Supplementarymaterial:Spatial and temporal synchrony in reptile population dynamics in variable environments.

Table S1:Total capturesof each species of reptile from long-term (13–22 years) live-trapping (205 524 trap nights), across nine sites, Simpson Desert, central Australia. Taxonomy follows Cogger (2000).

Species / Total captures / Family / Shelter / Diet / Active / longevity / Reference
Ctenophorus isolepis / 2514 / Agamidae / Spinifex / Ants & other invertebrates / Diurnal / Annual / Daly et al. (2007; 2008)
Ctenophorus nuchalis / 1303 / Agamidae / Burrows / Invertebrates / Diurnal / Annual / Daly et al. (2007; 2008)
Ctenotus ariadnae / 748 / Scincidae / Spinifex / Invertebrates / Diurnal / Perennial / Haynes (1996)
Ctenotus dux / 868 / Scincidae / Sand dunes / Invertebrates / Diurnal / Perennial / Haynes (1996); Pianka (1969)
Ctenotus pantherinus / 1474 / Scincidae / Spinifex / Termites / Nocturnal & diurnal / Perennial / Gordon et al. (2010)
Lerista labialis / 5663 / Scincidae / Fossorial / Termites / Nocturnal / Perennial / Greenville and Dickman (2005; 2009)

1

References for Table S1:

Cogger HG (2000) Reptiles and amphibians of Australia, 6th edn. Reed New Holland, Sydney, Australia

Daly BG, Dickman CR, Crowther MS (2007) Selection of habitat components by two species of agamid lizards in sandridge desert, central Australia. Austral Ecology 32:825-833

Daly BG, Dickman CR, Crowther MS (2008) Causes of habitat divergence in two species of agamid lizards in arid central Australia. Ecology 89:65-76

Gordon CE, Dickman CR, Thompson MB (2010) Partitioning of temporal activity among desert lizards in relation to prey availability and temperature. Austral Ecology 35:41-52

Greenville AC, Dickman CR (2005) The ecology of Lerista labialis (Scincidae) in the Simpson Desert: reproduction and diet. Journal of Arid Environments 60:611-625

Greenville AC, Dickman CR (2009) Factors affecting habitat selection in a specialist fossorial skink. Biological Journal of the Linnean Society 97:531-544

Haynes RS (1996) Resource partitioning and demography of twelve sympatric skinks (Ctenotus) in the Simpson Desert. Honours thesis. University of Sydney, Sydney

Pianka ER (1969) Sympatry of desert lizards (Ctenotus) in Western-Australia. Ecology 50:1012-1030

1

Appendix S1: Study sites used to test four potential spatial population structures of reptiles in central Australia. Each hypothesis is entered into the model via the Z-matrix. The Z-matrix is an n × m matrix of 0s and 1s, where n = number of sites (9) and m = each population. See figure S1 for study region map:

a)Asynchronous(m = 9): Reptiles at all nine sites have asynchronous dynamics (each site has a different population structure);

b)Oasis (m = 2): Reptiles at sites associated with ephemeral water sources (Tobermorey East, Tobermorey West, Field River South, Field River North and Kunnamuka Swamp East) will have different population processes to those at open desert sites (Main Camp, Shitty Site, South Site and Carlo; two population structures);

c)Productivity (m = 3) : Reptiles at sites within the same rainfall zone will have similar population dynamics (northern sites: Kunnamuka Swamp East, Carlo, Tobermorey East; western sites: Field River South, Field River North and Tobermorey West; and south-eastern sites: Main Camp, South Site and Shitty Site; three population structures);

d)Wildfire (m = 2): Reptiles at sites that have experienced a wildfire over the 22-year study period will have different population dynamics to those at unburnt sites (six sites burnt: Main Camp, Shitty Site, Field River South, Field River North, South Site and Kunnamuka Swamp East; three sites unburnt: Carlo, Tobermorey East and Tobermorey West; two population structures).

1

Figure S1: Annual rainfall at nine sites surveyed for biotic and abiotic interactions in the Simpson Desert, central Australia. The timing of extreme rainfall events is similar across sites. Data were recorded at site-based automatic weather stations (Environdata, Warwick, Queensland), installed in 1995.

Appendix S2: Bayesian multivariate autoregressive state-space models

The MARSS framework is hierarchical and allows modelling of different spatial population structures and parameters, while including both process (state) and observation variability. The two components of the model are the:

Process model, where X is abundance at each site n, u describes the mean growth rate of the sub-population and is set to zero. C represents coefficients of the covariates and care the covariates though time t. w is the error, which follows a multivariate normal distribution, with mean 0 and variance Q:

Observation model, where Z is a n × m matrix of 0s and 1s that assigns observations to a population structure, a denotes the mean bias between sites and set to zeroand V is error that follows a multivariate normal distribution, with mean 0 and variance Q.

All models are in log space. All data were de-meaned (z-score transformation) and thus u and a are equal to zero.

1

Expanded matrix model form

Reptile synchronous population model (m=1):

Process model:

Note: Reptilecaptures per 100 trap nights (log+1 transformed).

Observation model:

Note that subscripts below Pop represent each of the nine populations (sites).

Note that R is an9 x 9 matrix. Observation error was assumed to be the same within each species and the diagonals ().

Asynchronousmodel (m = 9)

Process model:

Note: Captures per 100 trap nights (log+1 transformed). Pop is population number.

Q is a 9x9 matrix. Process errors () are diagonal and unequal to allow process variation to differ for each population.

Observation model:

Note that R is a9 x 9 matrix. Observation error was assumed to be the same within each species and the diagonals () for the same species were set to be equal.

Oasis population model (m = 2):

Process model:

Note: Captures per 100 trap nights (log+1 transformed).Populations are either at oasis or open desert (open) sites.

Process errors () are diagonal and unequal to allow process variation to differ for each population.

Observation model:

Note thatR is a9 x 9 matrix. Observation error was assumed to be the same within each species and the diagonals () were set to be equal.

Productivity population model (m = 3)

Process model:

Note: Captures per 100 trap nights (log+1 transformed).Populations are either sites grouped as North, South or West.

Process errors () are diagonal and unequal to allow process variation to differ for each population.

Observation model:

Note that R is an9 x 9 matrix. Observation error was assumed to be the same within each species and the diagonals () were set to be equal.

Wildfire Model (m = 2):

Process model:

Note:

Captures per 100 trap nights (log+1 transformed).Populations are either at burnt or unburnt sites.

Process errors () are diagonal and unequal to allow process variation to differ for each population.

Observation model:

Note that R is an9 x 9 matrix. Observation error was assumed to be the same within each species and the diagonals () were set to be equal.

1