Populations and experimental design
To sample the genetic variance present in field populations, we caught eighty zebra finches from the wild and then conducted a partial cross-fostering experiment [42,49], under standardised laboratory conditions. Zebra finches were caught between August 1998 and February 1999 using mist nets at sites near Alice Springs and Townsville, Australia. Twenty birds of each sex were collected from each site, and transported by plane. For the breeding experiments, birds were kept outdoors in two large free-flight breeding aviaries at the University of Queensland. Each aviary housed twenty pairs of finches, which were introduced at the same time and allowed to form pairs naturally. All pairs bred during the course of this experiment. Ad libitum food and water were provided during the study period, including fresh green material. Birds from the two collection sites were housed separately, but offspring were cross-fostered between aviaries.
A reciprocal partial cross-fostering design was used to maximise the opportunity to estimate maternal and non-additive genetic components of variance [42]. For each reciprocal cross-foster event, the two nests between which chicks were transferred was referred to as a 'block' of nests. Broods typically consisted of four offspring, with two offspring being transferred between a pair broods. Broods within a block were matched with respect to hatching date and clutch size. Chicks were selected randomly for cross-fostering except for 'runts', which were not cross-fostered and always died before measurement. The identity of individual chicks was monitored by clipping their downy head-tufts until they were large enough to carry individually-numbered leg bands. Offspring were cross-fostered immediately after hatching, and body condition and immune response were measured 17 days later.
Measurement of traits
The element of immunocompetence that we measured was experimentally-induced T-lymphocyte cell-mediated immune response, an acquired component of the avian immune system[18]. We induced a cell mediated immune response through intradermal injection of phytohemagglutinin-P [15]. For each bird, 0.1 mg of phytohemagglutinin-P in 0.02 ml of phosphate buffered saline was intradermally injecting the right wing web, with 0.02 ml of phosphate buffered saline being injected into the opposite wing web as a control. The thickness of each wing web was measured at the injection site both immediately before and 24 hours after the injections. Twenty four hours is the standard reaction period in avian studies and is the point at which the swelling is typically maximum [15]. Measurements were taken three times to the nearest 0.001 mm using a digital micrometer and 'before' and 'after' averages were calculated for each wing. We then calculated the swelling for each wing, which was the difference between the 'before' and 'after' averages. Finally, cell-mediated immune response was calculated for each individual as the difference in swelling between the phytohemagglutinin-P injected wing and the control wing.
In this study body condition is defined as, and was measured as, the residual value from the regression of body mass on tarsus length [46]. To enhance the clarity of our writing we refer to this measure throughout this study as an index of body condition, although the reader should keep in mind that this index is derived from an estimate of residual body mass. Body mass was measured to 0.01 g using a Petit Precision balance (model MK-200 200 g × 0.01 g). Tarsus was measured to the nearest 0.5 mm using digital callipers. For parental individuals, all measurements were taken immediately before they began a breeding cycle.
Genotype-environment interactions
Because we collected birds from two different sites, we tested for possible genotype-environment interactions for our indices of both immune response and body condition. A two-way factorial ANOVA comprising nest of origin, nest of rearing and the interaction term for each block of nests was used [49-51]:
Zijkl = μ + Pi + Mij + Nik + Iijk + eijkl (1)
where, Pi = average effect of the ith cross-fostered block of nests, Mij = direct effect of the jth (genetic) mother within the ith block (j = 1 or 2), Nik = kth (unrelated) nurse within the ith block (k = 1 or 2), Iijk = M × N interaction within the ith block, and eijkl = residual error for the ith offspring of the jth mother raised by the kth nurse within the lth block of nests.
The Iijk term of Eq. 1 tested for the presence of a genotype-environment interaction in this experiment as nest of origin also represented genetic population of origin and nest of rearing also represented the population of rearing. Significance of nest of origin (Mij) and nest of rearing (Nik) was tested using the interaction term (Iijk) as the error, type III sums of squares for unbalanced designs. In all genetic models genetic relationships were inferred on the basis of the male and female providing care at the nest in question, as extra-pair paternity in zebra finch colonies is low (2.4% of chicks) [52].
When using individuals from two different populations there is also the risk that such populations could differ with respect to the parameters under study. Specifically, if the populations differed with respect to both traits then pooling individuals from the two populations might generate spurious covariance between the traits. It is important to note here that the populations need to differ for both traits and not just one of them. This is because, if populations only differ with respect to in one variable, this would just increase variation along a single axis. To assess these possibilities we therefore tested for differences between the source populations in both the phenotypic means and breeding values of our indices of both immune response and body condition.
