Study species and data recording
The bank vole is a common mammalian species in the Palearctic region . In central Finland, females produce up to four litters of 1-9 pups during the breeding season, and there is substantial variation in both litter size and offspring size both among females and between litters of the same female . Both the number and the size of offspring at birth are important fitness components. The size of offspring indicates quality, as it correlates positively with survival and breeding success [19, 25, 26], while litter size is adjusted to environmental conditions and is subject to balancing selection [25, 27, 28].
A laboratory population was established from wild individuals captured in Konnevesi, central Finland, during the summer of 2000 and subjected to artificial selection toward small and large litter sizes. Selection lines were founded from 150 females and 116 males. Both lines were pooled together in the analysis. All founder males were wild-caught, while some of the "founder" females were laboratory-born offspring of wild-trapped individuals (and thus had known parents). The selection procedure was a combination of between- and within-family selections. Litter size records were collected from generations 1-5 and birth size records were taken from generations 2-6. 1025, 874, 863 and 83 females had 1, 2, 3 and 4 litters respectively.
Animals were housed in standard mouse cages and maintained in a 16 L:8D photoperiod at 20 ± 2°C. Wood shavings and hay were provided as bedding, while food (labfor 36, Lactamin AB, Stockholm, Sweden) and water were available ad libitum. Pregnant females were checked once a day for parturition. After parturition, the birth size was measured using an electronic scale (± 0.01 g) and head width with a stereomicroscope.
The use of the animals adhered to ethical guidelines for animal research in Finland (The Finnish Act on Animal Experimentation, 62/2006) as well as the institutional guidelines. The study was conducted under permissions from the National Animal Experiment Board.
Statistical significance of fixed factors was initially studied with univariate models using SPSS statistical software (version 18.0). All random effects were excluded except for the residual and 'individual' for the litter size. Fixed effects fitted for the birth mass were the number of parity (four classes) and sex (two classes); for head width, the factors were sex and measurer (ten classes); for litter size, the factors were parity, age (in days) nested as a linear covariate within the parity. Alternatively in the univariate analysis, the size of the birth litter was used as a covariate for birth mass and head width to estimate variance components after the effect of litter size was removed. The effect of inbreeding on the studied traits was found to be statistically non-significant.
The (co)variance components were estimated with the average information Restricted Maximum Likelihood (REML) -procedure using ASReml version 2.0 [29, 30].
The following linear models were used:
Birth mass and head width:
In which y
are the vectors of phenotypic observations for birth mass/head width and litter size; b
are the vectors of fixed effects for birth size and litter size; a
and m are the vectors of direct additive genetic effects for birth size, litter size and maternal additive genetic effects for birth size; n and q are the vectors of maternal permanent effects for birth size (non-genetically determined effects that the mother has on all her offspring in all litters) and permanent individual effects for litter size (non-genetic effect on sizes of all litters of one female); c and k are the vectors of litter effects for birth size (environmental effect common for all the offspring in one litter) and temporary environmental effect for litter size (described later); finally, e
are the vectors of residuals for birth size and litter size respectively. Fixed and random effects are fitted to individual records by incidence matrices X
M, N, Q, L and K.
and the expectations of random effects are zero.
Variances and covariances:
In which A and I are the numerator relationship matrix and identity matrix respectively. σ2
a2 and σ2
m are the direct additive genetic variance for birth size and litter size and maternal additive genetic variance for birth size; σ2
n and σ2
q are the permanent environmental maternal variance for birth size and permanent individual variance for litter size; σ2
c and σ2
k are the common litter variance for birth size and temporary environmental variance for litter size; σ2
e1 and σ2
e2 are the residual variances for the birth size trait and litter size. σa1a2, σa1m and σa2m are the additive genetic covariances between corresponding genetic effects; σnq is the covariance between permanent maternal effects for birth size and permanent individual effects for litter size; σck is the covariance between common litter effects for birth size and the temporary environmental effect for litter size. In the univariate models, direct-maternal genetic covariance for birth size traits was set to zero because models including covariance did not converge. In the bivariate analysis, the residual covariance was set to zero because the dataset was composed of two separate parts: one containing records for litter size and the other for birth mass and head width. However, due to the functional relationship between litter size and offspring size, residual variation in the former is presumably correlated with the common litter environment of the latter. For that reason, actual residual variance of litter size was fixed to 0.01, and a dummy 'temporary environmental effect' was fitted for litter size in the bivariate models which was then allowed to correlate with the fitted litter effect for offspring. Without this temporary environmental effect for litter size, the correlation between permanent environmental effects tended to converge outside the parameter space.
Estimates of the ratios of variance components to the total phenotypic variance were calculated as: (heritability) h2 = Va/Vp; (maternal heritability) m2 = Vm/Vp; (maternal permanent environmental effect) n2 = Vn/Vp; (common litter effect) c2 = Vc/Vp; (permanent individual effect) q2 = Vq/Vp, in which the total phenotypic variance (Vp) was determined as a sum of the appropriate (co)variance components.
Statistical significance of the genetic and environmental covariances was assessed with Log Likelihood ratio tests by comparing a full model with a model in which tested covariance was constrained to zero.