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Patterns in the diversity of species begin to make sense when we reduce them to well-known biological processes and take care to specify the scale of the pattern. Doing this explains why diversity declines away from the tropics (the latitudinal diversity gradient). The extensive tropical regions supply more opportunities for large geographical ranges than any other biome. Allopatric speciation feeds on such large ranges. The large regions of the tropics also probably inhibit extinction. It is a mistake to explain the richness of the tropics by noting that there are more habitats in the tropics. The global scale develops in evolutionary time. On that scale, fine habitat subdivision is a coevolved property of the species in a biome. The more species, the finer they subdivide habitats. So, it is also wrong to imagine that the tropical gradient is nothing more than a species-area curve. The species-area curve is a pattern that exists on a more local scale than the latitudinal gradient, and depends on habitat variability growing as larger areas get included in a sample. We all think that decades ago we should have understood the pattern of diversity and productivity. But the literature isn’t even sure what the pattern is. Until recently, theory maintained that higher productivity should sustain more species. Evidence from poorer environments supports that theory. But most empirical evidence, including most experiments, show that diversity declines as productivity rises. Two errors confused us. First, we ecologists always assumed that the theory could not be wrong, so we refused to admit the facts, no matter how often we observed them. Second, we mixed our facts into a wild stew of scales and biomes. Diversity experiments, performed by increasing productivity on a local scale of time and space, tell us nothing about the productivity pattern at large scales. The regional pattern is unimodal. As productivity rises within a region, first diversity rises and then it falls. This pattern exists in mammals, birds, marine vertebrates and invertebrates, and some flora. We do not understand it.