Olive Ridley sea turtles nest along all of the Pacific Coast of Guatemala. Egg collection for human consumption is authorized as long as 20% of the eggs of each collected nest is given to hatcheries located along all the littoral 27. A total of 1,600 eggs collected on the previous night were bought to various collectors. The dates of incubation beginning were as followed: 16/11/2011 - 140 eggs; 22/11/2011 - 120 eggs; 23/11/2011 - 160 eggs; 24/11/2011 - 1000 eggs; 25/11/2011 - 160 eggs; 26/11/2011 - 20 eggs. We had no control on how the eggs were handled during the previous night but the hatching success was very high. Eggs were grouped in 80 nests (20 randomly selected eggs per nest) in this experiment. Among them, 40 have been incubated in hatchery (hatchery nests) and 40 have been used in 4 different experiments (experimental nests). Half of these 40 nests were buried in sand at 40 cm depth and half at 60 cm depth. Among each group of these 40 experimental nests, half (10) have been incubated in open beach under full shade and half (10) in full sun. Experiment was conducted at the hatchery of the Monterrico Natural Reserve for Multiple Uses.

Incubation time, longitudinal ttemperatures and 10 hatchling straight carapace lengths at the nearest 0.1 mm were registered for all monitored nests. Mean incubation temperatures and incubation durations were analysed using linear model 28 and hatchling sizes were analysed using linear mixed model with nest identity as a random factor 29. In all cases, fixed factors were depth of nests (40 or 60 cm) and with or without shade and their interaction. Mean incubation temperature and its first order interaction with other factors were added for analysis of mean incubation duration and hatchling size. A backward model selection was used by removing the least non-significant factor one at a time. A single factor was not removed if it was significant when involved in an interaction. F test after ANOVA (ANalysis Of VAriance) was used to detect the influence of factors after linear model 28 and Likelihood Ratio Test (LRT) test after ANOVA was used to detect the influence of factors after linear mixed model using R package glmmADMB 30.

The variability of daily temperatures among nests was measured as the mean of the daily standard deviation of temperatures recorded in nests from each treatment (shading status and depth). Welch modified two-sample t-test with unequal variances were used to test the treatments effect (depth and shading) 31.

The model of embryo growth integrates in a single framework both the growth rate dependency on temperature and the embryo growth 26. The parameters for growth rate dependency on temperature that maximized the logarithm of the likelihood (Ln L) of the observed hatchling size distribution were search for using the R package embryogrowth 32. The model is summarized here briefly but a complete description can be found in the original publication 26.

Biological temperature-dependent rate models based on Arrhenius and Eyring s equations have been formulated by Sharpe and DeMichele 33. The original formulation of Sharpe and DeMichele was modified by Schoolfield et al. 34 to remove the very high correlations of parameter estimators. Two kinds of equations using 4 or 6 parameters produced a curve with a maximum at an intermediate temperature and decreased bellow and above this temperature. The level as well as the position of the maximum can be manipulated using the parameters values.

The early growth of embryos is modelled using a modification of the Gompertz model 35 proposed by Laird 36 (eqn 1):

eqn 1

Where X(0) is the size or mass at nesting time (time=0), r(T) is the growth rate at the beginning of the curve, and K is the carrying capacity with

X_H is the hatchling size and r_K=2.09 is a constant used to slowdown growth at the end of incubation 26 to ensure that embryological stages are well positioned during incubation.

The dynamic of X (t )is governed by the Gompertz differential equation (eqn 2):

eqn 2

The gastrula is approximately a disk of 1.7 mm diameter and this size will be used as X (0) 37.

Growth rate r(T) can be calculated with models (4 or 6 parameters) from Schoolfield et al. 34 model and an incubation temperature T. With X(0) and K, and a time-series of r(T), the pattern of change of embryo size for this nest is evaluated using Runge-Kutta method of order 4 for the approximation of solutions of ordinary differential equations.

