The relationship between count-location and stationary renewal models for the chiasma process

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.