
MAGICC/SCENGEN 5.3 (Fordham et al., 2012c) was used to generate an annual time series
of future climate anomalies (2000 – 2100) using an evenly weighted ensemble of seven
atmosphere-ocean general circulation models (GCMs): CCSM-3; MRI-CGCM2.3.2;
ECHAM5/MPI-OM; MIROC3.2 (hires); UKMO-HadCM3; UKMO-HadGEM1; GFDLCM2.0. These seven GCMs were chosen, from among twenty CMIP3/AR4 GCMs (Coupled
Model Intercomparison Project 3 GCM database [www-pcmdi.llnl.gov/]), on the basis of
their skill in reproducing seasonal SST (1980-1999) at global and regional (Pacific and Indian
Oceans) scales and a convergence criteria (Fordham et al., 2013). We also generated
individual GCM forecasts using the Parallel Climate Model (PCM; Washington et al., 2000)
and the Community Climate System Model, version 3.0 (CCSM-3; Collins et al., 2006). Both
GCMs are commonly used in marine ecological studies (e.g., Boyd & Doney, 2002, Donner
et al., 2005) and have contrasting skill based on retrospective simulations. The PCM
performs poorly in reproducing recent seasonal SST at global and regional scales, while the
CCSM-3 is far better at hindcasting past SSTs. Collectively these models provide a suit of
representative climate futures, with the PCM predicting the lowest increase in summer
(March) SST and the highest increase in winter (August) SST, and the 7-model average
providing intermediate forecasts between those given by PCM and CCSM-3 for March SST
(Figure S1).
Modelling Abundance
Annual climate forecasts of August SST (2000-2100) were used as an input in the ENM
abundance models to generate a 100-year time series of spatial abundance predictions for H.
rubra and H. laevigata. The predicted abundance estimates for each species in each grid cell
(m-2) were subsequently multiplied by the total grid cell area and by the proportion of each
grid cell expected to encompass subtidal rock habitats (based on Watts et al., 2011). This is
because the presence of H. rubra and H. laevigata is restricted to subtidal rock habitats
(McShane & Smith, 1991, Shepherd, 1998). Abundance was not predicted at depths greater
than 30 m for H. laevigata and 20 m for H. rubra, because their abundance below these
depths can decline rapidly (Shepherd unpublished data) and commercial fishing is limited
(Mayfield unpublished data). Initial abundance of H. rubra and H. laevigata on reefs outside
its present-day distribution were set to zero. Thus, these habitats have suitable substrate
(rocky reefs), but are not colonized in the year 2000. Treating initial abundance as zero
allows these reefs to be colonized in the future through demographic processes (such as
dispersal) interacting with changes in environmental suitability (Fordham et al., 2012a).
Calculating carrying capacity
Carrying capacity was calculated by adjusting ENM abundance projections to account for
non-cryptic individuals. H. rubra and H. laevigata juveniles inhabit cryptic habitats
(Shepherd, 1990). Juveniles are difficult to count in dive surveys (Shepherd, 1990) and were
poorly represented in data used to parameterise the ENM. To account for the influence of
survey bias on estimates of abundance and K, we multiplied grid cell abundance by the ratio
of juvenile (size 8-74 mm in length) to adults (> 74mm) expected under a stable age
distribution. Carrying capacity did not include zero year olds since the model was a prebreeding stage matrix.
Pre-breeding Matrix
We developed a pre-breeding stage matrix (Akçakaya & Root, 2005). Matrix elements
governed transitions among seven length classes (size classes are provided in Bardos et al.,
2006), derived for a time step of 1 year from growth, fertility and mortality data for abalone
populations in Australia. Fertility and allometric growth rates were the same as those used by
Bardos et al. (2006) for a fast-growing abalone population. Survival in the largest size class
(>118mm) was set at 0.72 -1 years based on locally derived estimates for H. laevigata nonharvested populations (Shepherd, 1990). Survival rates for size classes used by Bardos et al.
