A parsimonious alternative to the pacemaker/accumulator process in animal timing

Models of animal timing often assume the existence of a pacemaker whose variance is produced by a Poisson process. Later stages in these models typically include an accumulator, additional sources of variance, and a process in which the accumulated value is compared to reference memory. Together, these stages produce a constant coefficient of variation (i.e. the `scalar property,' often observed in experiments) even though at least one of the sources of variance is not scalar. We propose a more parsimonious source of scalar variance. We define a linear failure rate function and demonstrate that its resulting distribution function, called the Rayleigh distribution, always produces the scalar property without requiring: (a) additional sources of variance, or (b) that comparisons with reference memory always be based on ratios. Continuous and discrete versions of this model are derived. This model may serve as a more parsimonious pacemaker than others currently proposed and may replace the pacemaker/accumulator process in timing models.