chain of lynx and drove of hares

A paper (and an introduction to the paper) in Nature this week seems to have made progress on the existence of indefinite predator-prey cyles. As in the lynx/hare dataset available on R. The paper is focusing on another pair, an invertebrate and its prey, an algae. For which the authors managed a 50 cycle sequence. What I do not get about this experiment is how the cycle can be tested via a rigorous statistical experiment.

“…the predator–prey system showed a strong tendency to return to the dominant dynamical regime with a defined phase relationship. A mathematical model suggests that stochasticity is probably responsible for the reversible shift from coherent to non-coherent oscillations, a notion that was supported by experiments with external forcing by pulsed nutrient supply.”

As I had not renewed my subscription to Nature in time, I could not check the additional material for details, but the modelling seems to involve a wavelet decomposition of the bivariate time series, with correlations between the two series…

Scottish sunbathing

Gaussian hare and Laplacian tortoise

A question on X validated on the comparative merits of L¹ versus L² estimation led me to the paper of Stephen Portnoy and Roger Koenker entitled “The Gaussian Hare and the Laplacian Tortoise: Computability of Squared-Error versus Absolute-Error Estimators”, which I had missed at the time, despite enjoying a subscription to Statistical Science till the late 90’s.. The authors went as far as producing a parody of Granville’s Fables de La Fontaine by sticking Laplace’s and Gauss’ heads on the tortoise and the hare!

I remember rather vividly going through Steve Stigler’s account of the opposition between Laplace’s and Legendre’s approaches, when reading his History of Statistics in 1990 or 1991… Laplace defending the absolute error on the basis of the default double-exponential (or Laplace) distribution, when Legendre and then Gauss argued in favour of the squared error loss on the basis of a defaul Normal (or Gaussian) distribution. (Edgeworth later returned to the support of the L¹ criterion.) Portnoy and Koenker focus mostly on ways of accelerating the derivation of the L¹ regression estimators. (I also learned from the paper that Koenker was one of the originators of quantile regression.)