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The concern of this stndy has been the chemical composition of Uaphnia omgnu, the algae (Selenustrum, cnpricornutuni, Ankistrodesmus convolutus) it was fed, the two growth media in which the algae were cultured and the water (Lake Huron, Michigan, USA) in which D. magnu was reared. A synthetic diet (fish chow+alfalfa) was used as a control. The effectiveness of these five diets on the health of the 1). inagna populations was ascertained by t,he weight and number of neonates thus produced. The diet, S. capricornufuin cultured in an organic medium, prodnced the largest mean brood size and the heaviest neonates in unstressed populations. The synthetic diet prodnced the smallest mean brocd size and the lightest neonates. Stressed organisms may produce smaller broods wit.h heavier neonates than unstressed organisms. The erolnticnary significance of this observation is discussed. Statistical studies suggetit that daphnids maintained on the synthetic diet derired no demonstrable nutritive value from the diet in terms of elemental composition or amino acid production. A great similarity in patterns cf amino acid quantity and type was noted in the algae and the daphnids. On further examination it was discoverctl that this pattern was widespread in other aquatic forms, bacteria, fungi, yeasts, casein and was common t o a variety of birds and mammals. It may be suggested that products that are made and stored, such as lipids. are less uniform in pattern among widely diverse species than those that have t o he produced and are not stored. such as amino acids.

Background A major goal of evolutionary developmental biology is to discover general models and mechanisms that create the phenotypes of organisms. However, universal models of such fundamental growth and form are rare, presumably due to the limited number of physical laws and biological processes that influence growth. One such model is the logarithmic spiral, which has been purported to explain the growth of biological structures such as teeth, claws, horns, and beaks. However, the logarithmic spiral only describes the path of the structure through space, and cannot generate these shapes. Results Here we show a new universal model based on a power law between the radius of the structure and its length, which generates a shape called a ‘power cone’. We describe the underlying ‘power cascade’ model that explains the extreme diversity of tooth shapes in vertebrates, including humans, mammoths, sabre-toothed cats, tyrannosaurs and giant megalodon sharks. This model can be used to predict the age of mammals with ever-growing teeth, including elephants and rodents. We view this as the third general model of tooth development, along with the patterning cascade model for cusp number and spacing, and the inhibitory cascade model that predicts relative tooth size. Beyond the dentition, this new model also describes the growth of claws, horns, antlers and beaks of vertebrates, as well as the fangs and shells of invertebrates, and thorns and prickles of plants. Conclusions The power cone is generated when the radial power growth rate is unequal to the length power growth rate. The power cascade model operates independently of the logarithmic spiral and is present throughout diverse biological systems. The power cascade provides a mechanistic basis for the generation of these pointed structures across the tree of life.

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