Stats resolve “kill the winner” paradox

In 1961, the British polymath G. E Hutchinson, dubbed the father of modern ecology, noted a conundrum in marine ecology: there was a huge diversity of plankton species.

The problem? Theoretically, this shouldn’t happen.

The Russian biologist Georgii Gause (1910-1986), first, arguably, sowed the seeds of the ‘competition exclusion principle’ in 1932, which states that if two species occupy the same ecological niche, in the same geographical range, then one should out-compete the other, leading to its extinction and a resultant lack of biodiversity.

Hutchinson had observed the exact opposite, however, and he named this puzzle the ‘Paradox of the Plankton’, more generally known now as the ‘biodiversity paradox’.

One proposed solution to the problem is known as the ‘Kill the Winner’ (KtW) model. This holds that different species in the same ecological niche will rise and fall over time in succession, each eventually toppled and replaced. However, none of the proposed solutions are terribly satisfactory. 

Now, new research published in Physical Review Letters holds the possibility of solving the paradox. Chi Xue and Nigel Goldenfeld of the Carl R. Woese Institute for Genomic Biology at the University of Illinois at Urbana-Champaign, US, have developed a mathematical model that more realistically extends and refines the KtW hypothesis.

While earlier KtW models were overly simplified, Xue and Goldenfeld have taken inspiration from statistical thermodynamics used to describe the way gas molecules collide. In doing so, their model allows for the kind of random population fluctuations, or ‘demographic stochasticity’, seen in nature.

Using bacteria-virus interactions as their subject, they hoped their mathematical model would demonstrate that individual bacteria-virus encounters would give rise to higher-level KtW dynamics. 

It didn’t happen. 

Instead, the modelled species were driven to extinction. “The breakdown of the original KtW model in the presence of stochasticity was a surprise to us,” says Xue, “We hadn’t expected this very reasonable model to fail.”

However, the pair soon realised that there was yet another real-world factor missing: species and ecosystems evolve. 

“In the case of the ecosystem in our marine biology example, there is coevolution of each bacteria strain and its host-specific virus as they compete in what can be described as an arms race,” says Goldenfeld. 

“As the bacteria find ways to evade the attack of viruses, the viruses evolve to counter the new defences.” 

With the inclusion of this ‘coevolution’, the model gave rise to KtW dynamics and the kind of biodiversity observed in nature, thus providing perhaps the first genuinely satisfactory solution to Hutchinson’s paradox.

Interestingly, Goldenfeld, who is also the director of NASA’s Astrobiology Institute for Universal Biology, sees some cosmic consequences of their work. 

“Understanding the fundamental mechanisms driving biodiversity,” he says, “will help us predict the observability of non-terrestrial life on worlds that will be within reach of our probes in the coming decades.”