Testing the model

Figure 3.3 a-f presents the median feeding times over infant age for each of the three troops. Data are only used from the first 12 months of the infant's life, as by this stage, mean time on the nipple (assumed to reflect intensity of lactation) is only 4.98% (sd=8.67) and the infant is assumed to be providing most of its own nutritional requirements. Sanple sizes in each graph are small and include data from mothers whose infants did not survive. However, it can be observed that in no troop did feeding time (or feeding and foraging time) exceed the value predicted by the model more than once.

As there were no significant differences in maternal feeding time over infant age between troops (Kruskall-Wallis ANOVAs by infant age: p>0.05), data for the three troops were combined. Data from mothers whose infants died were excluded from the analysis on the grounds that the reason for infant death may be related to feeding time. The data from these females are considered in Chapter 4.

Figure 3.3: Maternal time budgets by infant age (troop medians for all mothers).

a. b.

i k l u i * 0.005 J e l u i « 0.01

PHG: using feeding PHG: using feeding and foraging

90 fW) 10 12 I 2 100 70 feeding an foraging 1 2 6 10 II 12 I n f a n t a g e ( m o n t h s ) I n f a n t a g e ( m o n t h s ) C . d.

MLK: using feeding MLK: using feeding and foraging

100 70 2 12 I n f a n t a g e ( m o n t h s ) 100 70 50 20 I n f a n t a g e ( m o n t h s ) e.

STT: using feeding STT; using feeding and foraging

I n f a n t a g e ( m o n t h s ) I n f a n t a g e ( m o n t h s )

Figure 3.4 a-b presents the combined data for all troops, with both feeding time and feeding and foraging times shown. Figure 3.4a shows the two curves of predicted feeding time based on the minimum and maximum values for A (for all troops) and infant growth rate. Figure 3.4b shows the maximum and minimum curves of predicted feeding time based on two different estimates of maternal weight. Barton (1989) estimated female weight at Chololo as 13.38 kg from the regression equation of Dunbar (1992d; then in press), and recalculation of A with m = 13.38, gives a maximum value of 6.80 and a minimum value of 5.22 (over both infant growth rates). Strum (pers.comm.) has estimated that females during this study period weighed considerably less than the PHG non-raiders at Gilgil. Therefore a second estimate of 12.00 kg was used in the equation, giving maximum and minimum values of A of 7.38 and 5.67. Thus, in Figure 3.4b, the minimum value of A was taken from the higher estimate for maternal weight and the minimum growth rate, and the maximum value of A was taken from the lower estimate of maternal weight and the maximum growth rate.

It can be seen from Figure 3.4a, that the qualitative fit between observed and predicted values is poor when only feeding time is considered but is much better for foraging and feeding times combined (although still below predicted values when A is also calculated from the two). In Figure 3.4b the fit is again poor. Although the curve calculated for feeding and foraging time when m = 13.38 does appear to approximate the data, it should be remembered that this is unlikely to be a realistic estimate of female weight. Assigning calender month feeding data to infant age (the nearest age in months), and calculating a linear regression (when infants are below 12 months in age) gives;

ft = 34.72 + 0.62i,g,; t = 1.98, df=94, p=0.05, (r^=0.04) where/, = feeding time and = infant age in months.

The regression shows that whilst feeding time increases over age, the coefficient of the slope is small. As the model of maternal time budgets uses a power relationship to

Figure 3.4a: Maternai time budgets by infant age (with minimum and maximum values o f A).

feeding and foraging feeding 100 m a x . a n d m in . e s tim a te s d elta i= 0.005, m = 1 3 .0 1 . A = 5 .3 3 d e lta i= 0 .0 1 , m = 1 3 .0 1 , A = 6 .9 5 m oving (U e so cial resting 2 o

f

Figure 3.4b: M aternai tim e budgets by infant age (u sin g alternative fem ale w eigh ts).

feeding feeding and foraging

100 _{m ax. a n d m in.}

c.sti m ales delta i=0.005, m = 13.38, A =5.22 — delta i=0.01, m= 12.00, A=7.38 90 moving 80 70 social 60 resting 50 40 30 20 _{feed in g} 10 0 B irth 1 2 3 4 5 6 7 8 9 10 11 12

Infant age (m onths)

T able 3.4: S a m p le sizes fo r F ig u re 3.4.

m o n th 1 2 3 4 5 6 7 8 9 10 11 12

calculate feeding time, a power model was fitted to the data, where;

f = 32.07 + F = 4.94, df=94, p=0.03, (r^=0.05)

Although this gives a better fit than a linear regression, in both cases the value of r^ is very small, with infant age accounting for only 4% and 5% of the variability in feeding time for the linear and power models respectively. Neither regression model was significantly improved when using feeding and foraging time. These regressions use data pooled from all mothers and may therefore violate the assumption of independence of data points. Regressions were set for the 7 mothers with more than five months of behavioural data when infant age was less than 12 months. In no case did a power model fit individuals' data and in only 2 cases did the slope of the linear model differ significantly from zero.

The relationship shown in Figure 3.4a-b is also misleading in that it assumes that firstly, baseline feeding levels are constant throughout the year, thus confounding seasonal effects with those due to infant age, and secondly, that the value of A is constant over time. Whilst this study did not characterise individual feeding rates, several studies have shown that gross feeding time is not a good indicator of food or nutritional intake (e.g. Stacey 1986; Barton 1989; Muruthi et al. 1991). This suggests that A may vary both between groups and between individuals, and also as the nutritional quality, density and distribution of food resources changes (Dunbar and Dunbar 1988).

Feeding and foraging times have been shown to be influenced by season (see e.g. Post 1982), and data for non-lactating females suggest that they are spending more time feeding in 'wet' months and more time foraging in 'dry' months. Although this only reaches statistical significance for feeding time in STT and for foraging time in STT and MLK (Mann-Whitney: feed: PHG: z = -1.875, n=8=5, p=0.061; MLK: z = -1.469, n=6=5, p=0.142; STT: z = -3.289, n=6=5, p=0.014; forage: PHG: z = -0146, n=8=5, p=0.884; MLK: z = -3.421, n=6=5, p=0.0006; STT: z — -3.289, n=6=5, p=0.001), by subtracting maternal feeding time from a control or 'baseline' value each month it is possible to look

at the effect of infant age on feeding time, whilst controlling for any variation due to food availability or season and for differences between mothers due to the timing of births. Control levels were taken from the groups defined in Section 2.5.1. For MLK and PHG these were all non-lactating females in the troop, and in STT matched control pairs.

Figure 3.5 shows the median values for feeding relative to baseline for all females (sample sizes for maternal activity graphs as in Fig. 3.4). For months 1 to 6 feeding time is below baseline, whilst for months 7 to 12 feeding time rises above baseline. This relationship is similar when considering feeding and foraging time combined (see Fig. 3.6), with levels being below baseline until month 5 and then rising above baseline in month 6. In neither case is it possible to fit a significant regression model to the data.

Feeding time below baseline suggests that mothers are either having to spend more time in other activities and cannot meet the energetic demands of lactation through feeding alone, or that lactation is not as costly as has been assumed and that demands on mothers are not significantly higher than on females in other reproductive states. This analysis of maternal feeding time thus raises two separate questions: Firstly, what are the reasons behind the failure of Altmann's model to fit the data (Section 3.5)? Secondly, what are the reasons for and implications of levels of feeding below baseline in months 1 to 6 (Section 3.6)7