Estimation of parameters was performed using maximum likelihood with an identity link and a Gaussian distribution of SCL. The standard error of parameters was estimated using the square-root of the inverse of the Hessian matrix which is an asymptotic approximation of the variance-covariance matrix 38. The models are implemented in the R package embryogrowth 32.

First, growth rate r(T) has been fitted for hatchery and experimental Lepidochelysolivacea nests separately. Next, all the nests were grouped in a single dataset and growth rate r(T) has been fitted again. We used AIC and Akaike weight to select between 4 and 6-parameters models. AIC is a measure of the relative quality of fit, which penalized for too many parameters in the model 39 and Akaike weight gives the relative statistical support of several models tested on the same dataset 40. Likelihood ratio test has been used to test whether a single model for hatchery and experimental nests was sufficient or not to describe observed data.

The statistics

(Likelihood Ratio Test, with Ln L being the logarithm of the likelihood) is distributed as a χ2 with the degrees of freedom being the difference of number of parameters between the most complete model and the simplest one 41.

Distribution of temperatures recorded in the 80 Lepidochelysolivacea nests from the beach of Monterrico, Guatemala are shown in Figure 2 as well as the temperatures recorded in Carettacaretta nests from Turkey 42. Average incubation temperatures for the 80 nests ranges from 29.11 °C to 33.56 °C (mean=31.00 °C, sd=1.53 °C). Shaded nests were significantly cooler than those exposed to the sun by 2.11 °C (paired t-tests with Bonferonni correction, p<10^-9). Nests from hatchery were also significant cooler than the experimental ones (paired t-tests with Bonferonni correction, 1.32 °C difference between hatchery vs shaded, p<10^-9 and 3.44 °C difference hatchery vs sun, p<10^-9) (Figure 3A). Among the experimental nests, only shading status was significant to explain the difference between nests for average incubation temperatures. Depth and interaction between shading status and depth were not significant and respectively).

Incubation duration ranged from 43 to 55 days (mean=49.86 days, sd=3.63). Significant effect of mean incubation temperature and shading status for experimental data was observed and respectively) but not of depth as well as all interactions (all p>0.1). Incubation duration was longer for cooler temperatures and shaded nests (Figure 3B).

Straight carapace length of hatchlings (mean 40.86 mm, sd=1.82) was significantly different for experimental data according to depth factor (deviance= 5.492, df=1, p<0.02) but not for any other factors (all p>0.05). Embryos incubated at 40 cm were smaller (40.22 mm, sd=1.54 mm) than those incubated at 60 cm (41.07 mm, sd=1.36 mm) (Figure 3C).

An effect of shading at 40 cm (t = -6.7727, df = 9.15,p < 0.0001) and 60 cm (t = 5.0015, df = 11.441, p< 0.001) and depth for shade (t = -2.3516, df = 15.382, p-value < 0.04) and sun-exposed nests (t = 2.1895, df = 11.557, p < 0.05) were noticed on the daily standard deviation temperatures.

Parameters maximizing likelihood of observed hatchling size for each nest have been fitted first using the total set of 80 nests using the 4 and the 6-parameters equation describing instantaneous growth rate dependency to temperature. AIC for 4-parameters model was 380.97 whereas it was 390.05 for the 6-parameters model. Akaike weight gives a very strong support to retain the 4-parameters model (p=0.99). In a second step, parameters have been fitted separately for hatchery nests (Ln L=-97.83), for experimental nests (Ln L=-79.79) and for all nests together (Ln L=-186.55) with LRT being 1.90 (df=4, p=0.75). Thus, a single model for the two categories of nests was sufficient.

The fitted pattern of embryo growth for the 80 nests is shown in Figure 5. It should be noted that all fitted embryo sizes at the end of the incubation are comprised within the 95% confidence interval of observed hatchling sizes.

