The Genetic Basis of Individual-Recognition Signals in the Mouse

SummaryThe major histocompatibility complex (MHC) is widely assumed to be a primary determinant of individual-recognition scents in many vertebrates [1–6], but there has been no functional test of this in animals with normal levels of genetic variation. Mice have evolved another polygenic and highly polymorphic set of proteins for scent communication, the major urinary proteins (MUPs) [7–12], which may provide a more reliable identity signature ([13, 14] and A.L. Sherborne, M.D.T., S. Paterson, F.J., W.E.R.O., P. Stockley, R.J.B., and J.L.H., unpublished data). We used female preference for males that countermark competitor male scents [15–17] to test the ability of wild-derived mice to recognize individual males differing in MHC or MUP type on a variable genetic background. Differences in MHC type were not used for individual recognition. Instead, recognition depended on a difference in MUP type, regardless of other genetic differences between individuals. Recognition also required scent contact, consistent with detection of involatile components through the vomeronasal system [6, 18]. Other differences in individual scent stimulated investigation but did not result in individual recognition. Contrary to untested assumptions of a vertebrate-wide mechanism based largely on MHC variation, mice use a species-specific [12] individual identity signature that can be recognized reliably despite the complex internal and external factors that influence scents [2]. Specific signals for genetic identity recognition in other species now need to be investigated

Bounding Helly numbers via Betti numbers

We show that very weak topological assumptions are enough to ensure the existence of a Helly-type theorem. More precisely, we show that for any non-negative integers $b$ and $d$ there exists an integer $h(b,d)$ such that the following holds. If $\mathcal F$ is a finite family of subsets of $\mathbb R^d$ such that $\tilde\beta_i\left(\bigcap\mathcal G\right) \le b$ for any $\mathcal G \subsetneq \mathcal F$ and every $0 \le i \le \lceil d/2 \rceil-1$ then $\mathcal F$ has Helly number at most $h(b,d)$. Here $\tilde\beta_i$ denotes the reduced $\mathbb Z_2$-Betti numbers (with singular homology). These topological conditions are sharp: not controlling any of these $\lceil d/2 \rceil$ first Betti numbers allow for families with unbounded Helly number. Our proofs combine homological non-embeddability results with a Ramsey-based approach to build, given an arbitrary simplicial complex $K$, some well-behaved chain map $C_*(K) \to C_*(\mathbb R^d)$.Comment: 29 pages, 8 figure

The Genetic Basis of Inbreeding Avoidance in House Mice

Animals might be able to use highly polymorphic genetic markers to recognize very close relatives and avoid inbreeding [1, 2]. The major histocompatibility complex (MHC) is thought to provide such a marker [1, 3–6] because it influences individual scent in a broad range of vertebrates [6–10]. However, direct evidence is very limited [1, 6, 10, 11]. In house mice (Mus musculus domesticus), the major urinary protein (MUP) gene cluster provides another highly polymorphic scent signal of genetic identity [8, 12–15] that could underlie kin recognition. We demonstrate that wild mice breeding freely in seminatural enclosures show no avoidance of mates with the same MHC genotype when genome-wide similarity is controlled. Instead, inbreeding avoidance is fully explained by a strong deficit in successful matings between mice sharing both MUP haplotypes. Single haplotype sharing is not a good guide to the identification of full sibs, and there was no evidence of behavioral imprinting on maternal MHC or MUP haplotypes. This study, the first to examine wild animals with normal variation in MHC, MUP, and genetic background, demonstrates that mice use self-referent matching of a species-specific [16, 17] polymorphic signal to avoid inbreeding. Recognition of close kin as unsuitable mates might be more variable across species than a generic vertebrate-wide ability to avoid inbreeding based on MHC