grain: a computer program to calculate ancestral and partial inbreeding coefficients using a gene dropping approach

Abstract

GRain is freely available software intended to enable and promote testing of hypotheses with respect to purging and heterogeneity of inbreeding depression. The program is based on a stochastic approach, the gene dropping method, and calculates various coefficients from large and complex pedigrees. GRain calculates, together with the 'classical' inbreeding coefficient, ancestral inbreeding coefficients proposed by Ballou, (1997) J. Hered., 88, 169 and Kalinowski et al., (2000) Conserv. Biol., 14, 1375 as well as an ancestral history coefficient (AHC ), defined here for the first time. AHC is defined as the number that tells how many times during pedigree segregation (gene dropping) a randomly taken allele has been in IBD status. Furthermore, GRain enables testing of heterogeneity and/or purging of inbreeding depression with respect to different founders/ancestors by calculating partial coefficients for all previously obtained coefficients.

Genetic Diversity and Ancestral History of the German Angler and the Red-and-White Dual-Purpose Cattle Breeds Assessed through Pedigree Analysis

“…The GRAIN software package [16] was applied for the computation of Agricultural Sciences ancestral inbreeding coefficients. To describe possible disequilibrium of founder contribution to the reference population (RP, i.e.…”

“…We also calculated classical inbreeding coefficients together with ancestral inbreeding coefficient according to Ballou [15] and as suggested by Kalinowski [14], and A HC [16] using a modified version of gene dropping [23], [24] with 10 6 replications. Originally, Ballou's ancestral inbreeding coefficient (Fa_Bal) refers to the cumulative proportion of an individual's genome that has been previously exposed to inbreeding in its ancestors.…”

“…Originally, Ballou's ancestral inbreeding coefficient (Fa_Bal) refers to the cumulative proportion of an individual's genome that has been previously exposed to inbreeding in its ancestors. Without changing the original meaning of the parameter, Fa_Bal was recently defined as the probability that any allele in an individual has been autozygous (IBD) in previous generations at least once [16]. Kalinowski's approach to ancestral inbreeding gives a narrower meaning of the parameter, and is defined as the probability that any allele in an individual is currently autozygous (IBD) and has been autozygous in previous generations at least once.…”

“…Kalinowski's approach to ancestral inbreeding gives a narrower meaning of the parameter, and is defined as the probability that any allele in an individual is currently autozygous (IBD) and has been autozygous in previous generations at least once. The ancestral history coefficient is quite novel and by definition, tells how many times during pedigree segregation a randomly taken allele has been in IBD status [16].…”

“…Apart from a few studies [10] [13], most pedigree analyses involving dairy cattle were focused on classical in- [14], [15] are well established. In a recent publication, Ballou's and Kalinowski's ancestral inbreeding coefficients were redefined [16], and the authors introduced the ancestral history coefficient (A HC ) defined as the number that tells how many times during pedigree segregation (gene dropping) a randomly taken allele has been in IBD status.…”