Animals and housing

This study was completed in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health. The protocol was approved by Stanford University under the Administrative Panel on Laboratory Animal Care (APLAC, Protocol #33097). All efforts were made to minimize suffering. Xenopus laevis tadpoles of Gosner stages 44–54 (N = 61; Xenopus 1, Corp (Dexter, Michigan, USA)) were placed into aquaria (18.09 cm L x 11.13 cm W x 13.34 cm H). The tank included 0.1X Marc’s modified Ringer’s solution (MMR) to avoid osmotic stress [80], shelter made of PVC pipe, and an air pump with a bubbling stone to aerate the water tank. Tanks were maintained at 25℃ and 50% water changes (0.1X MMR) were performed every 2 days and as needed. Tadpoles were fed crushed tadpole food pellets (Josh’s Frogs, Owosso, Michigan, USA) three times per week. Animals were isolated for 24 hours without food prior to imaging and weighing to allow time for defecation and to avoid confounding our estimates of wet and dry body mass with food mass.

Imaging and data collection

Tadpole embedding, imaging, and measurement methods are available in the S1 Protocol and at protocols.io: dx.doi.org/10.17504/protocols.io.rm7vzk1wrvx1/v1 [81]. Briefly, each tadpole was anesthetized in a container with 10 mL of 0.03% buffered MS-222 for roughly 1 min [82]. We lightly brushed the tadpole’s body with a paint brush to confirm successful anesthesia by observing complete lack of movement. Next, we filled a chambered coverglass (5 cm L x 2 cm W x 1 cm H; Thermo Scientific, Waltham, Massachusetts, USA) halfway with fluid low-melting point 1.5% agarose. This agarose melts at 42℃, however, in practice, the agarose solution cooled rather quickly after we removed it from heat. We placed the tadpole into this chamber and positioned its body parallel to the length of the coverglass, but closer to one corner of the coverglass to improve the quality of the photographs and measurements. Placing the tadpole medially and parallel to the length of the coverglass resulted in poor quality photographs and decreased measurement accuracy during preliminary trials. After confirming optimal body positioning, we added 2–3 drops of MS-222 with a plastic transfer pipette to ensure anesthesia throughout the entire imaging process and then filled the chambered coverglass containing the tadpole with melted agarose. Ad hoc addition of MS-222 was necessary (e.g., if the tadpole twitched) to guarantee the efficacy of the procedure for all tadpoles. Each tadpole was embedded in the agarose for no more than five minutes.

Embedding tadpoles in the chambered coverglass allowed imaging of the whole tadpole from all three dimensions (dorsal, lateral, and frontal). Images were taken using a Leica Si9 microscope at a magnification of 0.6x and 1x. The pictures were taken using the default settings in the LAS EZ v. 3.4.0 (Leica Microsystems, Wetzlar, Germany). We included 1 mm grid paper placed in the same horizontal plane as the tadpole in every image to convert pixels to real distances. After imaging, we removed the tadpoles from the agarose media by gently breaking apart the agarose using a paint brush and then placed them into conditioned (isotonic) DI water to remove any agarose clinging onto the body. Once clean, we transferred the tadpoles into a petri dish to remove excess water and obtained the wet mass on an analytical scale (Model PMF523/E, Fisher Scientific, Pittsburgh, United States). This scale was used for all mass measurements.

We euthanized the tadpoles by applying 20% benzocaine gel to the body and confirming the animal was unresponsive prior to flash freezing in liquid nitrogen. Briefly, a small petri dish was placed in a container filled with liquid nitrogen until equilibrium was reached. The petri dish was then moved to an insulated container and filled with liquid nitrogen. Then, we placed the tadpole into the liquid nitrogen and covered the petri dish with a lid to guarantee euthanasia. The insulated container was filled with liquid nitrogen until the petri dish was halfway immersed and then covered with a lid to minimize heat transfer. We weighed the tadpoles on a pre-weighed glass slide 15 minutes after flash freezing. Next, we placed the glass slide with the tadpole in a separate petri dish and moved it to a drying oven set at 37℃ and left to dry for a minimum of 72 hours. A preliminary study showed tadpoles completely dried after only 48 hours and the mass did not decrease after 1 week. The dry mass was obtained by subtracting the weight of the glass slide from the final weight of the dried tadpole on the glass slide.

