Highly mineralized rigid-shelled eggs characterize one lineage of gekkotans. In contrast, poorly mineralized flexible-shelled eggs characterize basal lineages of gekkotans and all other squamates. Low oxygen permeability of rigid-shelled eggs is associated with small eggs and hatchlings, and long incubation lengths compared to flexible-shelled gekkotan eggs. These features represent a demographic cost for species with rigid-shelled eggs. This cost is offset, at least in part, because mortality due to desiccation and predation is reduced for rigid-shelled eggs relative to flexible-shelled eggs. Developmental traits may also compensate for the low oxygen permeability of rigid-shelled eggs. Oviposition, for example, occurs at earlier developmental stages for gekkotans with rigid- versus flexible-shelled eggs. Such early oviposition facilitates development because eggs move from the relatively hypoxic oviduct to the much better oxygenated nest environment. In this study, I tested the hypothesis that the growth of the yolk sac (YS) and chorioallantoic membrane (CAM) of gekkotans with rigid-shelled eggs is initiated and completed earlier than those of gekkotans with flexible-shelled eggs. I measured the surface area of eggs covered by the YS and CAM from oviposition to hatching and determined which of four non-linear models provide the best fit for growth curves. I also compiled a data set on embryonic metabolism of gekkotans and other lizards in order to place growth of the YS and CAM in the context of energy utilization of lizard embryos overall. Growth of the YS and CAM of gekkotans with rigid-shelled eggs is accelerated relative to that of gekkotans with flexible-shelled eggs and may serve to reduce overlap in the costs of YS and CAM development from that of the embryo. Adaptive variation in YS and CAM development may also extend to birds, crocodilians, and turtles as they also exhibit  life history variation that affects oxygen availability to embryos during development.

2.1 Observations on the growth of the YS and CAM

The YSCAM data set is comprised of observations that I made on the YS and CAM from oviposition to hatching. Data are from Andrews et al. (2013) plus observations on three additional gekkotan species, Correlophus ciliatus, Gehyra dubia, and Hemidactylus frenatus, made in my laboratory (Andrews, 2017) and at James Cook University in Australia (Table 2). I weighed all eggs at oviposition and staged one egg per clutch. Eggs were incubated at constant temperatures (25-29ºC) until their designated sampling date. At this time, they were fixed in buffered formalin. Eggshells were carefully removed to expose the extent of the vascularized YS and CAM on the egg surface. Scale drawings of the membranes were compared to a series of standard images to assess the % coverage of the YS and CAM relative to the surface area of each egg (for details, see Andrews et al., 2013). I quantified surface areas of the YS and CAM with reference to a fixed equator that divided the egg into two equal surface areas, the embryonic hemisphere was centered on the embryo and the abembryonic hemisphere included the remaining egg surface area. I also recorded embryo stage and age (with oviposition at age 0) at each observation. When eggs hatched, I weighed the hatchlings and determined incubation length as the difference in days between oviposition and hatching.

Observations on three of the seven species extended from oviposition to hatching. Observation on the remaining four species extended from oviposition to stages 36 or 37. I used the following convention for these species to compensate, at least in part, for the bias that results from curve fitting when data do not include asymptotic values. For G. dubia, G. variegata, and H. frenatus, species with observations of approximately one embryo per stage, I added one observation of 100 % YS and 100 % CAM at stage 40 and for C. turneri, a species with observations of approximately two embryos per stage, I added two such observations.

2.2 Observations on embryonic metabolism

The V̇O₂ data set comprises observations obtained from the literature for two RSG species, two FSG species, and 8 FSOL (lizards with flexible-shelled eggs other than gekkotans) species (Table 2). I used only data sets for which moisture and constant temperature conditions for incubation were ecologically appropriate, e.g., were associated with high survival during incubation. When eggs were incubated at more than one temperature or more than one moisture level, I selected the temperature closest to normal nest temperature and the highest moisture level, respectively. Because V̇O₂ and embryo dry mass exhibit parallel growth trajectories relative to stage (Thompson & Stewart, 1997; Thompson & Russell, 1999a; Nechaeva, Vladimirova, & Alekseeva, 2007; Ma, Guo, Su, & Ji, 2019), observations of V̇O₂ provide an index of embryonic growth for comparison with the growth of the YS and CAM.

Observations on all species extended from oviposition to hatching. While experimental protocols were consistent among studies, observations were either summarized as mean V̇O₂ for multiple embryos of the same age with sampling fixed at 2-3 d intervals (five species) or presented as individual observations measured on a daily basis (seven species). I therefore calculated mean V̇O₂ over 2-3 d intervals for the latter group and used these means in analyses to make sample sizes of the two groups of observations comparable. For comparative purposes, V̇O₂ was expressed as %V̇O₂ (V̇O₂ divided by the largest value of V̇O₂ observed).

