The “counting model” for crossover interference (Foss et al. 1993) was first tested on Drosophila data, where it was remarkably successful (Foss et al. 1993; McPeek and Speed 1995; Zhao et al. 1995; Lande and Stahl 1993). The single adjustable parameter (m) in this “renewal” model was presumed to be the number of “noncrossovers” (DSBs repaired without crossing over) occurring between every pair of adjacent crossovers. The value of 4 gave a significantly better fit than either 3 or 5. This value corresponded with the estimate of 20% for the fraction of rosy+ heteroallelic conversions that were crossed over for flanking markers (Hilliker et al. 1988). However, since Hilliker’s value was imprecise and was based on the data from just a single locus (on chromosome 3), while the counting model was tested against data from the X chromosome, the correspondence in the two values may have been fortuitous.
The data of Mehotra and McKim can be viewed as generalizing the estimate from the rosy locus to the entire nucleus, lending support to the counting model. They write, “Assuming all DSBs appear as c-His2Av foci, there is at least a 3:1 ratio of noncrossover to crossover products.” As the authors imply, the 3:1 value may be an underestimate, although they doubt that it is a large underestimate (K. McKim, pers. com.)
For the simple counting model, in which the counting frame is set at random (Foss et al. 1993), the number of crossovers is proportional to the number of DSBs. This assumption provided such a good fit to Drosophila data that variations of the model that assume nonrandomness have received little attention.
The data of Mehotra and McKim provide a test of this simple version of the model. Mehotra and McKim experimentally vary the density of DSBs and note whether crossovers respond in a linear or, by contrast, in a “homeostatic” manner (Martini et al. 2006) as demanded by the concept of an “obligate crossover” and as predicted by some versions of the counting model in which the frame is set nonrandomly with respect to DSBs. Based on their Figure 6, they state, “From a comparison of the frequency of c-His2Av foci and crossovers, it appears that Drosophila females have only a weak mechanism to ensure a crossover in the presence of a low number of DSBs.” In so far as the data might support some degree of homeostasis, they would imply that the simplest, uniform counting model is inadequate for Drosophila, at least when the number of DSBs is reduced. However, the data entries in Figure 6 have been normalized to the estimate for wild type, making interpretation of the curve a bit difficult. A more transparent test of linearity would be a simple plot of crossing over (cM) vs. DSB foci. In Figure 1 we present such a plot, using the data from Table 4, kindly supplemented by Mehrotra and McKim (our Table 1). http://www.plosgenetics.o...
The data are seen to be compatible with linearity and, hence, with the simple version of the counting model.
Discussion:
Mehrotra and McKim remark that “…generating an excess of DSBs, each with a reasonable chance of becoming a crossover, may be sufficient to ensure at least one crossover occurs on each chromosome.” This possibility for Drosophila is supported by the observation that the simple counting model, with random counting frame, accurately accounted for the roughly 5% of E0 tetrads that characterized the Drosophila X chromosome data used to test the counting model. It should be noted that some isolates of Drosophila freshly collected from the wild (Michael et al. 1999) have appreciably higher E0 frequencies, supporting the idea favored by Melhotra and McKim that, in Drosophila at least, the notion of an “obligate crossover” is a myth.
Getz et al. (2008) demonstrated that wild-type yeast has two phases of crossing over, only one of which manifests positive interference. Using Spo11 enzymes of reduced activity, Martini et al. (2006) demonstrated a nonlinear response of crossing over to a reduction in DSBs (“homeostasis”, indicative of an obligate crossover). The apparent lack of homeostasis in Drosophila, which appears to have only the interference phase of DSBr, suggests that homeostasis is not a property of that phase.
A property of the noninterference phase of yeast DSBr suggests an explanation for homeostasis in yeast different from one previously proposed (Stahl et al. 2004). The mutant ndj1 (tam1) has a reduced rate of chromosome pairing (Chua and Roeder 1997; Conrad et al. 1997; Peoples-Holst and Burgess 2005). The ndj1 mutant also manifests an increase in the fraction of noninterference phase DSBr events that result in crossing over (Getz et al. 2008). Since pairing in yeast is dependent on DSBs, the reduction in DSBs imposed, under some conditions, by leaky spo11 mutations (Martini et al. 2006) might reduce the rate of chromosome pairing and, as with ndj1, increase the fraction of noninterference phase DSBs that result in crossing over. [This hypothesis appears testable, at least in principle, since, in strains so far examined, noninterference DSB events are identifiable by the postmeiotic segregation of markers that make poorly repairable heteroduplexes (Getz et al. 2008)]. Arguing against this unifying interpretation is the claim by Martini et al. (2006) that interference is undiminished in those spo11 mutants that make fewer DSBs. That argument would, indeed, be cogent if DSBs and crossing over, on the one hand, and interference, on the other, had been measured under the same culture conditions (see Cotton et al. 2008).

Literature cited:
Cotton VE, Hoffman ER, Abdullah MFF, Borts RH (2008) The devil is in the details: The importance of genetic and environmental factors for yeast meiosis in Protocols for Meiosis edited by S. Keeney. Humana (In press). Preprints are available from Rhona Borts rhb7@leicester.ac.uk
Chua PR, Roeder GS (1997) Tam1, a telomere-associated meiotic protein, functions in chromosome synapsis and crossover interference. Genes Dev. 11: 1786-1800.
Conrad MN, Dominguez AM, Dresser ME (1997) Ndj1p, a meiotic telomere protein required for normal chromosome synapsis and segregation in yeast. Science 276: 1252-1255.
Foss E, Lande R, Stahl FW, Steinberg CM (1993) Chiasma interference as a function of genetic distance. Genetics 133: 681–691.
Getz TJ, Banse SA, Young LS, Banse AV, Swanson J, Wang GM, Browne BL, Foss HM, Stahl FW (2008) Reduced mismatch repair of heteroduplexes reveals “non”-interfering crossing over in wild-type Saccharomyces cerevisiae. Genetics 178: 1251–1269.
Hilliker AJ, Clark SH, Chovnick A (1988) Genetic analysis of intragenic recombination in Drosophila, pp. 73-90 in The Recombination of Genetic Material, edited by KB Low. Academic Press, San Diego.
Lande R, Stahl FW (1993) Chiasma interference and the distribution of exchanges in Drosophila melanogaster. Cold Spring Harbor Symp. Quant. Biol. 58: 542-552.
Martini ER, Diaz L, Hunter N, Keeney S (2006) Crossover homeostasis in yeast meiosis. Cell 126: 285-295.
McPeek MS, Speed TP (1995) Modeling interference in genetic recombination. Genetics 139: 1031--1044.
Peoples-Holst TL, Burgess SM (2005) Multiple branches of the meiotic recombination pathway contribute independently to homolog pairing and stable juxtaposition during meiosis in budding yeast. Genes Dev. 19: 863-874.
Stahl FW, Foss HM, Young LS, Borts RH, Abdulla MFF, Copenhaver GP (2004) Does crossover interference count in Saccharomyces cerevisiae? Genetics 168: 35-48.
Zwick ME, Cutler DJ, Langley CH (1999) Classic Weinstein: tetrad analysis, genetic variation and achiasmate segregation in Drosophila and humans. Genetics 152: 1615–1629.
Zhao H, Speed TP, McPeek MS (1995) Statistical analysis of crossover interference using the Chi-Square model. Genetics 139: 1045-1056.