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.
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).
Table 2.
Performance metrics for surveyed models. Rank is the model rank based on MSE and shown only for validation metrics obtained using repeated K-fold cross validation. # Var is the number of final predictor variables. AICc is the Akaike Information Criterion corrected for small sample size for likelihood models. MSE is the mean square error. MAE is the mean absolute error. r2 is the coefficient of determination. SD is the standard deviation. r2 is not implemented for model 7. Model 8 lacks standard deviation estimates because metrics are based on a single testing set of N = 12. The theoretical best model has a high r2, low errors (MAE or MSE), and a low AICc.
Fig 2.
Plot of performance metrics for surveyed models.
Models are as in Table 1 and the main text. Models 1–6 are likelihood models and models 6–8 are machine learning models. MAE is the mean absolute error and MSE is the mean square error. Error bars indicate ∓ 1 standard deviation of the mean. r2 is not implemented for model 7. Model 8 lacks error bars because metrics are based on a single testing set of N = 12. The theoretical best model has a high r2 and low errors (MAE or MSE).
Fig 3.
Actual versus predicted plots for select models.
These models compare measured and predicted values of dry body mass and include the wet body mass model (1), the best likelihood model (5), an adaptive lasso model (7B), and a neural network model (8). Each point is an individual tadpole. Val. MSE is the validation mean square error and Val. MPE is the validation mean percentage error. Test. MSE and Test. MPE are the mean square error and mean percentage error for the testing set of model 8. The solid line is the 1:1 line. The theoretical best model has low errors (MSE, MPE).
Fig 4.
Level plot of hyperparameter search results for neural network (model 8).
Layers is the number of neural layers, density is the number of neurons per layer, and MSE is the (validation) mean square error. Contour lines generally correspond to the discrete differences in MSE shown in the legend. The network with the lowest validation error had 11 layers and 1900 neurons.