The majority of studies expressed V̇O₂ as a function of egg age. This is problematic because embryos are arbitrarily assigned an age of 0 at oviposition. Age is thus not associated with stage of development; development of squamates is initiated at fertilization; by oviposition, stage varies considerably among species (Andrews & Mathies, 2000). Stage at oviposition, in the YSCAM data for example, ranged from 25 to 30, although all embryos were age 0. Stage is therefore the relevant dependent variable for comparative studies.

The first step was to adjust embryo age for variation in stage at oviposition. To make the YSCAM and V̇O₂ data sets compatible, I used the known association between stage and age in the YSCAM data to estimate the stages corresponding to ages in the V̇O₂ data. By convention, embryos that were stage 25 at oviposition were assigned to age 0. Ages of embryos that were oviposited at later stages were corrected to account for the time elapsed between stage 25 and the observed stage of oviposition. I regressed age on stage (three-parameter exponential models provided the best fits for all species). I used the resultant equations to estimate embryo age at stage 25, 26, 27, etc. The days elapsed between the adjacent stage intervals 25-26, 26-27, 27-28, 28-29, 29-30, and 30-31 were determined by subtraction. The resultant estimates of days per stage were pruned to include only observed intervals, ie., species with oviposition at stages 25 and 29, for example, would have had estimates for six and for the last two intervals, respectively. I then regressed the days elapsed per stage (D/S) for these observed intervals on incubation temperature (T) and stage interval (S), where 25 represents interval 25-26, 26, interval 26-27, etc. and included the T x S interaction term in the linear model. The resultant general relationship was:

D/S = 10.23 – 0.61 T + 0.31 S - 0.07 [(S – 27.80)(T – 27.77)],      

Eq. 1 R² = 0.99, F_3,26 = 892.4, P < 0.0001, where all terms made significant contributions to the model (P’s < 0.0001).

Temperature of embryos prior to oviposition should be the same as the mean body temperature of gravid females over a diel cycle (Parker & Andrews, 2006). The gravid females that produced eggs for this study were typically exposed to temperature gradients that allowed  them to thermoregulate normally. Observations on field body temperatures of geckos ecologically similar to those I studied (e.g., Brown, 1996; Angilletta, Montgomery, & Werner, 1999; Lapwong, Dejtaradol, & Webb, 2020; Kearney & Predavec, 2000) suggest that 28ºC would be an appropriate mean body temperature of gravid females. I used Eq. 1 to estimate the growth of embryos prior to oviposition for stage intervals 25-30. Intervals were summed to give the time elapsed between stage 25 and each observed stage at oviposition (ie., 25-26, 25-27, 25-28, etc.). I added the appropriate sum to observed ages and to incubation lengths for each species in both the YSCAM and the V̇O₂ data sets to correct for variation in stage at oviposition. Corrected ages were divided by corrected incubation lengths (x 100) to obtain an index of relative embryo age that ranged from 0 % when oviposition was at stage 25 to 100 % at hatching.

The second step was to predict embryo stage as a function of relative embryo age. Predictions were made independently for RSG and FSG species given that shell type seemed likely to affect the relationship between stage and age once differences in temperature and stage at oviposition were accounted for. Observed stage was regressed on relative embryo age (RAge) (three-parameter exponential models provided the best fits). The resultant relationships were:

Stage (RSG) = 40.2 – 13.8 Exp (-0.029 RAge)     (R² = 0.96, N_obs = 53, N_sp = 4)   Eq. 2

Stage (FSG) = 41.5 – 15.7 Exp (-0.022 RAge)     (R² = 0.96, N_obs = 80, N_sp = 3)   Eq. 3

The more rapid increase in predicted stage with respect to relative age of RSG than FSG embryos was statistically significant (P < 0.05) judging by the near non-overlapping 95% CIs for their respective growth rate parameters [-0.029 (-0.035 – -0.024) versus 0.022 (-0.027 – -0.017)] (Cumming, 2012, p. 158).). The mean difference between observed and predicted stages RSG and FSG species combined was (0.0085) and 80% of individual values were within -1.20 to 0.99 stages of the mean. I therefore used Eq. 2 to predict stage for RSG species and Eq. 3 to predict stage for FSG and FSOL species in the V̇O₂ data set (where stage was otherwise unknown).

