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

Table of contents

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

Presenting the data

Now let's look at some numbers. Consider a population with an annual survival rate of 0.95 (this value is in the same range as the survival rates for a number of marine mammals (see below)). All the following statements are correct, but the impact of the message can be quite different.

  1. The annual survival rate is 95%
  2. The annual mortality rate is 5%.
  3. The life expectancy is 19.5 years.
  4. The majority of the animals will become older than 13 years.
  5. Within 5 years, 23% of the animals will have died.
  6. One third of the animals survives no longer than 8 years.
  7. Within 14 years 50% of the animals will be dead.

Statements 1 and 2 are fairly neutral and "scientifically correct". If you want to paint a positive picture, you will use statements like 3 and 4, whereas statements 5 through 7 have a negative ring to them. To paraphrase an old song: "'t Aint what you say, it's the way that you say it"

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Some real numbers

Now that we know how we can calculate the numbers and how we can present them, let's look at some published data that is available for wild and captive populations. There have been 2 detailed studies done on captive populations, one dealing with all the data available until the time of publication (covering captivity data from 1940 to 1985 (DeMaster and Drevenak, 1988)) and a more recent one, evaluating the previous study and concentrating on the data from 1988 to 1992 (Small and DeMaster, 1995). Both studies took the data from the MMIR (Marine Mammal Inventory Report), maintained by the National Marine Fisheries Service. The MMIR has been shown to be quite accurate: "Overall, the Marine Mammal Inventory Report is an excellent source of highly accurate, unbiased, and complete data on census, status, and selected biological processes of marine mammals in captivity." (Temte, 1993).

There have been some studies done on wild populations of a few species of marine mammals. Of the species, covered in studies of captive marine mammals (DeMaster and Drevenak, 1988, Small and DeMaster, 1995), comparative studies of wild populations are available for:

Species Population Annual Survival Rate
Bottlenose dolphin Sarasota, Florida1 0.961
  Indian/Banana River, Florida2 0.92
  oceanaria (1940-1985)3 0.93
  oceanaria (1988-1992)4 0.951
Killer whale British Columbia and Washington5 0.976
  oceanaria (1940-1985)3 0.93
  oceanaria (1988-1992)4 0.937
Beluga oceanaria (1940-1985)3 0.94
  oceanaria (1988-1992)4 0.954
Steller sea lion Alaska6 < 0.930
  oceanaria (1940-1985)4 0.964
  oceanaria (1988-1992)4 0.969
California sea lion oceanaria (1940-1985)4 0.935
  oceanaria (1988-1992)4 0.952

1. Wells and Scott, 1990
2. Hersh, et al., 1990
3. DeMaster and Drevenak, 1988
4. Small and DeMaster, 1995
5. Olesiuk, et al., 1990
6. York, 1994

For bottlenose dolphins, the difference between the survival rates in captivity (both the whole period 1940-1992 and the subset 1988-1992) and the Sarasota population is not statistically significant. The survival rates for killer whales in captivity are lower than in the wild, whereas the survival rates for Steller sea lions are significantly higher in captivity than in the wild. For the California sea lion and the beluga, no data are available on the survival rates in wild populations.

There is little information about the reproductive rates and calf mortalities in wild cetaceans. Wells and Scott (1990), for the Sarasota population of bottlenose dolphins, calculated a maximum survival rate to age 1 of 0.811 (an average ASR to age 1 of 0.803). Olesiuk et al (1990) estimated the calf mortality in killer whales at 43%. Since they calculated calf mortalities as mortalities up to 0.5 years, this means a survival rate to age 0.5 of 0.57. Assuming a survival rate between age 0.5 and 1 comparable to adult whales (0.976), the ASR to age 1 could be 0.563. Small and DeMaster (1995) report calf/pup survival rates for the captive population (through December 1992) of 0.666 for bottlenose dolphins and 0.858 for California sea lions.

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An example: The survival rate of the Särkänniemi dolphins

Calculation of the survival rates for a known population is pretty straightforward. As an example, let's have a look at the dolphins in the Särkänniemi Delfinaario in Tampere, Finland. Five dolphins arrived at the facility on March 31st, 1985, so their first full day at the facility was April 1st, 1985. We will consider the period April 1st, 1985 until August 28th 2016, the date the remaining dolphins were moved to Attica Zoo in Greece, for this calculation. To be able to calculate the survival rate, we need to calculate the total number of animal days for that period. At the end of the sampling interval, 2 of the 5 original dolphins were still alive. During the sampling period, two calves were born that survived beyond one year of age. On August 18th, 1993 a male calf named Leevi was born and on September 9th, 1996, another male calf, Eevertti, was born. Both were still alive at the end of the sampling period. The days collected for Leevi and Eevertti since their first birthdays (August 18th, 1994 and September 9th, 1997) must also be included. So this leads us to the following data:

Name start date end date animal days
Niki 01-04-1985 18-11-2004 7171
Näsi 01-04-1985 29-10-2014 10803
Veera 01-04-1985 28-08-2016 11472
Joona 01-04-1985 07-09-1990 1985
Delfi 01-04-1985 28-08-2016 11472
Leevi 18-08-1994 28-08-2016 8048
Eevertti 09-09-1997 28-08-2016 6928
Total     57879

Now that we have calculated the total number of animal days, we can calculate the Daily and the Annual Survival Rates for this group:

DSR = 1 - (#deaths / #animal days) = 1 - (3 / 57879) = 0.999948168

ASR = DSR365.25 = 0.999948168365.25 = 0.981245861

So, based on the data collected so far, the ASR for the Särkänniemi dolphins is calculated to be approximately 0.981 (95% confidence interval: 0.960-1).

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