5.1 Ethics Statement
All procedures were reviewed and approved by the University of Western Australia animal ethics committee (UWA animal ethics permit RA/3/100/1145) and the Department of Parks and Wildlife (scientific licence SF008844).
5.2 Study site and egg collection
The N. depressus rookery at Cape Domett occurs on a gently sloping, 1.9 km-long, north-west facing beach in the East Kimberley region of Western Australia, Australia (14.798° S, 128.415° E). Freshly oviposited eggs were collected for transport to a laboratory in Perth, Western Australia on September 20 2012. Approximately, whole clutches (52 eggs) were collected from each of six nesting females (total 296 eggs) and stored in damp vermiculite within a portable refrigerator (model: Engel MT45FP) set to 8°C to suspend embryonic development thereby facilitating egg viability during transport (Harry & Limpus 1989). Eggs were transported by helicopter to Kununurra where they awaited further transport via a commercial airline to Perth. Inadvertently, eggs were held over in Kununurra due to a lack of cargo space, and consequently eggs reached the University of Western Australia about 100 h after oviposition. This time period fell outside the 72-h window of viability defined by Harry and Limpus .
In situ incubation temperatures were recorded in 11 nests on the nights of September 16 and 17 in 2012. Four Thermochron® iButtons (Maxim Integrated Products; DS1921H; accuracy ±1°C, precision 0.125°C) were placed at intervals into each nest chamber during oviposition, with the goal being to record temperatures at different depths within the nest chamber. The nests were situated at various locations within the ‘pink sand’ sections of the beach  and were marked with a GPS device (Garmin eTrex Vista HCx) and photographed for ease of relocation. A weather station (WeatherHawk, Signature Series 232) was erected midway along the beach on a small dune above the high tide mark. Weather data (air temperature, humidity, wind speed, solar radiation) were recorded at 30-min intervals.
The rookery was revisited 40 days later (25–26 October 2012) and all nests were relocated and excavated. Between 12 and 16 eggs that were closest to each of the four iButtons were removed from each nest (total of 138 from all nests). The depths of iButtons below the sand surface were measured to the nearest 10 mm before removal. All remaining eggs were reburied. The embryos inside the sampled eggs were euthanised by chilling for approximately 24 h. Chilling was achieved on the beach using ice, and eggs were relocated to a portable refrigerator set to 2–4°C within 2–3 h of collection. Chilling was maintained during transport by boat and road back to Kununurra. There, dead embryos were removed from their shells and fixed in 10% buffered neutral formalin for road transport to Perth. Ten of the eleven nests (nest IDs 1, 2, 3, 4, 5, 6, 10, 12, 13 and 15) contained viable embryos; eggs from the remaining nest showed no signs of development.
5.3 Incubation experiments
The six live clutches returned to Perth were either used in ‘back-switch’ experiments designed to delineate the TSP, or else were incubated at a constant temperature close to the estimated pivotal temperature. Ten eggs (2 each from 5 clutches) that were not used in back-switch experiments were incubated at a constant temperature of 30.1°C (Model i180), which was the estimated pivotal temperature for a population of N. depressus from the Pilbara region of Western Australia .
For the back-switch experiments, one egg from each clutch was buried in damp sand within one of 48 partially sealed containers. Containers were placed in one of four Steridium incubators (models: i180 and i500) set to either a male-producing temperature (28°C; 24 containers) or a female-producing temperature (32.5°C; 24 containers). During development, each container of 5–6 eggs was switched to the opposite temperature treatment for either 10% or 15% of embryonic development (96–240 h, depending on the time and temperature), after which time they were switched back to their original temperature (Table 1). Each back-switch treatment was replicated within a pair of incubators (one pair of 180 L incubators and one pair of 500 L incubators), and iButtons were placed next to an egg when each container underwent a switch to record the temperatures experienced by the embryos.
We used a development rate function developed for N. depressus by Box (2010) to calculate the day that embryos should have completed 35% of development to hatching when incubated at either 28°C or 32.5°C. Switches then began on this day (or when embryos were further developed—refer Table 1) and concluded when a further 10% or 15% of development to hatching should have been completed at the switch temperature (28°C or 32.5°C). Procedural controls were also included for the earliest switches, in which case embryos incubated at 28°C were switched to a different incubator at 28°C for the appropriate period, and then back again to the original incubator. A procedural control was also applied to eggs incubated at 32.5°C.
