Plant leaf shape is highly variable. The beauty of leaves can be purely aesthetic, but also derives from the mystery of adaptive significance. This mystery is especially compelling for species with strongly varying leaf shape on a single tree. The desert poplar (Populus euphratica Oliv.) is an ancient and protected species, and forms riparian forests in deserts of mid and west Asia, north Africa and southern Europe. More than half of all desert poplar forest is found along the Tarim River within the Taklamakan, a desert in northwest China. The Taklamakan is in the rain shadow of the Himalayas and the world’s second largest shifting sand desert. There, forest extent has been greatly reduced, mostly due to flow diversion for agriculture, but many old trees persist. The tree in the picture is the oldest recorded living desert poplar. The innermost ring in a core dates back to 1709 or earlier. The leaves on this tree vary widely in shape, from smooth to dentate, from narrow to broad, and from linear to lanceolate to ovate. Drought is a dominant stressor in this hyperarid environment with highly variable temperature and soil salinity. Leaf shape may relate to tradeoffs among water conservation, thermoregulation and growth rate. Is this extremely wide variation in leaf shape on a single tree an adaptation to the large temporal fluctuations in the environment? Alternatively, could leaf polymorphism be a neutral and thus non-adaptive consequence of variable gene expressions related to developmental stages. Answers to these questions can enrich the ecological and evolutionary understanding of trees and ecological drought.