The red flowers of the invasive African tulip tree (Spathodea campanulata; Bignoniaceae) stand out in a Puerto Rican rain forest. This species may occupy a mathematical hole, having an ecological strategy unoccupied by other species in the community. Recent mathematical advances now allow detection of holes and better understandings of species invasions and extinctions.
Imagine an island populated by small and large animals. A reasonable assumption would be that the island might also have medium-sized species—but what if none are found? These empty spaces, or ‘holes,’ may represent missing components of ecological communities. Identifying these holes may help researchers predict the outcomes of invasions, extinctions, and long-term evolution. What we don’t see may matter as much as what we do. My new paper in The American Naturalist (link, PDF) now provides a new way to answer the previously unanswerable question—does a community have holes, or not?
The trouble is that holes are difficult to detect. Imagine a volleyball. This three-dimensional shape has an empty space inside of it, but from a two-dimensional photograph you would never be able to tell that it isn’t solid. Ecological strategies work the same way. Along any individual strategy axis (like body size, or temperature tolerance), species may be able to take on small, medium, and large values—but when considering all axes together, some combinations may never occur, just like the hidden interior of the volleyball. Yet these holes may be exactly where a new species could invade a community, or where another species may have recently gone extinct.
Computers have not been able to solve this problem before now. As the number of dimensions in the ecological strategy space increases, the number of possible ecological strategies grows exponentially. That means there are too many places to find a hole for a computer to easily find. But there is now a new set of free software tools that will enable researchers to efficiently discover such holes (CRAN link to hypervolume package). These holes may represent forbidden ecological strategies or available but unrealized opportunities that have never yet been identified. We don’t know how common holes are in real ecological communities, but we won’t know until we look. Now we can.