2.3 Statistical analyses

To describe the relationships between %YS, %CAM, %V̇O₂ and stage, I fit observations for each species to four models: two- and three-parameter exponential models and three- and four-parameter logistic models (JMP software, JMP®, Vers. 15.0, SAS Institute, Cary, NC, 1989-2019, RRID:SCR_014242). The best model had the lowest AICc value. Evidence ratios (the Akaike weight of the best model divided by that of the next best model) were used to evaluate support for the best model. Evidence ratios near 1.0 mean that both models fit equally well and the higher the evidence ratio the stronger the support (Anderson, 2008). I used contingency tables to evaluate the degree to which best-fit models associated species with taxonomically appropriate groups. To illustrate overall growth patterns, I plotted of %YS, %CAM, and % V̇O₂ as a function of stage using species data that was aggregated within shell and membrane types using the best-fit model for each group (Table 3). I also used aggregated data to plot %YS and %CAM as a function of % V̇O₂ to put membrane growth in the context of embryo growth. When sample size was too small to compare RSG and FSG groups, the data was combined (indicated as RSG+FSG).

Comparisons between RSG and FSG groups (YSCAM data) and between RSG+FSG and FSOL (V̇O₂) groups were made with meta-analyses (Cumming, 2012) using Exploratory Software for Confidence Intervals (ESCI, copyright Geoff Cumming, 2011, RRID:SCR_006024). Mean effect sizes and their 95% confidence intervals were determined using random effects models. Effect sizes were growth rate (exponential and logistic models) and inflection point parameters (logistic models) of best-fit growth models. Parameters associated with asymptotes are not relevant for comparative purposes; the lower asymptote is an estimate of the independent variable when stage = 0, a point well outside the range of the data, and the upper asymptote was fixed at 100%. I assessed the difference in mean effect sizes for growth rate and inflection point parameters between RSG and FSG groups and between RSG+FSG and FSOL groups accorded to the amount of overlap of their 95% confidence intervals (Cumming, 2012, p. 158).

I did not run analyses corrected for phylogenetic signal for two reasons. 1) My sample sizes are small. The process of estimating phylogenetically independent contrasts and then conducting ANOVAs by groups within data sets progressively reduces the degrees of freedom available for statistical comparisons, and sample sizes of the YS, CAM, and V̇O₂ data sets are 6, 7, and 12 species, respectively. 2) The other reason is that the phylogenetic distribution of families with rigid- and with flexible-shelled eggs is dichotomous (Fig. 1). As a result, convergence or reversal do not contribute any variance to analyses, that is, data sets (of any size) will have only one independent contrast of rigid vs. flexible-shelled clades. Because phylogenetic analyses are used to assess the generality of phenomena considered to have evolved independently (Garland, Bennett, & Rezende, 2005), the one-time origin of rigid-shelled eggs in the Gekkota makes this taxon an evolutionary and statistically inappropriate target for such analyses.

Column Number. Column name. Comments.

1. Species.  Species used in analyses. Sources listed in text Table 2.

2. RSG+FSG, FSOL groups.  Groups used as the ‘by’ variable in some analyses.

3. RSG, FSG, FSOL groups.  Groups used as the ‘by’ variable in some analyses.

4. Data set.  YSCAM: observations made by the author on the relative surface areas of the YS and the CAM from oviposition to hatchling; VO2: observations from the literature on the relative metabolic rates of embryos from oviposition to hatching.

5. %YS.  Surface area of the YS expressed as a percentage of the surface area of the egg.

6. %CAM.  Surface area of the CAM expressed as a percentage of the surface area of the egg.

7. Supplemental Observations. See last paragraph of Section 2.1.

8. Stage. Embryo developmental stage at each observation in the YSCAM data set based on Dufaure and Hubert (1961).

9. Age. Embryo age at each observation in the YSCAM and the VO2 data sets. The day of oviposition is Age 0.

10. Days added to age. Days added represent the time elapsed between stage 25 and the observed stage at oviposition to correct for variable stages at oviposition. Values are based on a mean in utero temperature of 28C.  See Section 2.2 for details.

11. Corrected age. The sum of Age and Days added to age.

12. Relative age. Corrected age divided by Corrected incubation length.

13. Incubation length. Observed incubation length at the constant incubation temperature in Column 18.

14. Corrected incubation length. The sum of Incubation length and Days added to age (Columns 13 and 10).

15. VO2 mL/h. Metabolic rate at each observation.

16. VO2Max. Largest value of metabolic rate.

17. %VO2.  VO2 divided by VO2Max expressed as a percent. Se also Column 24.

18. Incubation temperature.  The constant temperature in degrees C during incubation.

19. Stage at oviposition. Mean embryo stage on the day of oviposition based on the Dufaure and Hubert (1961) scheme.

20. Hatchling mass g. Mean live mass on the day that eggs hatched.

21. Egg mass g. Mean egg mass at oviposition

22. Predicted stage. See Section 2.2 for calculations. Predictions were applied only to the VO2 data set where only stage was known.

23. Stage – Predicted stage. Observed stage minus Predicted stage for the YSCAM data set. This metric is an index of the accuracy of the prediction of stage.

24. Pruned temperature. Data pruned to one observation per species and displayed for age = 0.