“Biophysical modeling of water economy can explain geographic gradient of body size in anurans”

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Sidney F. Gouveia, Rafael P. Bovo, Juan G. Rubalcaba, Fernando Rodrigues Da Silva, Natan M. Maciel, Denis V. Andrade, and Pablo Ariel Martinez (Jan 2019)

The DOI will be https://dx.doi.org/10.1086/700833

Gradients of body size in anurans are only a part of a ‘water-economy story’, biophysical model says

A combination of current body size and resistance to dehydration may determine whether frogs will vary geographically in size or not

Lesser Treefrog (Dendropsophus minutus). This half-gram frog species is found in open habitats throughout South America. Populations of this species in more desiccating environments tend to attain larger body size as a means to reduce water loss through evaporation.
(Credit: Fernando Rodrigues Da Silva)

In the mid-19th century, the German physiologist Karl Bergmann found that warm-blooded animals (birds and mammals) from cold regions should be, on average, larger than their close relatives from tropical regions because being bigger enhances the conservation of body heat. Since then, ecologists and biogeographers have struggled to understand whether such a pattern would ever hold for cold-blooded animals (such as invertebrates, frogs and lizards) and, if so, whether the mechanism proposed by Bergmann would also fit. Recent studies have shown that, for frogs, what matters is the economy of water, and the existence of a variation in size takes place across a gradient of dehydration, not of temperature.

Here, by combining mathematical equations of the frogs’ biophysics, physiological experiments, and data from museum collections, a team of researchers from Brazil and Spain has taken a step further in cracking this riddle of geographic gradients of body size among frogs. They have demonstrated that not only is the need to conserve water the main cause of the variation of body size among these animals, but also that this pattern only emerges depending on the combination of current size and the total resistance of the frogs. Total resistance is mainly determined by the skin’s resistance to dehydration. Small and skin-resistant species are more prone to vary geographically in size in response to environmental dryness. Furthermore, their study hints at the existence of a gradient in resistance to dehydration, a pattern never tested or postulated before. In addition to casting light on a much-debated topic in ecology, these findings help to understand the consequences of climate change, which should alter the spatial patterns of aridity, thus imposing different consequences on frogs according to their features related to economy of water.


Geographical gradients of body size express climate-driven constraints on animals, but whether they exist and what causes them in ectotherms remains contentious. For amphibians, the water conservation hypothesis posits that larger bodies reduce evaporative water loss (EWL) along dehydrating gradients. To address this hypothesis mechanistically, we build upon well-established biophysical equations of water exchange in anurans to propose a state-transition model that predicts an increase of either body size or resistance to EWL as alternative specialization along dehydrating gradients. The model predicts that species whose water economy is more sensitive to variation in body size than to variation in resistance to EWL should increase in size in response to increasing potential evapotranspiration (PET). To evaluate the model predictions, we combine physiological measurements of resistance to EWL with geographic data of body size for four different anuran species. Only one species, Dendropsophus minutus, was predicted to exhibit a positive body size–PET relationship. Results were as predicted for all cases, with one species – Boana faber – showing a negative relationship. Based on a mathematical model verified empirically, we show that clines of body size among anurans depend on the current values of those traits and emerge as an advantage for water conservation. Our model offers a compelling mechanistic explanation for the cause and the variation of gradients of body size in anurans.

Modelagem biofísica de economia de água pode predizer gradiente geográfico de tamanho corporal em anuros

Gradientes geográficos no tamanho corporal expressam restrições climáticas sobre os animais, mas a existência e a causa dessas restrições permanecem controversas para ectotérmicos. Quando aplicada aos anfíbios, a hipótese da conservação de água postula que quanto maior o tamanho corporal, menor é a perda de água evaporativa (EWL) ao longo de gradientes de desidratação. Para abordar essa hipótese mecanisticamente, utilizamos equações biofísicas bem estabelecidas de trocas de água em anuros e propomos um modelo de transição de estados que prediz um aumento no tamanho corporal ou na resistência à EWL como especializações alternativas ao longo de gradientes de desidratação. O modelo prediz que as espécies para as quais a economia de água é mais sensível à variação no tamanho corporal do que à variação na resistência a EWL deve aumentar em tamanho em resposta a um aumento na evapotranspiração potencial (PET). Para avaliar as predições do modelo, combinamos medidas fisiológicas de resistência à EWL com dados geográficos de tamanho corporal para quatro espécies de anuros. Esperava-se que apenas uma espécie, Dendropsophus minutus, exibiria uma relação positiva entre tamanho corporal e PET. Os resultados foram como preditos para todos os casos, com uma espécie – Boana faber – mostrando uma relação negativa. Baseado em um modelo matemático verificado empiricamente, mostramos que gradientes de tamanho corporal em anuros dependem da combinação de tamanho corporal e resistência e emergem como uma vantagem para conservação de água. Nosso modelo fornece uma explicação mecanística convincente para a causa e a variação de gradientes de tamanho corporal em anuros.