Laboratory primates are often housed in same-sex pairs to avoid single-housing and when breeding is to be prevented. However, pair formation is not without risks, as fights and injuries may occur. No data are available on pair formation in female common marmosets (Callithrix jacchus), a species used extensively in laboratories. Therefore, this study focuses on the pairing of unfamiliar common marmoset females, aiming to assess its success rate and whether age can predict the result. Data on the study animals and success of the pairings were extracted from laboratory back-records: a total of 28 pairings was obtained. In addition, behavioural data were collected on six of the 28 pairs. Almost 80% of pairs were compatible beyond one week, and most of the fights occurred well within the first week after pair formation. Pairs in which one of the females was sexually immature (ie < 15 months) were significantly more compatible than pairs in which both females were post-pubertal. First encounters were characterised by sniffing of the unfamiliar monkey. Aggressive behaviours occurred frequently following pair formation but they were unidirectional, and in only two pairs was veterinary treatment required. This study shows that pairing of unfamiliar common marmoset females is a safe practice if one monkey is sexually immature, a result that supports observations of both group and pair formation in other primate species. However, given the potentially detrimental effects of removing young females from their natal groups, we argue that it is preferable to remove two sisters from their natal group when female pairs are required. However, when a single sexually mature female requires a pair mate so as to avoid single-housing and no mature sibling is available, an older, but still sexually immature, unfamiliar female that has had a normal development within the family should be considered as a pair mate.

Stochastic encounter-mating (SEM) models describe monogamous permanent pair formation in finite zoological populations of multitype females and males. In this paper we study SEM models with Poisson firing times. First, we prove that the model enjoys a fluid limit as the population size diverges, that is, the stochastic dynamics converges to a deterministic system governed by coupled ordinary differential equations (ODEs). Then we convert these ODEs to the well-known Lotka–Volterra and replicator equations from population dynamics. Next, under the so-called fine balance condition which characterizes panmixia, we solve the corresponding replicator equations and give an exact expression for the fluid limit. Finally, we consider the case with two types of female and male. Without the fine balance assumption, but under certain symmetry conditions, we give an explicit formula for the limiting mating pattern, and then use it to characterize assortative mating.

The stochastic process resulting when pairs of events are formed from two point processes is a rich source of questions. When the two point processes have different rates, the resulting stochastic process has a mean drift towards either -∞ or +∞. However, when the two processes have equal rates, we end up with a null-recurrent Markov chain and this has interesting behavior. We study this process for both discrete and continuous times and consider special cases with applications in communications networks. One interesting result for applications is the waiting time of a packet waiting for a token, a special case of this pair-formation process. Pair formation by two independent Poisson processes of equal rates results in a point process that is asymptotically a Poisson process of the same rate.

We present several results refining and extending those of Neuts and Alfa on weak convergence of the pair-formation process when arrivals follow two independent Poisson processes. Our results are obtained using a different, more straightforward, and apparently simpler probabilistic approach. Firstly, we give a very short proof of the fact that the convergence of the pair-formation process to a Poisson process actually holds in total variation (with a bound for convergence rate). Secondly, we extend the result of the theorem to the case of multiple labels: there are d independent arrival Poisson processes, and we are looking at the epochs when d-tuples are formed. Thirdly, we extend the original (weak convergence) result to the case when arrivals follow independent renewal processes (this extension is also valid for the d-tuple formation).