Empirical estimation of skin resistance to water loss in amphibians: agar evaluation as a non-resistance model to evaporation

Compared with that of other terrestrial vertebrates, the skin of amphibians is particularly unique in the sense that it is actively engaged in respiration and the osmotic regulation of body fluids; thus, most amphibians possess a skin that is freely permeable to gas, water and ions (Wells, 2007). This characteristic, however, also implies that amphibian's skin imposes a weak barrier to water evaporation, which makes them especially vulnerable to dehydration (Shoemaker et al., 1992). Thus, the determination of evaporative water loss (EWL) rates and the skin resistance to evaporation (r_s) are two key components commonly targeted in studies focusing on the maintenance of the amphibian's water balance. The EWL process is counteracted by the total resistance to evaporation (r_t), which is composed of the r_s itself and the boundary layer resistance (r_b) of saturated moist air next to the skin surface (Feder and Pinder, 1988). While the r_b varies on the basis of a complex interaction between morphological features (body shape and size) and the physical properties of the environment (temperature, wind speed, relative humidity), the r_s is a direct function of the skin structural properties (Shoemaker et al., 1992; Lillywhite, 2006; Hillman et al., 2009). So, for an evaporative biophysical model lacking a physical barrier to water evaporation (i.e. r_s=0), r_t will equate to r_b. In this manner, one can use such models to estimate the r_s of an amphibian measured under the exact same conditions as the biophysical model (i.e. r_s=r_t−r_b).

To mimic the evaporative properties of a wet-skinned ectotherm such as an amphibian, the 3% agar method (hereafter ‘agar method’) developed by Spotila and Berman (1976) has become the standard empirical technique to estimate r_b (Young et al., 2005). This agar method consists of constructing frog-shaped models made of 3% agar solution that mimic the shape and size of the live (or preserved) animal. A pivotal assumption in this approach is that the surface of the agar model imposes no barrier to water evaporation (r_s=0), thus equaling that of a free-standing water surface. Hence, the resistance to water evaporation on agar models is entirely determined by r_b. This assumption was originally verified by Spotila and Berman (1976), who showed that agar models evaporated at similar rates to a water-saturated surface (a wet blotter paper). However, the rationale that amphibian agar models would lose water by evaporation at similar rates to water-saturated surfaces has been broadly assumed but not scrutinized. Amphibians' body fluids contain a number of organic and inorganic compounds that set an osmotic concentration known to affect the colligative properties of an evaporating surface (Maruyama and Hasegawa, 2020) and, by consequence, EWL and r_s estimates (Anderson et al., 2017). Thus, water does not constitute the most adequate proxy to verify the adequacy of agar as a null (r_s=0) evaporative model for amphibians. Moreover, agar models have been built using various levels of agar concentration (e.g. Navas and Araujo, 2000; González-Bernal et al., 2012; Anderson et al., 2018; Cruz-Piedrahita et al., 2018, Lertzman-Lepofsky et al., 2020), which is known to influence the rate of water evaporation (Maaloum et al., 1998; Maruyama and Hasegawa, 2020) and, consequently, the estimation of r_b. In the present paper, we tested the use of agar at different concentrations as a material capable of mimicking the evaporative properties of an amphibian as set exclusively by the establishment of a boundary layer (i.e. r_s=0; r_t=r_b). Accordingly, we measured the rate of EWL and estimated the respective resistance from bodies of the same size and shape of (i) standing pure (distilled) water, (ii) a sodium chloride physiological solution mimicking the osmotic properties of generalized amphibian body fluids (see Table S1), and (iii) jellified agar prepared at different concentrations using either water or the sodium chloride physiological solution as diluent. With this, we were able to assess the competence of the agar method as a non-resistance biophysical model for amphibian skin evaporation.

