The Relationship Between Count-Location and Stationary Renewal Models for the Chiasma Process

Corresponding author: Sharon Browning, 447 Blocker Bldg., Texas A&M University, College Station, TX 77843-3143., browning{at}stat.tamu.edu (E-mail)

Communicating editor: S. TAVARÉ

It is often convenient to define models for the process of chiasma formation at meiosis as stationary renewal models. However, count-location models are also useful, particularly to capture the biological requirement of at least one chiasma per chromosome. The Sturt model and truncated Poisson model are both count-location models with this feature. We show that the truncated Poisson model can also be expressed as a stationary renewal model, while the Sturt model cannot. More generally, we show that there is only one family of count-location models for the chiasma process that can also be expressed as stationary renewal models. The models in this family can exhibit either positive or negative interference.

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