Genetic covariance
We used two related methods to test for a genetic correlation between our indices of immunocompetence and body condition. To facilitate comparisons with other studies, we first used the standard method for analysing cross-foster experiments, which is based on using offspring values alone [49]. We used BLUP methodology to calculate breeding values [49] and plotted these against each other to visualise the pattern of covariance. However, analyses based on full-siblings alone may lead to biased estimates of additive genetic components since pre-fostering maternal effects and dominance genetic variance cannot be partitioned out from additive genetic effects [49,53]. The confounding of genetic and environmental factors may be of particular concern in birds, where the egg environment may provide a source of direct maternal effects [20].
To avoid the potential problems associated with genetic estimates based on comparisons between full-sibs alone, we used an under-utilised second method based on a mixed model [42] to test for a genetic correlation. An important advantage of this type of model is that it allows both offspring and parental trait values to be used to distinguish a number of sources of variation, thereby enabling the separation of additive genetic variance from dominance genetic variance and direct maternal effects [42,49]. The degree of similarity between ten types of relatives (Table 1) was then used to estimate six genetic and non-genetic causal components contained in each of these observational components, which are displayed in the design matrix X (Table 2).
The observation vector y comprised ten observational components of variance (yi) that were estimated by the various methods listed in Table 1. All components were computed using methodology taken directly from Riska et al. [42], with the exception of y9. The estimation of the direct-maternal additive genetic covariance which is isolated by observational component 9 has been the source of some confusion in the literature. Rutledge et al [54] first proposed σAOAM could be estimated using the interaction term in (1), which more recently was also advocated as an appropriate way of estimation in Lynch and Walsh (1998). However, this method of estimation was subsequently shown to be incorrect [55,56]. Riska et al [42] outlined that component 9 could be estimated in another two equivalent ways, but we did not find the exact numerical agreement between these two methods suggested by these authors (unpublished results). We therefore used an established alternative method for estimating component 9 described by [55,57], which uses the difference between the covariance between full sibs raised by different nurses, and the covariance between unrelated sibs raised by the same nurse. We note that a limitation of the Riska et al [42] approach is that using the same mean squares for the estimation of different causal components generates covariance between the estimates which is not accounted for in the model as implemented either by Riska et al [42,55] or here (i.e. the off-diagonal elements of the V matrix are set to zero, see below). By using the estimation method of component 9 employed here, this potential problem is likely to be exacerbated as the estimate of component 9 is a linear combination of the mean squares used in other observational components (5 and 6). Nevertheless, component 9 as estimated here has an established interpretation, and facilitated the isolation of the important σAOAM causal component.
Variances of the observational components were used as the diagonal elements of the square matrix V, with off-diagonal elements all zero. To obtain variances for each observational component [49] for components 1–4:
VAR(σ2) = (VAR(A) VAR(B) + COV(A, B)2) / (N) (2)
where A and B represented the two kinds of individuals whose covariance is being estimated and N is the number of bivariate observations. The variance of components 5–10 were estimated as weighted sums of the variances of the appropriate mean squares, where the variance of a mean square is given by (Ref [49], equ. A1.10c):
VAR(σ2) = (2MS2) / (N + 2) (3)
in which MS represents the mean square of the term of interest and N is the number of blocks. The causal components of variance were estimated as elements of the vector:
b = (X'V-1X)-1X'V-1y (4)
with covariance matrix:
S = (X'V-1X)-1. (5)
where the square root of the corresponding diagonal element of S was used to estimate the standard error of b. Phenotypic variance was estimated as the sum of the elements of b and its corresponding standard error approximated by the square root of the summed diagonal elements of S.
Estimation of the genetic correlation between our indices of body condition and cell-mediated immune response level required all observational components to be estimated as cross-covariances [58]. Cross-covariances were estimated as the product of the values of our indices of body condition and immune response for each individual and the sums of products partitioned according to the source of variation (Falconer 1981). The variances of these cross-covariances (used as the diagonal elements of the square matrix V) were determined by calculating separate variances of cross-covariances for (i) our index of body condition in parents and our index of immune response in offspring, and (ii) our index of immune response in parents and our index of body condition in offspring. The mean was then taken of these two variances of cross-covariances. The additive genetic correlation (rA) and an estimate of its standard deviation were calculated using equations 19.2 and 19.4 in Falconer [58], respectively. The proportion of additive genetic variance in our index of body condition explained by genetic variation in our index of immune response was then calculated as the square of the genetic correlation [43].
Authors' contributions
DJG helped to design the project, collected animals from the wild, conducted all crosses and measurements, performed statistical analyses, and helped to write the paper. MWB helped with the statistical analyses and the writing of the paper. IPFO helped to design the project, collect animals, and write the paper. All authors read and commented on drafts of the manuscript, and approved the final manuscript.
Acknowledgements
We thank R. Brooks, C. Godfray, F. Hausmann, L. Kruuk, T. Price, S. Scott, R. Whitney and three anonymous referees for their help; the Australian Research Council for funding; the University of Queensland for ethical permission; and the Northern Territory and Queensland governments for collection permits.
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