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Lee et al: Supplementary Materials and Methods
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Demography: A population of African elephants, ranging over 8000 km2 of the Amboseli basin
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ecosystem in southern Kenya, has been observed continuously since 1972. Animals have individually
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known life histories (n = 2652), documented through continuous censuses and sightings. Individuals
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were recognised from distinctive ear veins, notches and holes [1]. Birth dates were known (±1 day to
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± 6 mo) from 1972 (76% of the current population). Older individuals were aged from rates of
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maturation, historical photographs, and tooth ages at death [1]. Cause of death was coded as
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human-related or natural / unknown and a death date determined from last known sighting or
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carcase location. Mortality is age and sex-specific in this population, but the age profiles have not
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changed enough over the 40 years considered here [1] to affect overall mortality rates.
Environmental experience used monthly rainfall, which was highly seasonal and bimodal, in
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an annual cycle of October to September to determine a drought index of the number of months
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with < 20 mm rain relative to total annual rainfall *100 [2] (Dry Season Intensity, DSI). The Drought
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Index was used rather than NDVI [3] since rainfall and demographic sequences start in 1968 well
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before high-resolution satellite photographs. In this sample, years with a DSI > 2.5 were coded as
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drought years, typically reflecting >5 months of no rain and less than 200 mm of total rain in the year
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(mean annual rainfall = 322 mm). Based on calf birth dates, they were assigned to drought
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experiences if they had one annual cycle with drought within their first two years of life, or for
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gestation, if either the first or second year of gestation fell within an annual drought cycle.
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Maternal quality: Elephant females have an age-based dominance hierarchy [4,5]; the oldest female
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is the leader or matriarch of a family. Therefore a key feature of maternal quality is her age. Age is
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also a proxy for size since elephant females continue to grow in height until ~30 years of age (see
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Supplementary Fig. 1). Maternal age was determined for each calf birth, and coded by number of
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previous births experienced (parity). The range of maternal ages overlapped considerably for each
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category of maternal parity (parity First: 8.91-17.7 years; parity Second: 10.34-26.1 years; parity 3+:
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13.0-66.0 years; n = 2202).
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Age at first reproduction: 455 females with age known at <6mo accuracy commenced reproduction
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during the study allowing determination of age at first-known parturition, since conceptions that did
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not result in a live birth may have been missed. Sperm production commences at 10-12 when males
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are half the size of an adult female, resident with their natal families [6], unable to mate effectively,
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and unable to compete with other larger males [7]. Independent males under 25 are highly sexually
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active [8], but have a lower probability of paternity than do full musth males where musth
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represents the annual period of male hormonal and sexual activity [7,9]. First transitory signs of
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musth can last from several hours to several days and could be easily missed, so first musth used
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here represents males observed with clear musth signs in proximity to oestrous females and/or
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engaging sexual activity (testing females, attempting to mount; e.g. [7]).
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Measures of size: We have photogrametically assessed the shoulder height of individual elephants
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since 1991 [10], and hindfoot length from footprints since 1976. There were 1495 measures on 431
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individual males and 436 individual females. Males contributed 442 foot lengths and 387 shoulder
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heights (with 101 simultaneous measures of both). Females contributed 283 foot lengths and 616
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shoulder heights (130 simultaneous measures of both). There were 86 repeated measures of heights
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for males and 226 for females (range 2-4), and 193 foot lengths for males and 90 for females (range
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2-7). These repeated measures were at different ages, and samples sizes were unbalanced between
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foot length and shoulder height, as well as for other factors.
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We fit nonlinear curves (Supplementary Fig. 1) using SPSS v18 (IMB Corp, Chicago) to size
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measures using asymptotic growth curves for foot length (Males, n = 442, r2 = 0.960: Foot length =
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53.7 (52.9-54.5 95%CI) – 34.64 (33.88-35.40 95%CI) * e(-0.067 (-.071- -.063 95%CI)+age); Females, n = 270, r2 =
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0.964: Foot length = 42.8 (42.1-43.4 95%CI) – 24.77 (23.92-26.91 95%CI) * e(-0.103 (-.112 - -.114 95% CI)+age))
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and von Bertalanffy curves for shoulder height (Males: n = 378, r2 = 0.918: Shoulder height = 301
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(294-308 95%CI) * (1 – e–.07663 (.699-.0833 95% CI) *(age+5.13 (-5.71 - -4.54 95%CI))); Females: n = 617, r2 = 0.865:
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Shoulder height = 235 (232 – 237 95%CI) * (1 – e–.12596 (.1170-.1349 95% CI) *(age+4.15 (-4.63 - -3.67 95%CI))).
