J.D. van der Toorn (1997,1998)
A survival guide to survival rates
Updated January 2017
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:
- on day 0, 10 animals are acquired
- two years later (on day 730) one of the animals dies which leaves 9 animals alive.
- at that same date we take our sample, so we have 10 animals which have lived 2 years upto
the sample date. The average longevity is then 2 years. (This is the method used in the FAO
paper).
- For the calculation of survival rates, we have collected 7300 animal days and we have
recorded 1 death. This leads to a daily survival rate of 0.99986 or an annual survival rate of
0.951. This translates to a life expectancy for this "population" of 19.98 years. (This is the
method used by Wells and Scott (1990) and Small and DeMaster (1995) to calculate survival
rates for the wild and captive populations).
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.
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.
- The average life span of a dolphin in the wild is 45 years; yet half of all
captured dolphins die within their first two years of captivity. The survivors
last an average of only 5 years in captivity. (Dolphin Project Europe, 1996)
This is incorrect. 45 years is the (maximum) longevity for dolphins in
the wild, not the average life span (life expectancy) (Wells and Scott,
1990). The same study showed that the Annual Survival Rate for the
Sarasota population was 0.961, which translates to a life expectancy
of about 25 years. Small and DeMaster (1995) calculated an ASR for
the captive population of 0.951, which translates to a life expectancy of
19.9 years. If the life expectancy in captivity would be only 5 years, the
associated ASR would be 0.819, which is not even close to the
measured value.
- At least 134 orcas (killer whales) have been taken into captivity from the
wild since 1961. One hundred and three (77%) are now dead (WDCS, 1999)
While this information may be correct, no conclusions can be derived from this
since no timing details are given which would allow the calculation of animal days or
years.
- Of the 103 which died, average length of survival in captivity was under six
years (range: 1 day - 27.2 years) (WDCS, 1999)
Selecting data on animals based on the fact that they are dead introduces a bias
towards the shorter lived individuals. The ones that are doing better and are still
alive are excluded from the statistics.
- Of 54 known pregnancies in captivity since 1968, only 21 calves (39%)
have survived. (WDCS, 1999)
This seems to suggest that calf survival in captivity is low. While a 39%
survival rate may seem low, it is in the same order of magnitude as wild calf survival, estimated
by Olesiuk et al (1990) at 43% for the BC population.
- Another indicator that dolphins are living as long in zoological collections as in
the world is research by Drs. Deborah Duffield of Portland State University and Randall Wells
of the Chicago Zoological Society. Their data show that the average age of dolphins in their
natural environment is similar to that of dolphins in public display facilities. This work
corroborates a study published in 1988 by DeMaster and Drevenak (Marine Mammal Science,
4:297-311, 1988) which pointed out that survival of dolphins in aquariums "may be better
than or equal to survival in the wild." (Dolphin Quest, 1999)
The Duffield and Wells (1991) study quoted uses average age of animals as an indicator. As pointed out
earlier, this is not a reliable measure, unless the populations have been stable for a long period
of time. This is uncertain for the Sarasota population and not true for the captive population.
In addition, the quote from DeMaster and Drevenak (1988) is incorrect. Actually, they noted: "<...>
At this time it is not possible to compare survivability of animals in captivity with that of
animals in the wild.<...> Additional data from free-ranging animals are needed to determine
if captive animals have similar life expectancies."
- The average life expectancy for bottlenose dolphins in their natural environment in the best
studied population is 7.0 years for females and 10.1 years for males. The average age at death for
captive bottlenose dolphins over the last 20 years has been 11.1 years for females and 10.9 years
for males. (Minnesota Zoo, 1999)
This is an incorrect quote from the Duffield and Wells (1991) paper. The numbers quoted are
the average ages at death recorded, not life expectancies (the paper does not mention life expectancies).
Also the numbers involved are low: the age at death for wild females was based on only one animal (the only
confirmed female death).
When you get involved in discussions about marine mammal survival, keep the
following things in mind:
- look out for false comparisons (like comparing longevity with life expectancy)
- stay away from life expectancy estimates: use survival rates instead.
- verify claims about life expectancies and survival times by converting them to
survival rates. (see conversion tools on the Survival Rates Toolkit page)
- know and verify the published data about this subject.
- look for proper reasoning in your own statements and those of others. A useful
tool for this is the Baloney Detection Kit (Sagan, 1996).
- 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
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.
This paper has been presented at:
- the 24th Annual Conference of the International Marine Animal Trainers
Association, November 5-8, 1996, Gold Coast, Australia.
- the 25th Annual Symposium of the European Association for Aquatic Mammals,
March 14-17, 1997, Duisburg, Germany
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:
- Updated the Särkänniemi data, reflecting the situation on October 1, 1999.
- Added information about reproductive rates
- Added a chapter on average longevity vs. survival rates
- Updated examples in the Conclusion section to included references from both the anti-captivity
movements and the captive display industry
- Added information about confidence intervals added as an appendix
- Added the Survival Rate Toolkit, with tools for calculating survival rate related data
On January 28th, 2017 the following changes were made:
- Updated the Särkänniemi data, reflecting the situation on August 28th,
the date the remaining dolphins were moved to Attica Zoo in Greece.
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