where Y _ij is the dependent variable, B ₀ is the overall intercept, S _i is the random effect of the i ^th study, B ₁ is the overall regression coefficient of Y on X, X _ij is the value of the continuous predictor variable (fat intake, fixed effect), b _i is the random effect of the experiment on the regression coefficient of Y on X, and e _ij is the residual error. The data were weighed with the square root of the number of animals used in each treatment using the WEIGHT statement.

Twenty two out of 64 treatments corresponded to control diets without added fat, and 16, 16 and 10 corresponded to diets enriched in oleic acid, linoleic acid and α-linolenic acid, respectively. Supplementary lipids were fed as free oils (30 treatments) and oilseeds (12 treatments). Supplementary fat was (mean ± SD and range) 3.43 ± 1.420 [0.80-6.50] % dry matter, or 74.3 ± 40.40 [15.0-207.0] g/d, or 1.30 ± 0.630 [0.25-3.45] g/kg body weight. Experiments carried out with dairy goats to investigate the effects of unsaturated plant lipid supplementation on milk fat FA contents are limited in number, compared with those carried out with dairy cows. Because of the few number of available treatments in our meta-regression, it was not possible to study the effects of the type of plant lipids supplied (i.e. rich in oleic, linoleic or α-linolenic acids) or the fat sources used (oils vs. oilseeds). On the other hand, the interference due to diet composition, if any, should be minimal because there were no differences between NOLIP and LIP treatments, except for the extra fat added (Table 1).

In the present study, the contents of C4:0 and C6:0 in goat milk fat were not reduced with increasing daily fat intake. Furthermore, the negative effects of plant lipid intake on the FA synthesized de novo in the mammary gland were clear from C8:0 upwards. Indeed, the slope of the C10:0 equation was ten-fold higher than that of the C8:0 equation (Table 2). Although there are not published meta-regressions that allow a direct comparison, in several experiments carried out with dairy cows (Mustafa et al., 2003; Collomb et al., 2004; Akraim et al., 2007; Liu et al., 2008; Chilliard et al., 2009) and ewes (Mele et al., 2006; Zhang et al., 2006; Gómez-Cortés et al., 2008; Hervás et al., 2008, Bodas et al., 2010) fed similar amounts of unsaturated plant lipids (between 1 and 3 g/kg body weight), the negative effects on de novo synthesized FA are clearly observed from C6:0 and C8:0. Also, Glasser et al. (2008) found out that lipid supplementation to dairy cows, resulting in an increase of FA with 18 atoms of carbon in duodenal flow, linearly decreased the yield of C4:0 to C16:0 in milk. These differences suggest that dietary unsaturated plant lipids could have dissimilar effects on rumen digestion or lipid mammary metabolism in dairy cows, goats and ewes, as pointed out by Chilliard et al. (2003) and Sanz-Sampelayo et al. (2007).

On the other hand, Hansen et al. (1984), working in vitro with goat mammary cells, proposed that a greatly enhanced supply of long chain FA could inhibit the incorporation of de novo synthesized FA into triacylglycerol, owing to competition for the diacylglycerol acyltransferase, which in turn would decrease de novo synthesis of FA. Bernard et al. (2009a) found that the increase in long chain FA captured by the mammary gland reduced the activity of the enzymes involved in FA synthesis in the udder. Furthermore, it has been previously observed, working in vitro with mammary cells, that lowering the ratio acetyl-CoA carboxylase to FA synthetase modifies the pattern of synthesized FA towards those of shorter chain (Bauman & Davies, 1974). In agreement with that, the values of the slopes were increasingly higher in the regression equations obtained in the present work for C8:0, C10:0, C12:0, C14:0 and C16:0, to such extent that the value of the slope in the C16:0 equation was four-fold higher than the average of the slopes in the C10:0, C12:0 and C14:0 equations (Table 2, Fig. 1), i.e. the longer the chain of the saturated milk FA, the greater the negative effect of the intake of high quantities of unsaturated plant lipids. On the other hand, from the equations in Table 2, it was calculated that the average contents of medium chain saturated FA in milk fat were lowered more than 60% in the treatments with the highest fat intakes compared with no added lipid ones. Since medium chain saturated FA consumption is considered a risk of cardiovascular disease in people (Ulbricht & Southgate, 1991), the marked reduction of their content in the milk fat is positive from the point of view of human health.

Linear increases in the milk fat contents of both C18:0 and C18 UFA due to the increments in daily fat intake (Table 2, Fig. 1), can be explained by the higher dietary supply of long chain unsaturated FA. Any unsaturated FA of 18 atoms of carbon present in the rumen can be a source of stearic acid through biohydrogenation, thus increasing the availability of preformed stearic acid to the udder. Again, the increase of C18 UFA contents in milk fat was likely due to dietary unsaturated FA that escaped unchanged from the rumen, although in the case of oleic acid, it could be also due to Δ-9 desaturation of stearic acid in the mammary gland (Chilliard & Ferlay, 2004). From the equations in Table 2, it can be calculated that the increments of C18:0 and C18 UFA contents in milk fat as daily fat intake increased did not account for the lessening of medium chain saturated FA contents, which indicates that the contents of other FA, probably cis and trans mono- and polyunsaturated FA from rumen metabolism of dietary FA, were also increased in milk fat in response to plant lipid supplementation (Chilliard et al., 2007).

In conclusion, the meta-regression carried out in this work allowed to obtain quantitative relationships between the amount of unsaturated plant lipids consumed by dairy goats and the changes in the contents of some milk FA. Our results corroborate that dietary unsaturated plant lipids have a more pronounced negative effect on medium chain saturated FA contents as their chain length increases. The milk fat contents of C18:0 and C18 UFA were increased as daily fat intake rose, but the increments observed did not account for the lessening of medium chain saturated FA contents.