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## Hippo background study.pdf

**Transboundary Species Project – Background Study**
**Hippopotamus**
**APPENDIX 2**
**Relationship between A ge and Body W eight for Hippopotamus**
Laws (1968) gives a relationship between age and body length for hippopotamus based on a
sample of 1,219 hippos (505 males and 714 females) culled in Queen Elizabeth National Park, Uganda,between 1961 and 1966. Pienaar (

*et al* 1966) give body length and weight data from a sample of 104hippo (52 males and 52 females) culled in the Letaba River in Kruger National Park in 1964. Thesetwo data sets enable the construction of a formula which predicts body weight from age.

The data of Pienaar (

*et al* 1966) were examined to see if there were any reasons why male and
female data could not be combined into a single data set. Although the regressions on the separate datasets for males and females yield slightly different results, an inspection of the figures suggest that thereis a wide overlap between the male and female body weights for any given body length. On allometricprinciples it would not be expected that animals of the same species which have same body lengthwould differ in body weight. The data were combined and a regression was used to determine thevalues of the constants in the relationship –

**Body weight (kg) = a.(Body length (cm)) b**
The regression (performed on logarithms of the data values) yielded the results of

**a** = 1.49 x 10-4

and

**b** = 2.79. Pienaar (

*et al ibid*) point out that the hippo in the Letaba were in poor condition as a

result of a drought which had affected Kruger National Park since 1962. Because of this, the regression

constants were adjusted by inspection so that the body weights predicted by the formula were closer

to the higher values in the data set rather than the central values. The final values used were

**a** = 2.5

x 10-4 and

**b** = 2.70.

Laws (1968) used von Bertalanffy’s (1938) formula for predicting body length from age but notes
that the derived values apply only to animals between the ages of 5 and 25 years old. Laws completes

the curves for the full age span (0-50 years) by simply extrapolating graphically. von Bertalanffy’s

curve has the form

**y = A(1 - e-Bt) **which describes a growth curve where adult animals achieve an

asymptotic weight. It is not suitable for hippo where adults continuing growing throughout their life.

To rectify this I have added a ‘ramp’ function to the formula.

**Body length = A (1 - e -B(Age + C ) + D.Age)**
Adult male hippo are heavier than females of the same age and Laws gives a separate von
Bertalanffy formula for each sex. I used the values given by Laws’ two formulae to generate a set ofbody lengths for males and females between the ages of 5 and 20 years. To these data sets I added thevalue of 86.11cm for the body length of hippo at birth (which is the value which gives a birth weightof 42.14kg (Smuts & Whyte 1981 p171) and the values of 360cm and 343cm as the body lengths forthe oldest males and females (from Pienaar

*et al*’s data).

Curves were then fitted according to the above formula by iterating the values of the above
constants (

**A-D**) within a spreadsheet. The results were very satisfactory and permitted a close fit

between the data and the predicted values for body length.

**Transboundary Species Project – Background Study**
**Hippopotamus**
**APPENDIX 2**
The analysis could have been left there but one feature of the fitted curves bothered me. When
body weights are derived from the two body length formulae, female hippo up to the age of 11 yearsappear to be heavier than their male counterparts(see figure opposite). Both Laws’ and Pienaar

*etal*’s data agree that adult hippo males are heavierthan female hippos of the same age and it seemsunlikely that the two curves ‘cross over’ in themanner shown. The effect is due to the bodylengths given by Laws’ formulae for female hippobetween the ages of 5 and 13 years and it seemslikely that it is an artefact of the analytic technique.

Up to a certain age, male and female hippo probablyhave identical body lengths and body weights andthe differences only start to emerge at about 10years old.

The data were re-analysed with the constraint that males and females must possess identical
characteristics up to a certain age and only diverge thereafter. This necessitated some changes to thebody length formula given on the previous page. For males to be able to grow larger than females onlyafter the given age, the ‘ramp function’ must operate independently for each sex and must only comeinto play after the given age. The revised formula is –

**Body length = A(1-e -B (Age + C)) + D(Age - E)***

**Age > E**
**E** is the threshold age after which males and females diverge and it is determined by iteration

along with the other constants. By using a logical function in the spreadsheet formula, the ramp
function can suppressed for ages less than

**E**. The constants

**A, B, C** and

**E** are assumed to be identical

for both males and females and only the slope of the ramp function (

**D**) is allowed to differ between

the two sexes. Iteration was performed by maintaining separate data sets for males and females and

examining the combined sum of squares for the differences between observed and predicted values for

both sexes simultaneously. The revised constants which come from this analysis are shown below –

The body lengths and body weights corresponding to ages 0 - 45 years are shown in

**Table 8** on

the next page and depicted graphically in

**Fig.3 **on page 4.

**Transboundary Species Project – Background Study**
**Hippopotamus**
**APPENDIX 2**
**Body Length**
**Table 8. Age-specific body lengths and weights for hippo derived in this study**
Source: http://nnf.org.na/RARESPECIES/InfoSys/additionalContent/HippoAgeWeightRelationA2.pdf

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