We obtained a total of 27 measures from each tadpole image using Fiji v. 1.54f [83]. Fifteen were linear measurements (Table 1, Fig 1, S1 Fig) including (1) the dorsal length, width, and area for the body and the tail, (2) the lateral body height, tail length and height, and the body, tail, tail muscle, and limb bud areas, and (3) the frontal body width and area. We also obtained 12 additional (composite) variables, including tail muscle area, tail volume, body volume estimated in different ways (Table 1), and the wet and dry body masses of each tadpole.

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Table 1. Initial input variables used in all models. M is model (see Data analysis in Methods). View is the 3-dimensional origin of each trait. NA is not available, L is lateral, D is dorsal, F is frontal, and Composite is traits obtained from two views. T is tail, Tm is tail muscle, B is body, A is area, L is length, W is width, and H is height. 1 and 2 indicate traits included in the initial and final fits for each model (M1–8), respectively.

https://doi.org/10.1371/journal.pone.0345767.t001

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Fig 1. Tadpoles embedded in agarose media and anatomical traits measured.

(A) Dorsal measurements obtained in this study (see Table 1). (B) Lateral measurements obtained in this study (see Table 1). BL is body length, BW is body width, BL is body height, BA is body area, TL is tail length, TW is tail width, TH is tail height, TA is tail area, TmA is tail muscle area, and LBA is limb bud area. Images C, D are composite images obtained by stitching individual images (see Methods and Materials).

https://doi.org/10.1371/journal.pone.0345767.g001

Data analysis

We compared the performance of eight models to test our predictions that morphology, namely body volumes, are reliable estimators of dry body mass. The eight models included those of wet body mass (model 1), length measurements (model 2), surface areas (model 3), volumes estimated in two different ways (models 4–5), and all data (models 6–8). The first five models were ordinary least squares (OLS) regression models optimized using least squares in a maximum likelihood framework. Models 6–8 were machine learning models including one random forest, two adaptive lasso, and one neural network. Briefly, random forest models are optimized by averaging across many decision trees, which each use a subset of the data and input variables for prediction [84]. The first lasso model sparsely optimized the mean square error while the second gave the sparsest model within one standard error of the minimum loss, e.g., the mean square error [85]. We included machine learning models since each has beneficial properties that may outperform likelihood-based models. For example, random forest models allow for the modeling of potential non-linearities, the adaptive lasso optimizes prediction ability while reducing the number of necessary input variables and exhibits the oracle property [85], neural networks can model all possible interactions in a dataset, and all can perform automatic feature selection (taking multicollinearity into account). We used variance inflation factors (VIF) and a cutoff of VIF = 10 to remove collinear terms from each likelihood model [86]. For example, we obtained estimates of body width from both dorsal and lateral views but either may serve as an optimal predictor of dry mass. We show the initial and final variables for each model in Table 1. We natural log-transformed all data except limb bud area which we square root transformed since some tadpoles did not have limb buds. All reported statistical tests used an alpha of 0.05. Finally, we evaluated prediction ability in each model after confirming that each model exhibited appropriate model diagnostics.

We used repeated K-fold cross-validation to evaluate model performance as determined primarily by the mean square error and its standard deviation. We also measured the mean absolute error, r², and their standard deviations. Briefly, repeated K-fold cross validation is an extension of cross-validation where cross-validation is repeated many times using K data (training/validation) splits to obtain average performance metrics across repeats [87,88]. Additionally, cross-validation is a standard two-step procedure used to determine the generalizability of predictive models. The first step is to fit the model to a subset of the data (the training set) to obtain parameter estimates. The second step assesses the generalizability of the model by using the parameter estimates to obtain model performance metrics on unseen data (the validation set). Specifically, we used 200 repeats of 5-fold cross-validation to guarantee each randomly sampled validation set contained at least 10 samples (N = 61 samples / 5 folds = 12.2 samples per validation set) and to estimate error for each prediction metric using at least 1,000 (200 x 5) validation sets. We implemented this procedure for models 1–6 using the caret package v. 6.0-94 in R v. 4.4.1 [87,89]. To obtain comparable metrics for the adaptive lasso, we back-calculated the population mean and standard deviations for all performance metrics across 200 samples of (non-repeated) 5-fold cross-validation using the R package glmnet 4.1-8 [90,91]. We were not able to obtain estimates for the r² of the adaptive lasso since this is not currently implemented in glmnet 4.1-8. Next, we describe how we fitted the neural network model and obtained its performance metrics.

