J.D. van der Toorn (1997,1998)
A survival guide to survival rates
Updated January 2017

Table of contents

Introduction
Some definitions
Mathematical background
Presenting the data
Some real numbers
An example: The survival rate of the Särkänniemi dolphins
Average longevity vs. survival rates
Conclusion
Hints and tips
References
Appendix: Confidence intervals
Paper history
Survival rates toolkit

Average longevity vs. survival rates

In online discussions on the BBC Animal Zone web site and on the alt.animals.dolphins newsgroup, some people claimed that the life expectancy of dolphins in captivity was only 5.3 years. Apparently, that number came from William Johnson's book "The Rose-tinted menagerie" (1990). In chapter 4.1, Johnson states:
"According to statistics provided by the UN's Food and Agricultural Organisation (FAO), dolphins in the wild can live up to 30 years, but their average life expectancy in captivity is a mere 5.3 years. "

However, this is a serious misquote of the original report. It illustrates a lack of understanding of the subject matter, which is not uncommon in discussions about survival. To clarify the issue, let's examine the original FAO paper (Cornell and Asper, 1981) This paper does not deal with life expectancy, but with average longevity up to 1976. This has virtually no relationship with life expectancy. Basically what the authors did is tally up the time survived in captivity up to 1976. They added the life span of animals that were dead before that date (real longevity of those animals) and the ages of animals in captivity that were still alive at the time. So an animal born in 1975 would count for one year only, even though that particular animal might even be alive today, in which case its longevity would exceed 24 years.

Part of the aim of the paper was to compare numbers of animals brought or born into captivity prior to the Marine Mammal Protection Act (MMPA) and the so-called post-MMPA animals. A direct quote from the paper:
"Less than four years have passed since the implementation of the Act, therefore the maximum longevity of animals collected after the Act would be 3 years and 8 months. Most post-Act animals have not been in captivity for so long, and many have only been recently acquired".

The method of calculating life expectancies (or actually survival rates, from which life expectancies can be derived) is quite different from the methods used in the FAO paper and comparing the numbers from this paper to life expectancies from other papers is invalid.

DeMaster and Drevenak (1988) say, with respect to the average number of days survived in captivity (which is the same as the average longevity mentioned above):
"However, these statistics are of no real use in evaluating the husbandry record of the public display industry unless the entire cohort of animals that are used in estimating this statistic is dead. When this is not the case, this method of calculating longevity is very sensitive to the proportion of animals that have been recently acquired. In this study most of the animals included in the marine mammal inventory were not dead. Because some animals have survived in captivity for over 30 yr, it is not possible to do a meaningful analysis of the data at this time with this statistic because of the limited number of animals that could be used in the analysis".

To show the difference between the methods consider the following hypothetical case:

To demonstrate the difference between the methods even further, lets vary the number of deaths occurring on day 730

Nr of deaths Average longevity Survival rate Life expectancy
0 2 yrs undetermined undetermined
1 2 yrs 0.951 19.98 yrs
2 2 yrs 0.904 9.99 yrs
3 2 yrs 0.861 6.66 yrs
4 2 yrs 0.819 5.00 yrs
5 2 yrs 0.779 4.00 yrs
6 2 yrs 0.740 3.33 yrs
7 2 yrs 0.704 2.85 yrs
8 2 yrs 0.670 2.50 yrs
9 2 yrs 0.637 2.22 yrs
10 2 yrs 0.606 2.00 yrs

As you can see, the number of deaths has no influence on the average longevity in this case. The number remains the same, no matter how many deaths occurred. However, the survival rate and the derived life expectancy go down drastically if more deaths occur. Only when all animals in the sample are dead at the end of the sample period do the average longevity and survival rate yield match.

In short, the average longevity and the life expectancy are vastly different. They cannot and should not be compared. If you want to compare the captive population with wild populations, always check the original references to make sure you compare the same parameters.

Conclusion

Now that we have examined the terminology involved and have seen some published data, let's examine some examples of flawed or incomplete representations, both from anti-captivity organizations and from the captive display industry.