(2006) were modified proportionally so that the upper limit on survival was 0.72 -1 years for
abalone > 118 mm. The RAMAS stage matrix is provided below for three cryptic juvenile
size classes (8–30, 30–52, 52–74 mm) and three adult size classes (74–96, 96–118, 118mm to
∞).
Environmental Variability
Abalone recruitment and abundance is highly variable, even in the absence of fishing,
probably due to variability in SST (Shepherd & Brown, 1993). We estimated temporal
variability in survival rates from a long term census (1970 to 1987) of H. laevigata
(Shepherd, 1990), following approaches published elsewhere (Fordham et al., 2012b). After
removing variance due to demographic stochasticity (Akcakaya, 2002), the standard
deviation for survival of animals ≥ 3.5 years (or > 52-74 mm in length) was estimated as
0.301 (1970-75) and 0.180 (1976-1987) and the coefficient of variation (CV) as 0.533 and
0.282, respectively. We used the more conservative estimate (CV = 0.282) to initially model
variation in survival rates for animals > 74 mm. Because inter-annual variation in survival is
relatively high for young animals (Shepherd & Breen, 1992) we modelled a 20% higher rate
of variation for animals with lengths between 8 – 74 mm (S. Shepherd unpublished data). We
used a ten year time series of larval abundance for Haliotis discus hannai and Tegula spp. to
estimate temporal variability in the number of recruits per adult (Sasaki & Shepherd, 1995).
Variability in water turbulence heavily influences recruitment across the geographic range of
Haliotis discus hannai and Tegula spp (Sasaki & Shepherd, 1995). Similar observations have
been made for abalone in Southern Australia (Shepherd et al., 1992). The CV in recruitment
for Haliotis discus hannai and Tegula spp. was 0.78 and 0.85 respectively. A study of H.
rubra recruits ( < 8 mm in length; equal to < 12 months of age) in three distinct populations
in New South Wales (Australia) between 1987 and 1988 (McShane & Smith, 1991) also
showed high variability in the number of recruits per adult (CV ranging from 0.916 to 1.097).
We initially modelled environmental variability for H. laevigata and H. rubra using a CV of
0.85 for fertility − we chose not use the fertility estimate for H. rubra because it was
calculated from just two years of data. We then adjusted the vital rate variability parameters
to match the observed variability in the H. laevigata abundance time series − variability
computed as CV of 𝑙𝑜𝑔 (
𝑁𝑡+1
𝑁𝑡
) (where N is the population size a time t). This method is
described in more detail in Anderson et al. (2009). The revised CV parameters were 0.2 and
0.78 for survival and fertility, respectively.
Sensitivity Analysis
We undertook a comprehensive sensitivity analysis to determine the influence of spatial and
non-spatial parameters on model predictions. To ensure sampled values covered the entire
parameter space, we used Latin hypercube sampling (Iman et al., 1981) with 50 sampling
dimensions drawn from realistic ranges of the following parameters: Rmax (± 10%), dispersal
(± 10%), variability in vital rates (± 10%), carrying capacity (± 20%) and harvest off-take (±
20%). The values for each parameter were selected from uniform increments within these
ranges (see Conroy & Brook, 2003 for a practical example). For each iteration of randomly
selected parameter values, we projected the population to 2100 (based on 500 stochastic
replications) and recorded final population abundance for persistent runs only. We used
general linear models (GLM; Gaussian distribution with identity link) to explore the relative
importance of different parameter values on predicted total abundance in 2100 (McCarthy et
al., 1995). We calculated the standardised regression coefficients (coef/S.E.) for each term in
the saturated model (n=5) as a relative metric of prevalence sensitivity to variation in vital
rates (McCarthy, 1996). Confidence intervals (5th and 95th percentiles) for the coefficients
were generated through a bootstrapping procedure (10000 bootstraps) that modelled the
relationship between parameter values and total abundance in 2100.
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