Eggs in both the back-switch and Tpiv experiments were weighed at the start of incubation and thereafter every seven days to assess embryonic viability. Unviable eggs (those that lost weight and became discoloured) were removed from incubation boxes. On each occasion, containers were repositioned randomly in the incubators to minimise any impact of subtle temperature gradients within incubators. Containers were checked daily after 35 days of incubation (one week before the earliest expected hatch date) and incubation time was recorded as the time from the start of incubation to when pipping commenced. The four days between oviposition and the start of incubation were not included in the incubation time, as eggs were cooled during this period and embryonic development was suspended . Once pipping commenced, hatchlings were weighed and euthanised by an intracoelomic injection of 0.4 mL sodium pentabarbitone at a concentration of 160 mg/kg. Hatchlings were labelled and stored in 10% buffered neutral formalin for later dissection.
5.4 Identification of hatchling sex
The gonads of marine turtle hatchlings are small (<500 μm) and attached to the kidney . Consequently, the left kidney of each preserved individual was removed. Kidneys were then prepared as paraffin-embedded sections and stained with haematoxylin and eosin for light microscopy . The sex of each specimen was identified based on the differentiation of gonadal medulla and cortex, where males have seminiferous tubules in the medulla and a regressed cortex, and females have a disorganised medulla and a thick, well-developed cortex ,. Each specimen was classified as male, female or unknown on three separate occasions, without reference to previous assessments, and a repeatability analysis was conducted to determine the reliability of the classification. Any specimens where a gonad was not visible or was unable to be classified were resectioned and reexamined until each individual could be classified as male or female.
5.5 Calculation of a non-linear function for embryonic development rate
Development rate, expressed as a function of temperature, was calculated from data on incubation duration using the program DEVARA [http://delta-intkey.com/devar/] ,. Hourly temperature records (from iButtons) and the average incubation time (in days) of eggs in each container provided the inputs for DEVARA. Data from eggs incubated only at constant temperatures (Tpiv experiment and two back-switch controls) were used, and temperatures were sub-sampled to six values per day to reduce the amount of information read by the program. DEVARA fits a non-linear model expressing development rate (r
) as a percentage per day, as a function of temperature:
The parameters fitted by DEVARA describe the maximum development rate (b1), its corresponding temperature (b3) and the temperature at which development rate approaches zero (b2). Parameters b4 and b5 control the asymmetry and steepness of the curve and were fixed at 6 and 0.4, respectively, as is recommended when development rates at extreme incubation temperatures are unknown .
5.6 Delineation of the thermosensitive period (TSP)
Using the parameters estimated for the non-linear development rate function defined above, hourly temperature records from the back-switch experiments were converted into developmental increments. These increments were integrated to determine the cumulative proportion of development that was completed on each day. The length of each switch window was thereafter described as a developmental proportion (e.g. 12% of development). If any back-switch regime produced a sex ratio different to that expected from the dominant incubation temperature, then the TSP was assumed to fall within the portion of development where the temperature was switched.
5.7 Determination of the pivotal temperature (Tpiv) and transitional range of temperatures (TRT)
The relationship between incubation temperature and sex ratio was calculated using TSD software version 4.0.3 [http://max2.ese.u-psud.fr/epc/conservation/TSD/index.html] developed by . This program is widely used to compare the fit of up to five threshold models using maximum likelihood (Richards/a-logistic, Weibull, Weibull*, Hill and Hill*) where * indicates the a-logistic or ‘asymmetrical’ version of the model. Data from constant temperature incubation were intended to be used for this analysis, but the program requires that three or more temperatures produce mixed sexes in order for the fit of different models to be compared . Of the five constant incubation temperature regimes applied in this study (Tpiv experiment, male back-switch controls and female back-switch controls), only one produced mixed sexes. Hence, sex ratio and temperature data from field nests were added to the laboratory data to produce a more rigorous estimate of a sex ratio function.
As the TSD software is designed for constant temperature data, temperature records from field nests were converted to constant temperature equivalents (CTEs; ). Effectively, the CTE is the temperature above which half of development occurs (i.e. a developmental median) and thereby the relationship between development rate and temperature must first be established. Furthermore, when incubation temperatures are variable, the CTE during the TSP (and not the entire incubation period) is most relevant for fitting the TSD function . Hence, we used our development rate function (Figure 2) to convert the nest temperatures that fell within the TSP into hourly developmental increments. These increments were ranked and integrated to determine the temperature above which half of development occurs (the CTE).