The fitted instantaneous growth rate according to temperature is shown in Figure 6 for Lepidochelysolivacea from Guatemala. The curve fitted for Mediterranean Carettacaretta4243 is also shown for comparison.

Temperature during incubation of ectothermic animals can have profound consequences on the fitness of individuals and then selection should act to adapt response of embryos to temperature.

The effect of shading on incubation temperature was anticipated based on several previous reports for turtles 44454647 but also lizards 48. Indeed, we found that the shaded experimental nests have a lower mean incubation temperature than the experimental nests exposed to the sun. Hatchery nests are also shaded and have still a lower temperature (Figure 3A). However, we did not detect a significant effect of depth probably because the differential between both depths (40 and 60 cm) was not sufficient to produce enough change in temperature. As a consequence, shaded nests take longer to emerge when compared to the nests directly exposed to sun and incubation temperature could modulate this effect (Figure 3B).

Hatchlings from eggs incubated at 40 cm were significantly smaller than those from eggs incubated at 60 cm (Figure 3C) but a direct effect of temperature or shading was not observed. We do not have definitive explanation for this effect. Mass of hatchling has been shown to be dependent on incubation temperature in many reptiles 49505152 but also on dryness of substrate 53. On the other hand, effect on size is not consistent among studies nor within the same study. For example, no effect has been observed in the turtle Pelodiscussinensis23 but a slight decrease of carapace length has been measured in the sea turtle Carettacaretta as the moisture increased 54. But, in the same experiment and for the same turtles, carapace width and plastron length did not show any consistent pattern of increasing with higher moisture 54.

Here we do not detect an effect of temperature on size but an effect of depth of the nest. This effect could be mediated by moisture difference between two depths: it is possible that eggs incubated at 40 cm lost more water that those located at 60 cm, the latter being closer to the water table (sea water that infiltrates by porosity in sand) 55. Eggs incubated in dryer substrate accumulate less water during incubation 56. The mechanism linking substrate water content and size of embryos has been well studied in the freshwater Chrysemyspicta57. Water within the eggs plays a key role in the mobilization of yolk reserves by reptile embryos and consequently influences hatchling mass 57.

Carettacaretta nests mainly out of the intertropical region whereas Lepidochelysolivacea has a distribution more centred on the equator 16. The northernmost nest for a sea turtle has been deposited by a Carettacaretta in South of France at the latitude 43°16.05'N 58. As a consequence, the nest temperatures experienced by Lepidochelysolivacea (Figure 2A and B) are generally much higher than temperatures experienced by Carettacaretta (Figure 2C). The growth rate depending on temperature in olive ridleys showed a pattern of increase from 20 °C to 35 °C. However, it should be noted that the part of the curve from 20 °C to 27 °C is extrapolated based on Schoolfield model of thermal reaction norm 34 because no lower temperature than 27 °C was recorded in Lepidochelysolivacea nests from Guatemala (Figure 2). On the other hand, temperature as low as 22 °C was recorded in Carettacaretta nests in Turkey 42 and the pattern of growth rate for these two species at low temperatures was very similar (Figure 6). However, the pattern differs completely for incubation at high temperatures. The growth rate continued to increase up to 35 °C for Lepidochelysolivacea whereas it went down for Carettacaretta around 32 °C. This is consistent with the observation that incubation duration increased at 32 °C as compared to 31°C 43 and that no Carettacaretta hatchlings survived when incubated at 32 °C and above 21.

The variability of temperatures among different nests incubated in same conditions was measured. We detect an effect of depth but much more an effect of shading (Figure 4). Such a measure is particularly important because it permits to explain why, in the same beach and at the same time, heterogeneity of incubation conditions was observed. The thermal microhabitats have been overlooked for sea turtle and generally for reptiles. This is particularly important in the context of prediction of the impact of climate change. The climate models available give prediction at the regional scale 59 very far away from the beach scale and even intra-nesting beach level as shown here. This downscaling is challenging to be able to produce realistic models of incubation of reptile eggs.