Unlike mammals, fish continue to grow throughout their lives, to increase the size of their eyes and brain, and to add new neurons to both. As a result of visual system growth, the ability to detect small objects increases with the age and size of the fish. In addition to the birth of new retinal ganglion cells (RGCs), existing cells increase the size of their dendritic arbors with retinal growth. We have used this system to learn design principles a vertebrate retina uses to construct its neural circuits, and find that the size of RGC arbors changes with retina and eye size according to a power law with an exponent close to 1/2. This power law is expected if the retina uses a strategy that, independent of eye size, simultaneously optimizes both the accuracy with which each RGC represents light intensity and the image spatial resolution provided to the fish's brain.ganglion cells ͉ optimality A s fish grow and their eyes become larger, the area of the retina increases, new retinal ganglion cells (RGCs) are added, and the RGCs that are already present increase the size of their dendritic arbors (1-5). Because the same visual world is imaged on a larger retina containing more RGCs (6), the resolution of the visual system also increases with growth (7). The retina therefore presents a neural circuit with a scalable architecture (one in which performance is increased by simply making the circuit larger) and offers the possibility of studying the design principles underlying this scalability because fish retinas are available over a large range of sizes. Our goal is to discover design principles governing the size RGC dendritic arbors.The size of RGC dendritic arbors determines two important functional properties of the eye. First, because of way the eye's imaging system and retinal circuits are organized, the retinal area covered by an RGC dendritic arbor determines what region of the image is sampled by the RGC and thus its ''pixel'' size; the smaller this pixel size, the greater the resolution of information provided to the brain about spatial properties of the image. Second, a dendritic arbor collects information about the light intensity in the RGC's patch of the visual world, and, because neural signals are noisy, the accuracy with which this intensity information is represented by the RGC depends on the extent of averaging and thus also on the pixel size: larger arbors average over a larger amount of the retinal area and thus provide the brain with more accurate intensity information. These two properties of the eye (spatial resolution and accuracy in the representation of intensity) therefore depend in opposite ways on the RGC dendritic arbor size and present the retina with a problem in how to optimize the information about the image passed on to the brain.One can imagine three distinct design principles for scalable retinal circuits that RGCs could use to deal with these conflicting demands in retinas of different sizes. The first principle is for evolution to find a RGC dendritic size that represents light...