We implemented a feed-forward neural network using keras3 v. 1.2.0 and tensorflow v. 2.16.0 in R [92,93]. In general, a neural network is a network-based machine learning technique that explores network parameters with the goal of minimizing a loss (error) function. Neural networks include two hyperparameters that help define the network and its complexity; the neural layers define the depth of the network while the neurons per layer (neural density) control the number of attempted linear transformations per layer. Here, the linear transformations refer to the weight and bias parameters, similar to a slope and intercept. While data are linearly transformed many times within the neural network, a single parameterized neural network produces a single set of predictions (like regression). Fitting a neural network involves iteratively finding the weights and biases at each neuron that minimize the loss function. This is accomplished by using a training set to sample network parameters (the weights and biases at each neuron), a validation set to tune hyperparameters (where model performance is evaluated after each iteration), and the testing set to give an unbiased estimate of out-of-sample model performance (generalizability) using unseen data.

We used a cross-validation approach for fitting and evaluating neural networks across a range of chosen hyperparameters (neural layers and number of neurons per layer). Prior to fitting the model, we split the data into 60-20-20% training, validation, and testing sets to guarantee the model validation and testing steps were performed on at least 12 samples and the model was trained using at least 30 (N = 36) samples. We selected hyperparameters by determining the hyperparameter combination that resulted in the lowest validation error (mean square error). Here, we define validation error as the median of 3 replicate model fits for each hyperparameter combination. This is necessary to reduce sampling error since fitting neural networks includes a stochastic component that affects model performance. The hyperparameters we varied included the number of neural layers from 0 to 25 (by one) and the number of neurons per layer from 200 to 2,500 (by 100), each using a learning rate of 0.001 across 200 epochs. We selected this arbitrarily broad range after determining the standard suggestions of 1–3 layers and neurons per layer of 0.5X, 1X, and 2X the sample size did not yield usable results, but we still included these in the hyperparameter search [94–96]. We also applied a stop rule to end sampling if the validation error (mean square error) did not decrease after 50 epochs to protect against oversampling local minima across the search space and decrease computation time. We obtained the final out-of-sample performance metrics (mean square error, mean absolute error, and r²) using the testing set. All sampled networks contained a normalizing layer (to improve model quality and reduce computation time), used Rectified Linear Unit (ReLU) activation for signal propagation (to avoid vanishing gradients), and used an Adam optimizer for automatic tuning of the learning rate [97,98].

Comparison of models for estimating dry mass

We found several viable modeling alternatives for predicting dry mass. Most models exhibited similar variances with small differences in mean validation metrics (Table 2). While using volumes in model 5 improved our estimates compared to all other likelihood models, some of these models may still be of practical use to many readers. For example, although using wet body mass (model 1) underperformed relative to body volumes (model 5), wet body mass was still a significant predictor of dry body mass. Measuring wet body mass is relatively simple and this simple approach may be suitable for many studies despite a difference in the mean percentage error of 8.66% relative to model 5. Models 2–4 provide intermediate and viable alternatives for obtaining estimates of dry body mass and only require users to obtain four to six independent measurements. To obtain accurate estimates of dry body mass using likelihood models, we recommend using model 5, which includes six measurements: the lateral body height, dorsal body length, dorsal body width, lateral tail height, dorsal tail length, and the dorsal tail width.

We used machine learning models to provide additional alternatives, including the adaptive lasso and neural network models. The adaptive lasso models (7) should be used with caution since they reach a high level of prediction accuracy at the cost of outputting slightly biased estimates. This makes the lasso models appropriate for determining the magnitude of group effects and covariances, but not for accurately estimating or interpreting individual dry body mass. The neural network model (8) exhibited good quantitative performance, but it may not be ideal for many situations and comes with many drawbacks. First, we do not have an ideal way of performing model comparisons among neural networks and other model classes because the validation metrics are based on a single testing set and not cross-validation. While methods such as stratified K-fold cross validation [99] are available for neural networks, this would still require performing a computationally expensive hyperparameter search for each testing set. An alternative that would enable direct comparisons to other models would be to define one or many testing sets for all models at the cost of reducing the sample size of the testing and validation sets for other models. A second drawback to using model 8 for predicting dry mass is that it exhibits the undesirable behavior of predicting the same value for some of the largest tadpoles and this can be seen as a vertical ridge in Fig 3, which can impact downstream applications and interpretability. Third, the neural network model comes with the significant drawback of requiring all of the variables in Table 1 for predictions. As discussed, machine learning models can provide many advantages, given that we understand the properties of the implemented model.