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Hints and tips

When you get involved in discussions about marine mammal survival, keep the following things in mind:


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References

Barlow, J. and P. Boveng (1991)
Modelling age-specific mortality for marine mammal populations.
Marine Mammal Science 7(1): 50-65
Cornell, L.H. and E.D. Asper (1981)
A census of captive marine mammals in North America
In Mammals in the seas, volume III. General papers and Large Cetaceans, pp. 137-150.
FAO Fisheries Series No.5 volume III
Food and Agriculture Organization of the United Nations
DeMaster, D.P. and J.K. Drevenak (1988)
Survivorship patterns in three species of captive cetaceans.
Marine Mammal Science 4(4): 297-311
Dolphin Project Europe (1996)
Captivity Fact Sheet. Dolphin Project Europe Newsletter #2
This Newsletter used to be online. However, the Dolphin Project Europe web site and the web site of the International Dolphin Project, which also hosted the newsletter have disappeared. There now is a new web site for the Dolphin Project, but the Newsletters are no longer available
Dolphin Quest (1999)
Dolphin Quest - Frequently Asked Questions
Online at: http://www.dolphinquest.org/faqa.html
Duffield, D.A. and R.S. Wells (1991)
Bottlenose dolphins: comparison of census data from dolphins in captivity with a wild population.
Soundings 16(2): 11-15
Fad, O. (1996)
The killer whale (Orcinus orca).
Soundings 21(2): 18-32
Hersh, S.L., D.K. Odell and E.D. Asper (1990)
Bottlenose Dolphin Mortality Patterns in the Indian/Banana River System of Florida.
In S. Leatherwood and R. R. Reeves, eds.
The Bottlenose Dolphin, pp. 155-164, Academic Press, London, San Diego
Johnson, W.J. (1990)
The rose-tinted menagerie
Iridescent Publishing
Online at: http://www.iridescent-publishing.com/rtmcont.htm
Minnesota Zoo (1999)
Discovery Bay - 20 Questions commonly asked of our dolphin trainers
Online at: http://www.wcco.com/partners/mnzoo/dolphinfaq.html
Olesiuk, P.F., M.A. Bigg and G.M. Ellis (1990)
Life history and population dynamics of resident killer whales (Orcinus orca) in the coastal waters of British Columbia and Washington state.
in P. S. Hammond, S. A. Mizroch and G. P. Donovan, eds.
Individual recognition of cetaceans: use of photo-identification and other techniques to estimate population parameters, pp. 209-243. International Whaling Commission, Cambridge
Sagan, C. 1996.
The demon-haunted world. Science as a candle in the dark.
Headline Book Publishing, London. 436 pp.
Small, R.J. and D.P. DeMaster (1995)
Survival of five species of captive marine mammals.
Marine Mammal Science 11(2): 209-226
Small, R.J. and D.P. DeMaster (1995a)
Acclimation to captivity: A quantitative estimate based on survival of bottlenose dolphins and California sea lions.
Marine Mammal Science 11(4):510-519
Temte, J.L. 1993.
The Marine Mammal Inventory Report: independent verification of a captive marine mammal database.
Marine Mammal Science 9(1): 95-98
WDCS (Whale and Dolphin Conservation Society) (1999)
Whales in captivity
Online at: http://www.wdcs.org/wdcs2/captive/facts/whales.html
Wells, R.S. and M.D. Scott (1990)
Estimating bottlenose dolphin population parameters from individual identification and capture-release techniques.
In P. S. Hammond, S. A. Mizroch and G. P. Donovan, eds.
Individual recognition of cetaceans: use of photo-identification and other techniques to estimate population parameters, pp. 407-415. International Whaling Commission, Cambridge
York, A.E. (1994)
The population dynamics of northern sea lions, 1975-1985.
Marine Mammal Science 10(1): 38-51

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Appendix: Confidence Intervals

Confidence intervals for the DSR can be calculated from a binomial distribution, where the binomial parameter is set to (1-DSR) or DMR. Drevenak and DeMaster (1988) used a method of interpolation to get the confidence intervals. However, the confidence interval can be calculated from the Standard Error (SE), which can be calculated directly. The Standard Error for a binomial distribution (as a proportion rather than absolute numbers) can be calculated as:

Substituting the standard parameters with the variables we use in the DSR calculations we get:

The confidence interval is then defined as:

(DSR - 1.96 * SE) <= µ <= (DSR + 1.96 * SE)

where µ represents the real value of the DSR.

For more information see:

Sokal, R.R. and F.J.Rohlf (1995)
Biometry, 3rd edition. The principles and practice of statistics in biological research.
W.H. Freemand & Company, N.Y.

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Paper history

This paper has been presented at:

A formal version has been published in:
Marine Mammals: Public Display and Research 3(1): 27-38.

This online version has been updated in October 1999. The following changes were made:

On January 28th, 2017 the following changes were made:

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