brokenstick

Brokenstick is a term used in statistics, ecology, probability, and data analysis to describe problems or models involving breaking a stick into pieces to yield random segments.

In ecology, the broken-stick model (MacArthur, 1957) is a simple neutral model for species abundance distributions. The unit-length stick is broken at random into S pieces, and the resulting piece lengths, when arranged from largest to smallest, are used as expected relative abundances for S species. The model provides a null hypothesis for comparing observed rank-abundance curves to neutral expectation and is implemented in various ecological analyses.

In probability, the broken-stick problem asks what happens when a stick is broken at two random points along its length. The three resulting segment lengths can form a triangle with probability 1/4. The problem is a classic example in geometric probability and leads to distributions of segment lengths that can be analyzed and simulated.

In statistics, the broken-stick model also refers to piecewise linear regression with a single break point, used to describe relationships that change slope beyond a threshold. The break point is typically estimated from data, and the model yields two linear regimes joined at the knot.

In software and data analysis, formulations or implementations named brokenstick appear in R, Python, and other environments to fit the ecological broken-stick model or to analyze related segmentation problems. Overall, brokenstick highlights the use of random fragmentation or threshold-based changes in modeling complex systems.