We measured EWL rates from eight different groups (N=10 per group), composed of distilled water, a 230 mOsm kg⁻¹ NaCl physiological solution and jellified agar prepared at concentrations of 1%, 3% and 5% using either distilled water or 230 mOsm kg⁻¹ NaCl solution as diluent. To obtain agar models of different concentrations, we weighed commercially available agar-agar powder (>99% purity) using a high precision scale (model AR2140, Ohaus Adventurer, accuracy of 0.0001 g) and prepared solutions in distilled water or NaCl physiological solution at 100°C. Then, we allowed the obtained agar solutions to cool down and gellify at a constant air temperature of 25°C (0.2°C accuracy) inside a BOD climatic chamber (EL101/2RS, Electrolab, São Paulo, Brazil) for ∼90 min. We prepared the physiological solution by the stepwise dilution of NaCl in distilled water until its osmolality reached the desired level of 230 mOsm kg⁻¹, which was verified with a freezing-point depression osmometer (Semi-Micro osmometer K-7400, Knauer, Germany) previously calibrated against a standard solution (Knauer, Y1241; 400 mOsm kg⁻¹) and distilled water.

In all cases, we poured the different solutions into glass Petri dishes (hereafter referred to as our biophysical models) of 90 mm diameter and 15 mm depth until they were filled with 50 ml of the corresponding solution (4 mm less than their maximum height capacity). We estimated the surface area exposed to evaporation (πr²) to be 63.62 cm². We performed all EWL measurements with the solutions and gels contained in these dishes for the sake of standardization and improved accuracy in the estimation of the exposed surface area, thus eliminating this potential error source. In all cases, we prepared the solutions and gels immediately before EWL measurements.

An open flow-through system was ventilated with dry air drawn from two silica-drying columns and was pumped into the inlet port of an acrylic chamber at a rate of 1300 ml min⁻¹ set by an airflow controlling unit (SS-4 Subsampler, Sable Systems). Air temperature (25°C; 0.2°C accuracy) was maintained constant with a BOD-type climatic chamber (EL101/2RS, Electrolab). Changes in air relative humidity (RH) values (%) were continuously monitored by a RH analyzer (RH-300, Sable Systems) connected to the excurrent port of the acrylic chamber. The output of the RH analyzer was fed to a data acquisition system (UI-2 A/D converter, Sable Systems) that allowed for the instantaneous monitoring of RH changes.

Before measurements, dishes containing solutions and gels were maintained inside the climatic chamber at 25°C for a 90 min period to allow for thermal equilibrium. During this period, they remained covered with a plastic film wrap to prevent moisture loss. For EWL determination, dishes were put individually inside an acrylic measurement chamber (1 liter volume) and carefully positioned in the center of the chamber floor. Special care was taken while handling the dishes containing water and NaCl solution to avoid spills. Experiments were terminated after the acquisition of a 15 min period of steady-state readings, which usually happened <100 min from the beginning of the experiments. Immediately after halting the experiment, we opened the chamber and recorded the surface temperature of the dish models with a high-resolution (640×480 pixels) infrared thermal camera (ThermaCAM SC640, FLIR Systems). This non-contact temperature-measuring technique has proved to be highly accurate in measuring surface temperatures of evaporating pure and saline solutions (e.g. Nachshon et al., 2011; Shahraeeni and Or, 2011) and also agar surfaces (Martynenko and Misra, 2021). The thermal camera was mounted on a tripod 20 cm above models and remained inside the BOD chamber to reach steady-state thermal equilibrium (James and Sirault, 2012). A transparent PVC strip curtain mounted at the entrance of the climatic chamber prevented sudden changes of temperature and humidity during thermal image acquisition, which usually happened within 30 s of the opening of the measurement chamber.

EWL rates were calculated from the enrichment of water vapor in the airflow streaming through the chamber containing the biophysical models. Baseline RH values were obtained from the average of trials taken for an empty chamber immediately before and after the biophysical model measurement. Baseline and biophysical model RH values (%) were first converted into water vapor density (WVD) values (g m⁻³) based on standard mathematical formulations and experimental air temperature. For simplicity, we used the online calculator available from HyperPhysics (http://hyperphysics.phy-astr.gsu.edu/; hosted by the Department of Physics and Astronomy, Georgia State University). Thereafter, absolute EWL (μg H₂O s⁻¹) was determined by using the equation: EWL=(VD_e−VD_i)F, where VD_e and VD_i are the WVD of the excurrent and incurrent air from/to the solution chamber, respectively, and F is the airflow rate (cm³ s⁻¹) (Withers et al., 1982). We calculated the area-specific EWL rate (μg H₂O cm⁻² s⁻¹) by dividing the absolute EWL by the evaporating surface area of the biophysical models. Resistance to water evaporation was determined following the original formulation in Spotila and Berman (1976): Resistance=VDD/EWL, where VDD is the water vapor density gradient (μg cm⁻³) between the saturated WVD at the evaporating surface temperature and the partial WVD of air temperature, and EWL is the area-specific EWL. Surface temperature of the evaporative solutions and gels was determined from the infrared thermal images taken at the end of each trial (see details below).