Future modeling improvements

There are many practical alternatives for data collection and potential future improvements to the presented models. For example, in this study we used agarose media to embed tadpoles in chambered coverglasses but a potentially viable alternative is taking morphological measurements using optical micrometers and measuring tadpoles in chilled water to minimize movement but allow respiration and minimize stress. If users wish to implement end-point euthanasia, measurements may also be taken using photogrammetry [100,101], which may allow for more accurate estimation of body volume. Future improvements to our models include increasing the sample sizes to allow for larger training, validation, and testing sets. Furthermore, robust linear models [102,103] might offer solutions for potential heteroscedasticity issues with predictions made from model 8. We also encourage empirically validating predictions or even comparing predictions among models 1–8 to determine whether the data qualities suit the needs of downstream analyses. In downstream analyses where dry body mass is used as an independent variable, users may set weights or use measurement error models [104,105] where the weights or errors are proportional to the mean absolute error (log scale) or the mean percentage error (raw scale) reported for each model. Future users of these techniques should carefully consider whether the errors associated with each model presented here are compatible with their study design, given the effect sizes they are trying to detect. Specifically, the high r² (0.75–0.77) for the best models presented here should not be interpreted in isolation outside the context of potential errors in the models. Other future directions include improving our knowledge of tissue densities and we discuss these next.

Detailed knowledge of tissue densities and how they change over time would greatly improve predictions of dry body mass [48]. This is because body proportions and estimated body volumes are related to body mass through density. Our approach in this study was to assume constant tissue density throughout the body but we relaxed this assumption by modeling some body parts independently of each other. However, the body is made of tissues of varying densities and water content including fat, muscle, cartilage, and bone [106–108]. Therefore, if we knew the average tissue densities or water content in different body regions, we could more accurately model the relationship between body volumes and wet or dry body mass. These relationships are further complicated by development, since changes in the volumes or densities of particular tissues in amphibians, like cartilage and bone [73], will affect the average tissue density or water content across body regions. For example, developmental changes in the relative proportion of bone and brain tissue in amphibians will change the average tissue density in the skull, in turn changing the relationship between skull volume and skull mass. This means the growth and development of tissues with different densities can alter the relationships between body proportions, volumes, densities, masses, and consequently, physiological rates. Notably, the relationship between metabolic rates and masses in mammals can vary across different tissues and this is likely due to differences in fat content or density [109,110]. Future research using micro-CT or similar methods would allow us to estimate the volumes of various tissues with distinct densities [111,112]. In summary, understanding the density of structures throughout the body and how they change through time is an important area of future research.

The application and future directions of this research should help to advance our understanding of biological processes. We recognize three key areas including identifying the sources of natural variation in physiological rates, the mechanisms underlying growth and metabolism, and the mechanisms linking populations with macroecological and macroevolutionary patterns. In the context of physiological ecology, learning how body mass channels physiological rates (potentially through environmental or biotic covariates) is a question of rich history and open inquiry, with metabolic rates perhaps among the most studied type of physiological rate across taxa [5,15,16,19,34,113,114]. We are still learning how rates might scale up to whole organisms and empirical research often struggles with high degrees of intraspecific variability [16,31,34,115]. Since physiological rates, including metabolic and growth rates, are often correlated with body size or are standardized using body size, understanding how mass indices, including dry mass, vary within and among tissue types, individuals, and species is necessary for deeper knowledge of the anatomical and physiological mechanisms that determine physiological rates. Importantly, recently developed methods allow the integration of intraspecific and interspecific data in a phylogenetic context [116] and the integration of intraspecific and interspecific data in combination with different body mass indices seems crucial in elucidating the mechanisms underlying growth and metabolic scaling. This is because each body mass index makes different assumptions about how body size and different tissues relate to metabolism through mass, density, and metabolic activity. For example, use of dry body mass in such models measures body size independently of water which does not metabolize. Outside the relatively limited context of physiological ecology, learning how physiological rates are regulated through biotic covariates like behavior seems a worthwhile endeavor for gaining an integrative understanding of the behavioral mechanisms that underlie physiological rates. Some examples include learning how metabolic rates, body temperature, and growth rates change due to environmental temperature and at different levels of parental resource provisioning, abilities to thermoregulate, or other behavioral events like hibernation [36,37,117–119]. Furthermore, with continued development of the described methods and sampling of adult amphibians and other vertebrates, we expect knowledge of dry body mass in combination with physiological rates and longitudinal models to yield new insights into the individual-level drivers of macroecological and macroevolutionary patterns, such as patterns of biogeography, ecogeographical gradients, and evolutionary trade-offs [15,31,120,121]. Finally, this research has potential applications for understanding the biology of aging, gestation, obesity, or sleep and how body mass and metabolic rate are related to various disorders and health outcomes in amphibians and other animals [25,33,122,123].