It should be clear from the above that we do not yet have a widely accepted, general, synthetic explanation for the LDG. Even if all or parts of the above synthesis are substantially correct, many parts are incomplete and many holes need to be filled. I am optimistic that substantial progress can be made. Several areas of research should be especially promising.
Comparative biogeography and macroecology
There has been great progress in documenting empirical patterns of biodiversity: across scales of space and time, levels of biological organization, taxa and habitats. There has been less progress in comparing and synthesizing the results, in part because systematists, ecologists and biogeographers tend to be specialists. This is unfortunate. On the one hand, the LDG is very general, suggesting that similar processes operate in similar ways on the different organisms in different habitats. On the other hand, the roles of historical events and contemporary environments, and of evolutionary and ecological processes, are not independent or mutually exclusive. Moreover, the LDG is just the most well known of several pervasive geographical patterns of biodiversity. Others are the gradients of species richness with elevation on land, depth in the ocean, and aridity in terrestrial environments (e.g. Lomolino et al., 2010; Colwell, 2011).
There is much to be learned by taking advantage of ‘natural experiments’ and making comparisons among the different gradients, scales, levels of organization, taxa and habitats. The variables that potentially affect diversity – tectonic and glacial history, seasonality, temperature, productivity, abiotic stress, biotic interactions, abundance and biomass – sort out in different ways in these different systems, offering potentially valuable insights. For example, the correlations among seasonality, NPP, temperature and latitude, which potentially confound analyses of the LDG in the terrestrial realm are effectively absent in the marine realm. In the oceans NPP is controlled largely by nutrient supply and is highest in areas of upwelling and outflows of large rivers. So productivity is largely independent of temperature and latitude, but biodiversity is highest in tropical waters (e.g. Tittensor et al., 2010). The historical effects of Pleistocene glaciations on pelagic marine organisms, although not inconsequential, were likely to have been quite different from those on plants and animals on the northern continents. Similarly, comparisons of elevational and latitudinal diversity patterns have the potential to separate the effects of glacial history and seasonality from those of productivity and temperature. Also relevant are mechanisms responsible for the frequently observed peak of diversity at intermediate elevations, a phenomenon seldom seen across latitude (e.g. McCain, 2004; Colwell, 2011).
Comparisons of diversity at different levels of biological organization will also be relevant. The LDG is not restricted to species; it also holds at higher and lower levels of organization. Recent studies have documented LDGs of clades of multiple species (e.g. Hawkins et al., 2012; Romdal et al., 2012). Supplemented with information from the fossil record and molecular phylogenies on the timing and location of dispersal, speciation, divergence and extinction, such studies are elucidating historical patterns of biodiversity and providing insights into the dynamical processes. At the other extreme, there is increasing evidence of LDGs within species, including human cultures and languages (Collard & Foley, 2002; Pagel & Mace, 2004). Rapoport's rule was originally based on within-species variation as expressed in range sizes of recognized subspecies. Finally, there appears to be a LDG of genetic diversity within populations, as evidenced by numbers of mitochondrial genotypes within local populations of several kinds of terrestrial vertebrates (Adams & Hadly, 2012).
Comparisons of species richness, genetic diversity, geographical range limits, local abundance and spatial distributions between alien and native species offer additional insights. Exotics introduced by humans within the last few hundred years provide invaluable ‘unintentional experiments’ in ecology and evolution (Sax, 2001; Sax et al., 2002; Wiens & Graham, 2005). For example, the pattern that polar but not equatorial limits of geographical ranges of introduced terrestrial vertebrates are closely correlated, and that tropical continents but not islands, appear to be resistant to colonization by introduced species are consistent with the DMP, limitation by abiotic factors at high latitudes, and biotic interactions in the tropics (Sax, 2001). There is much to learn by expanding macroecological studies of exotics to other systems, such as terrestrial insects and marine organisms.
The most invasive organism is our own species. In only about 50,000 years anatomically modern humans have spread out of tropical Africa to colonize the entire Earth and become the most dominant species. Recent studies of subsistence cultures have documented a Rapoport's rule of tribal ranges and a LDG of languages and cultures (Collard & Foley, 2002; Pagel & Mace, 2004; Burnside et al., 2012; Gavin et al., 2013). Because these patterns have been established rapidly and independently on different continents, they presumably reflect convergent responses to similar ecological conditions. They are consistent with effects of biotic interactions, especially with diseases and plant and animal food resources.
Theory and models
There is also a need for more and better theory to articulate promising questions, guide the design and analysis of empirical studies, and evaluate mechanistic hypotheses. To produce a widely accepted general synthetic theory of biodiversity will be a real challenge. Just to provide a relatively satisfying explanation of the LDG would be a major accomplishment, let alone to develop a more comprehensive theory that places the LDG in the context of other pervasive patterns of diversity across geographical space and evolutionary time.
A major challenge in developing biodiversity theory is the inherent complexity of the problem. Most efforts have used either qualitative verbal or graphical frameworks (Connell & Orias, 1964; Janzen, 1970; Connell, 1971; Rosenzweig, 1995), simple analytical treatments that incorporate only a few coexisting species (e.g. MacArthur, 1972; Tilman, 2004), or whole-system models that focus on emergent patterns rather than underlying mechanisms (e.g. Hubbell, 2008; Harte et al., 2008; Harte, 2011; Storch, 2012). This is understandable, but for ideal interplay between theory and data we need models that can incorporate explicit mechanistic processes and make predictions for assemblages of tens to hundreds of species. This will necessarily entail computer simulation models.
I am fairly optimistic that considerable progress can be made using models that incorporate a relatively small number of assumptions and parameters and are firmly grounded in basic biophysical principles such as mass and energy balance, biomechanics and physiology, and metabolic scaling (e.g. Hammond & Niklas, 2009, 2011a,b).