Before measurements, we supplied the thermal camera with initial parameters of emissivity, air and background temperatures, and distance from the object. We assumed an emissivity of 0.96 for the distilled water and NaCl solutions, and 0.97 for agar gels (Kinoshita and Yoshida, 2017). As water vapor can interfere with thermal imaging, we applied a post-measurement correction by using a subroutine on the ThermaCAM Researcher Pro 2.9 software to match each image to the exact RH conditions prevalent inside the climatic chamber at the moment of image acquisition. With this aim, RH inside the climatic chamber was continuously monitored with a psychrometer device (PCE-320, PCE Instruments, accuracy 0.1%). For each image, we estimated the average surface temperature by manually tracing a polygonal shape covering the entire surface area of the solution (limited by the Petri dish), and then we extracted the average temperature of all pixels within the selected area. Image processing was performed by using the ‘ThermStats’ R-package (Senior et al., 2019) that contains routines for converting thermal images into raw data with pixel values corresponding to surface temperatures.

We performed one-way analysis of variance (one-way ANOVA) to evaluate differences in EWL rates and mean r_t among treatments. We also tested the overall effect of osmotic potential (i.e. water versus physiological solution as diluent in the preparation of the agar gels) on EWL and r_t using one-way ANOVA. Whenever significant differences were found, we followed each ANOVA with post hoc Tukey's test comparisons to identify significant differences between pairs of measurements. Before the analyses, we confirmed assumptions of normality and homoscedasticity for all our models with a Shapiro–Wilk test, a Levene's test and visual examination of model residuals. All analyses (including the infrared thermal processing) were performed in R (v3.3.6; http://www.R-project.org/) employing RStudio (v1.2.5033; http://www.rstudio.com/) with the ‘car’ and ‘emmeans’ packages for statistical analysis, and ‘tidyverse’ packages for graphical purposes. In all cases, a significance level of P<0.05 was used. Unless otherwise stated, all values are presented as means±s.e.m.

We found that the rate of EWL varied among the different treatments (F_7,72=16.01, P≤0.001) along with the total resistance (r_t) to EWL (F_7,72=30.42, P≤0.001). In general, as agar concentration increased, the rate of EWL gradually decreased while the corresponding values of resistance increased regardless of the use of water or physiological solution as diluent (Fig. 1, Table 1). However, agar gels prepared with physiological solution exhibited significantly lower EWL rates (F_5,54=14.04, P≤0.001) and higher r_t values (F_5,54=21.4, P≤0.001) relative to agars made with distilled water (Fig. 1, Table 1). EWL variation due to changes in agar concentration includes the effect of structural changes in the formation of the jellified matrix. This factor is known to affect water vapor pressure via chemical interactions (Wiggins, 1990; Aşkin and Yilmaz, 2004; Davies et al., 2010) and by affecting the complex porous matrix of fibers of the agar gels (Davies et al., 2010). Indeed, the pore size of the jellified agar model through which water moves is determined by agar content (Pernodet et al., 1997; Maaloum et al., 1998). In this way, agar solutions of low concentrations have larger interstitial spaces that offer lower physical interference (low flow resistance) on water movement (Davies et al., 2010), thus facilitating the evaporative water efflux. On top of these effects, the use of the physiological solution in the preparation of the agar gels added an extra osmotic restraint to water evaporation. This effect was entirely additive, being practically unchanged across all treatments (Table 1). Therefore, our results are in agreement with the rationale that agar content and the osmotic property of its diluent affect the rate of water loss and thus the estimation of resistance to EWL in biophysical agar models from amphibians.