The CTE parameter and sex ratios measured from all ten viable field nests were used in combination with laboratory data, and the Hill equation produced the lowest AIC value. The Hill equation has the form:
where sr(t) is the sex ratio at a given temperature t, P is the pivotal temperature, S describes the steepness of the transition from male to female producing temperatures and K is a parameter that describes the asymmetrical shape of the function. The fitted values of P, S and K and the corresponding TRT were noted and used as reference points for a further ten models, which were fitted from random subsets of five field nests (Table 2). By using only five of the ten field data points available, we were able to meet our goal of retaining an independent data set to test our mechanistic framework (Figure 1). For each of the ten subsets, there was more than one equation that produced an equally good fit (∆AIC <2); however, the Hill equation consistently produced the lowest AIC value across all subsets. Hence, we used the Hill equation to make a standardised comparison of the TSD equation generated by each of the ten datasets, and used the mean residuals to select a consensus model that could be used to estimate the Tpiv and TRT of the Cape Domett population.
5.8 Sand temperature reconstruction and projection
NicheMapR is an R version of the mechanistic modelling program NicheMapperTM;  and was used to predict hourly sand temperatures by simultaneously solving heat and mass balance equations based on physical properties of beach sand and on regional climate data (e.g. ,). The parameters of the microclimate model were not ‘tuned’ to the observed sand temperatures. Rather, the sand properties for the Cape Domett rookery were estimated from relevant literature (e.g. ,) or were measured empirically (Table 5). Percent sand moisture was measured by determining the wet and dry weights of sand samples collected from a range of depths from each field nest during excavation in October. Solar reflectance of sand sampled from two nests in the wavelength range 300–2,100 nm was measured using two spectrometers (Ocean Optics USB2000 for the UV-visible range and NIRQuest for the NIR range) and two light sources (Ocean Optics PX-2 pulsed xenon light for the UV-visible range and HL-2000 tungsten halogen light for the visible-NIR range), all connected with a quadrifurcated fibre optic. The probe on the end of the fibre optic was held within an ocean optics RPH-1 probe holder at a constant angle (45°) and distance from the surface, and each measurement was expressed relative to a Spectralon 99% white reflectance standard (Labsphere, Inc., North Sutton, NH, USA), and weighted by solar irradiance. There was no significant difference in the solar reflectance of the two samples (unpaired t-test; p = 0.959).
Daily maximum and minimum temperatures, relative humidity and wind speeds were collated from data generated by the weather station we installed at the rookery between September 18 and October 24, 2012. Rainfall data during this period were obtained from the nearest Bureau of Meteorology weather station at Wyndham (http://www.bom.gov.au). These weather values were used as inputs into NicheMapR, and sand temperatures were predicted for user-specified depths (range 36–80 cm) using the parameters in Table 2 and assuming 0% shade. Predicted temperatures at a particular depth were then compared to actual nest temperatures measured at the same depth, using the r2 statistic.
Historical (1990–2013) climate data for Cape Domett (daily maximum and minimum temperatures, relative humidity, rainfall and solar radiation) were obtained from the Australian Water Availability Project (AWAP). Gridded long-term average wind speed data were obtained from Australian National University Climate software package (ANUCLIM; ). Both the AWAP and ANUCLIM databases are derived from interpolated data records from weather stations across Australia. These historical climate data were interpolated at a point approximately 25 km south of the Cape Domett rookery (15.003° S, 128.383° E).
The AWAP climate data, combined with the shade and sand parameters defined earlier, were used as inputs into the microclimate model within NicheMapR to estimate sand temperatures at 50 cm depth for the 23 years from 1990 to 2013. To investigate the influence of climate change on sand temperatures, the 2007 air temperatures from the AWAP database were adjusted in accordance with the Commonwealth Scientific and Industrial Research Organisation’s (CSIRO) projections of future air temperatures for Australia . Under a low emissions scenario, AWAP air temperatures were increased by 0.6°C or 1.8°C for the years 2030 and 2070, respectively. Under a high emissions scenario, air temperatures were increased by 1.5°C or 3.4°C for the same years.
5.9 Model validation
The DEVARA function was used to convert the hourly sand temperatures predicted by NicheMapR (or the actual temperatures measured in nests) into developmental increments for the five nests not used to fit the TSD function. Development was assumed to have started on the date of oviposition; hence, the first developmental increment we calculated was for the hour immediately following oviposition. All the hourly development increments calculated for a particular temperature record were integrated to determine the proportion of development completed on each day and thereby identify the dates that formed the boundaries of the TSP. We calculated a CTE for all temperatures that fell within the TSP (as described earlier) and CTEs were inputted into the TSD function (Figure 4B) to estimate the sex ratio of the embryos sampled at the various depths in each nest. Sex ratios were classified as female (<5% males), mixed (5–95% males) or male (>95% males). Predicted sex ratios were then compared to the actual sex ratios of the sampled embryos, which allowed us to assess how effectively our physiological model estimated sex ratios from hourly temperature records (Figure 1).