Statistical physics of many-species ecosystems

7 problems

• How predictable is the species composition of an assembling microbial community?

  Partially resolved

  When a mixture of many microbes is grown in the same food again and again, the community that forms is similar at the level of broad families but differs in its exact species. How much of the final composition can be predicted in advance, and from what measurements, is not known.

• Can high-diversity chaos persist in a closed community without immigration?

  Open

  Models show that many species can coexist if their populations keep fluctuating chaotically, but each crash brings some species close to zero, where they can die out. It is unknown whether a closed community with no new arrivals keeps its diversity or slowly loses species until it settles into a simple steady state.

• Phase diagram of random many-species Lotka-Volterra dynamics beyond stability

  Partially resolved

  In the standard model of many interacting species with random interaction strengths, weak interactions lead every community to the same single steady state. Beyond a threshold strength the behavior changes, and it is not settled whether the community then has many possible steady states, keeps fluctuating chaotically, or both.

• How diverse natural communities stay stable despite May's random-matrix bound

  Contested

  In 1972 Robert May showed that a community with many randomly interacting species should almost always be unstable, so that small disturbances grow. Real ecosystems are very diverse and persist, so real interactions must violate some assumption of his argument.

• Are fluctuating phases in microbial microcosms the chaotic phase of theory?

  Open

  Laboratory communities of bacteria change from stable coexistence to lasting population swings as more species are added or as they interact more strongly, as random-interaction models predict. It remains to be shown that the experimental swings are the same phase the theory describes, rather than a different effect.

• Do pairwise competition outcomes predict multispecies coexistence?

  Open

  One could try to predict which species survive together by testing them two at a time and applying simple rules. If interactions involving three or more species at once matter, these two-at-a-time tests will fail for large communities.

• Why hundreds of plankton species coexist on a few resources

  Open

  The competitive exclusion principle says that, at steady state, no more species can coexist than there are limiting resources such as nitrogen, phosphorus and light. Ocean and lake plankton contain hundreds of species living on about ten resources, which is the paradox of the plankton.