We found that EWL rates of agar models do not equate to the EWL rates of a ‘free water surface’. However, this finding does not constitute a drawback of the agar method in the estimation of r_s, as the application of the method demands an accurate model of zero integumental resistance for the animal being examined and not for pure water. Indeed, amphibian body fluids are not composed of pure water; instead, and as a result of the presence of dissolved solutes, an ideal r_b-only evaporative model should match the osmotic properties of the body fluids of the animal it intends to emulate. In this regard, our results indicate that the 5% jellified agar and agars at 1% and 3% prepared with physiological solution matched both the EWL rates and r_t values obtained for a physiological solution mimicking the osmotic properties of a generalized amphibian (Table S1). Therefore, the adoption of any of these options can yield appropriate estimates of amphibian skin null-resistance models to evaporation. However, as the preparation of agar gels using physiological solution requires an extra step and because a denser agar offers a mechanically more stable model (less flimsy), for practical reasons, we advocate the adoption of the 5% agar concentration for animal model manufacture during the application of the agar method.

The variability in r_b among the different agar concentrations prepared with distilled water and with physiological solution ranged between 0.02 and 0.5 s cm⁻¹, which may sound negligible (see Table S2). This error, however, computes into the calculation of r_s, and the magnitude of the bias it introduces will depend on the value of r_t. For instance, we ran a series of simulations over a range of hypothetical r_s values typically expected for amphibians (1–10 s cm⁻¹; Table S3) (R code and details used to perform this simulation are available from Zenodo, https://doi.org/10.5281/zenodo.6550910) to determine the potential error in r_s calculation associated with differences in r_b due to variation in agar concentration. Although this approach simplifies some of the critical attributes of animal-like models (e.g. body size, shape and complex surface-to-volume relationships), our analysis shows that, as expected, the proportional error in r_s estimation increases with the decrease in r_s and with the dilution of the agar content (Fig. 2A) or the addition of physiological solution (Fig. 2B). Indeed, while the proportional error in r_s estimation was kept under 10% for r_s values greater than 5 s cm⁻¹, this error almost doubled as agar content was diluted from 3% to 1%, leading to a maximum 30% overestimation for r_s values equaling 1 s cm⁻¹ with 1% agar concentration. In contrast, the proportional error in agars prepared with physiological solution increased with the increase in agar content, which led to an underestimation of r_s by about 20% for r_s values equaling 1 s cm⁻¹ with 5% agar concentration. Therefore, although the error in r_s estimation due to bias in r_b associated with agar concentration might be relatively low and possibly negligible for animals with high skin resistance to evaporation, this effect rapidly scaled up with the decrease in skin resistance and/or variation in agar content. Our analysis unequivocally indicates the relevance of considering agar concentration as an important factor in the application of the agar method.

Other factors besides agar content can interfere with an accurate estimation of r_b. For example, the molding of the agar jelly into the shape of the amphibian (see Christian et al., 2017; Riddell and Sears, 2017), especially for small bodied species, the correct positioning of the model to mimic the posture of a live animal during the EWL measurement (Pough et al., 1983), and the effect of animal activity (Wygoda, 1984), are particularly challenging steps of the method, which may introduce certain levels of inaccuracy. If that happens, the error will then cascade into unreliable estimates of surface area, EWL rate per unit of surface area and, ultimately, the calculation of r_b. The impact of these and other empirical error sources on the accuracy of r_s estimation in amphibians remains to be verified but, broadly taken, it may explain the occasional encounter of negative values of r_s (see Young et al., 2005; Riddell et al., 2017; L.M.S., R.P.B. and D.V.A., personal observation). Indeed, even though negative r_s values are biologically non-sensical as it would imply that the agar model lacking a skin barrier loses water at a lower rate than an animal that does have such a barrier, the accumulation of even small imprecisions during the empirical measurement of the many parameters required for r_s calculation may scale up to the point of yielding negative r_s values. Although the use of the more concentrated 5% agar models herein proposed bears the potential to increase the likelihood of obtaining negative r_s values (particularly for low skin resistance species), we are confident that this risk does not invalidate the arguments supporting our recommendation and, hopefully, will not discourage its adoption.

In conclusion, our results clearly demonstrate the competency of the agar material at 5% concentration for building biophysical models to simulate the evaporative properties of amphibians in the absence of an integumental barrier (i.e. r_s=0) and, therefore, allowing the empirical estimation of r_b. We also found that agar gels at concentrations of 1% and 3% prepared with a 230 mOsm kg⁻¹ physiological solution were equally adequate (although less practical) for the same purpose.

Parts of this paper were greatly improved by discussions held with Jean François Le Galliard and by the comments of two anonymous reviewers.