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Abstract

The total number of lethal equivalents as defined by Morton, Crow and Muller (1956) is a function of three parameters: M, the number of loci at which deleterious mutations can occur, q, the frequency of the deleterious alleles at each locus, and s, their selective value. A new approach based on multi-generation inbreeding data is outlined and used to infer these three parameters as well as the dominance coefficient, h, in a self-incompatible species, Brassica rapa L. Germination and flowering data from thirty bud-selfed lines of fast-cycling B.rapa were assessed over three generations. Germination and flowering were significantly postponed by inbreeding but germination and flowering success were not so strongly decreased. Estimates of the average s values were obtained but it was not possible to get separate estimates of M and q. For both characters, the average dominance coefficient was particularly low. The number of lethal equivalents at the zygotic level was around two for germination and three for flowering, which, owing to the self-incompatibility of B.rapa, is an unexpectedly low value. These results may be explained by past biparental inbreeding which in turn may have increased self-compatibility thus allowing the purging of more deleterious alleles than under strict self-incompatibility.

Nonequivalent lethal equivalents: Models and inbreeding metrics for unbiased estimation of inbreeding load

“…These GLMM and GEE models can easily be applied to individual survival data and, in principle, readily allow estimation of variation in inbreeding depression across ages, sexes or environments. Additional but more rarely used models can be found in Makov and Bittles (), Ralls, Ballou, and Templeton (), Lee, Lascoux, and Nordheim (), Lascoux and Lee () or Hedrick, Hellsten, and Grattapaglia (). However, as we will show, some of these models do not preserve the population genetic assumptions (additivity on a logarithmic scale) underlying Morton et al.…”

Algebraic Differential Equations for Entire Holomorphic Curves in Projective Hypersurfaces of General Type: Optimal Lower Degree Bound

“…as is guaranteed by the inequality (36) of Theorem 11.6. But the first inequality obviously entails the second one, hence we deduce that all positive cohomologies: 0 = H q X, Ω (ℓ ′′ 1 ,...,ℓ ′′ n−1 ,0,0) P n+1 ⊗ O X (t ′′ ) (q = 1, 2 ··· n) of R vanish as soon as: (37) t ′′ d + ℓ ′′ 1 + n−1 i=1 ℓ ′′ i . We observe that this fact is valid also when ℓ ′′ n 1 +1 = · · · = ℓ ′′ n−1 for some largest integer n 1 0 with ℓ ′′ n 1 1, because the second exact sequence (33) we used is subjected to no restriction.…”