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Residuals from these sex-specific nonlinear curves (relative height or relative footlength)
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were used to model the impact of covariates (maternal parity, drought experience, gestational
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environment and sex) on growth. We visualized these effects (Figure 1 of the main paper) by fitting
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new von Bertalanffy curves using nonlinear least squares in R nlme 4 package for R version 3.1-89
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[11], using the parameters from separate-sex growth models (above) as starting values. We first
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subdivided the data by sex, and then tested whether parameters differed across drought and birth
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order by fitting a nonlinear mixed effects model with the factor of interest as a random effect. We
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used the coefficients of these models to plot the curves in Figure 1.
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We obtained qualitatively similar results for all modeling approaches: the inclusion or
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exclusion of non-significant terms or random effects had little effect on the outcome of our analyses,
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nor did varying the starting parameters of our nonlinear regressions. We included figures based on
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the parameters of nonlinear regressions (0-30 years), but the residual values used for hypothesis
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testing were based on a larger age range (0-70 years) that was more representative of growth over
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the lifespan.
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References:
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1.
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Amboseli, Kenya. J. Zool. 255, 145-156.
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Moss, C.J. 2001 The demography of an African elephant (Loxodonta africana) population in
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January, Anaheim, CA, pp. 179-184. Boston: American Meterological Society.
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Pettorelli, N., Vik, J.O., Mysterud, A., Gaillard, J.M., Tucker, C.J. & Stenseth, N.C. 2005 Using the
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satellite-derived NDVI to assess ecological responses to environmental change. Trends Ecol Evol
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Archie, E.A., Morrison, T.A, Foley, C.A.H., Moss, C.J. & Alberts, S.C. 2006 Dominance
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Wittemyer, G. & Getz, W.M. 2007 Hierarchical dominance structure and social organisation in
African elephants, Loxodonta africana. Anim. Behav. 73, 671-681.
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Lee, P.C. & Moss, C.J. 1999 The social context for learning and behavioural development among
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wild African elephants. In Mammalian Social Evolution (eds. H.O. Box & K. Gibson), pp. 102-125.
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Cambridge: Cambridge University Press.
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Poole, J.H. 1987 Rutting behaviour in African elephants: the phenomenon of musth. Behaviour
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Rasmussen, H.B., Ganswindt, A., Douglas-Hamilton, I. & Vollrath, F. 2006 Endocrine and
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behavioral changes in male African elephants: linking hormone changes to sexual state and
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reproductive tactics. Horm. Behav. 54, 539-548.
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Hollister-Smith, J., Poole, J.H., Archie, E.A., Vance, E.A., Georgiadis, N.J., Moss, C.J. & Alberts,
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S.C. 2007 Age, musth and paternity success in wild male African elephants, Loxodonta africana.
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Anim. Behav. 74, 287-296.
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10. Lee, P.C. & Moss, C.J. 1995 Statural growth in known-age African elephants (Loxodonta
africana). J. Zool. 236, 29-41.
11. Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D. and the R Development Core Team. 2008 nlme:
Linear and nonlinear mixed effects models. (R package version 3).
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Supplementary Figures
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Supplementary Figure 1: Growth curves for (A) Shoulder height (cm) and (B) foot length (cm)
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with loess curve fit for males (triangles) and females (circles) shown. All data plotted. Analyses
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used the relative-size-for-age derived from individual residuals from mean non-linear regression
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curves fitted for age and sex.
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Supplementary Figure 2: (A) Cumulative survival probability over 40 years for calves which
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survived to 12 months of age, comparing between firstborn and not firstborn; (B) Comparing
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drought and no drought survival. Calves under 12 months were excluded to remove the
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majority of the effects of early mortality on life expectancy.
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