  Animal interval timing is often studied through the peak interval (PI)
procedure. In this procedure, the animal is rewarded for the first response
after a fixed delay from the stimulus onset, but on some trials, the stimulus
remains and no reward is given. The common methods and models to analyse the
response pattern describe it as break-run-break, a period of low rate response
followed by rapid responding, followed by a low rate of response. The study of
the pattern has found correlations between start, stop, and duration of the run
period that hold across species and experiment.
  It is commonly assumed that in order to achieve the statistics with a
pacemaker accumulator model it is necessary to have start and stop thresholds.
In this paper we will develop a new model that varies response rate in relation
to the likelihood of event occurrence, as opposed to a threshold, for changing
the response rate. The new model reproduced the start and stop statistics that
have been observed in 14 different PI experiments from 3 different papers. The
developed model is also compared to the Time-adaptive Drift-diffusion Model
(TDDM), the latest accumulator model subsuming the scalar expectancy theory
(SET), on all 14 data-sets. The results show that it is unnecessary to have
explicit start and stop thresholds or an internal equivalent to break-run-break
states to reproduce the individual trials statistics and population behaviour
and get the same break-run-break analysis results. The new model also produces
more realistic individual trials compared to TDDM.
