Distinguishing between determinate and indeterminate growth in a long-lived mammal

Study population

Asian elephants are an endangered species 51] distributed discontinuously across Southeast Asia and the Indian sub-continent. The
Union of Myanmar has the second largest wild population of Asian elephants numbering
up to five thousand individuals 54], 55], and the largest captive one, also of around five thousand elephants 54]. Of this captive population, 2700 are government owned through the Myanma Timber
Enterprise and are used for sustainable logging 52]. Not all the elephants are born in captivity; historically, elephants have been captured
from the wild to supplement the population 56] and these comprise almost half of the elephants alive today.

The logging elephants are classified as semi-captive, as there is no provisioning
or selective breeding 50]. The animals are never culled, so there cannot be selective survival based on size
that is human-driven (although there can of course be due to natural causes of death).
The elephants are released into the forest at night for up to fourteen hours to forage
at will and mate unsupervised 56], where both wild and captive bulls have access to oestrus females. Elephants work
between mid-June and mid-February with a rest period during October 57]. This working season is timed to coincide with the monsoon (July-October) and cool
(November-February) seasons, so that no work is done during the intense heat of the
dry season (March-June), when temperature-related mortality is highest 58]. Each elephant has a maximum tonnage that they move each year, and have strict limits
to daily and weekly work that cannot be exceeded – in 2010 these limits were set to
no more than eight hours a day, with a break at noon, and no more than five days of
work in a week 36].

Elephants are born weighing approximately 100 kg and standing at around 1 m. Following
birth calves remain at the heel of the mother, being exclusively dependent on lactation
until around 6 months and continuing to suckle until the age of around 3–5 years 59]. Calves become independent at the age of 5 when they are separated from the mother
and trained. From age 5 years until 17, elephants are only used for light work, becoming
part of the true working population after this. Alongside this the elephants become
reproductively mature, with bulls experiencing first musth at around the age of 15
and females beginning oestrus cycles at around 10–12 years 60]. Whilst the timing of sexual maturity is similar in males and females, the first
recorded reproduction by a female is at age 5 and the age at peak fecundity is 19 years,
followed by a slow decline 36]. In contrast male Asian elephants are unlikely to reproduce until around the age
of 25 60]. Myanmar timber elephants are defined as adults at the age of 17 and are able to
drag logs and engage in heavy work, continuing up until around 55 years old, at which
point they are retired from work 50]. Asian elephants can live for up to 80 years, and can therefore spend decades in
retirement 37]. Their reproductive careers can also span many decades 61], with reproduction declining more steeply from age 50, but mothers continuing to
give birth into their 60’s 50]. Mothers are given time off work from mid-pregnancy (at around 11 months) through
to a year after birth 56], and are then given lighter work up until the infant is weaned, at which point the
mother returns to heavier work.

Each elephant is marked with its own unique identification (ID) number, and important
life-history information is recorded in log books as dictated by law 50], 62], and includes, but is not limited to, birth origin (captive or wild), mother ID,
health information and dates of birth and death. Age of wild-born individuals is assessed
visually at capture to the nearest year using skin pigmentation, ear tears and folding,
facial concavity and size (for younger individuals) 53], 63]. These assessment measurements have shown to be particularly accurate for young elephants
64]. Any body measurements taken by vets at their two weekly health checks are also included
in these log books. This population, containing a large number of known individuals
of both sexes for whom data have been collected over time, is ideal for testing the
growth patterns of both sexes over the entire lifespan.

Data selection

Height and weight were recorded in five logging camps in Myanmar: Pyinmana, Monywa,
East Katha, West Katha and Kawlin. Weight was measured using EziWeigh 3000 scales,
and was recorded to the nearest 1 kg, whilst the other measurements were taken with
tape measures, and in most cases recorded to the nearest inch. At some camps, measurements
were taken in centimetres. As a result, all measurements were converted into centimetres
during collation of data, but are only correct to the nearest multiple of 2.54 cm
(i.e., 1 in.). In total 450 elephants aged between 0 and 71 were included in this
study, with each individual having at least one body measurement. Of these, 255 were
female and 195 were male.

In Pyinmana (n?=?72), individuals were measured monthly between December 2011 and October 2012.
Elephants were recorded cross-sectionally just once in Monywa in 2012 (n?=?74). In East Katha (n?=?73), data were collected monthly from December 2012 until the end of 2013. In West
Katha (n?=?58), monthly measurements have been taken since June 2012, with data up until March
2015 available. Kawlin (n?=?173) data have been collected monthly since November/December 2012, with records
up until April 2015 available. However, for camps where monthly measurements had been
taken, some months did not have data. Some historic height measurements from the logbooks
from Kawlin elephants, taken sporadically since 1972, were also available for use.

Statistical analyses

All analyses were conducted using R 3.1.3 65]. To test for the presence of indeterminate growth in elephants, as measured by both
their weight and height gain across age, we implemented non-linear least squares models
for each sex using the nls function, with a response variable of weight or height. We applied three commonly
used self-starting growth functions as the explanatory variable to obtain the best
fit: Gompertz, three-parameter logistic and von Bertalanffy 17], 43]. The growth function producing the best fit was selected by the coefficient of determination,
with the highest value providing the best fit. We used age in years as the input parameter.
In all models we calculated i) age at which 95 % of asymptotic weight/height was reached,
as a marker of age at growth cessation ii) proportion of asymptotic weight/height
achieved by age at weaning and independence (defined as age 5), to investigate how
much growth had taken place up to this important life history transition point, ii)
proportion of asymptotic weight/height achieved by age at sexual maturity (defined
as age 15), as an indicator of whether growth continued after sexual maturity and
could therefore be defined as indeterminate and iii) the age at which growth was most
rapid, to investigate the overall pattern of growth.

We tested each of the three growth functions in three different subsets of our dataset
as follows. First, we implemented them in captive-born individuals of known age (n?=?348). The average measurements and age of individuals from the monthly measures
available for them between 2011 and 2015 were used for this analysis, therefore historic
data for individuals were also excluded at this stage as this could give an unrepresentative
size at the average age. We produced separate growth curves for males and females,
for both height and weight as they may have different growth patterns. We then produced
additional sets of growth curves that included the wild-born and unknown origin individuals
(n?=?104) alongside the captive-born individuals using the same self-starting growth
functions, in order to compare the growth curves to those in which all individuals
have accurate age data.

Finally, we made a third set of growth curves that took into account within individual
variation and longitudinal measurements. Only captive elephants with a minimum of
five separate measurements of data (mean number of measures per individual?=?7.9)
were selected for this analysis (n?=?220 measurements from 48 individuals for height and 45 individuals for weight),
so as to have enough longitudinal measurements without reducing the sample size substantially.
We also included the historic measurements from Kawlin, providing growth data over
a much longer period (up to 43 years); as many of these measurements were taken yearly
for over up to several decades. For these curves, there was not complete growth data
across the entire lifespan of individuals to justify a fully longitudinal model and
the polynomial approach used for mixed longitudinal studies is not suited to data
that has an asymptote 66]. Instead we applied another approach for longitudinal data using the groupedData, nlsList and nlme functions from the package nlme version 3.1–120 67]. We specified ID as a grouping factor in the grouping call, and in the non-linear
mixed model the function SSasympOff was used in order to allow data to originate through points other than 0. We set
the asymptote as a random effect, allowing it to vary by ID to account for between-individual
differences.

Availability of supporting data

The data set supporting the results of this article will be made available in the
Dryad repository.

We also supply one Additional File including a table and two figures (Additional file
1).

Ethics approval

The data collection supporting this study was approved by the University of Sheffield
Ethics Committee.