Alaska Sea Grant

Killer Whale Math

Terrie Williams and her colleagues wanted to calculate whether it was possible that killer whales had eaten the missing sea otters.

They started with this information:

  1. 40,000 otters were missing.
  2. They had disappeared over a period of six years.
  3. Sea otters provide the following food values:
    Female sea otter 23 kg x 1.81 kcal/g = 41,630 kcal per female otter
    Male sea otter 34 kg x 1.81 kcal/g = 61,540 kcal per male otter
    On the average, a sea otter provides 51,505 kcal
  4. Killer whales need the following amounts of food:
    Female killer whale needs 51 kcal x 3784 kg = 193,000 kcal per day
    Male killer whale needs 59 kcal x 4870 kg = 287,331 kcal per day
    On average, a killer whale needs 240,165 kcal per day
  5. There were an estimated 4000 killer whales in the area, but 90% of them had a diet of fish only.

If killer whales fed only on sea otters, how many sea otters would one killer whale need to eat every day?

240,165 kcal needed by killer whale/51,505 kcal provided by sea otters = 4.6 sea otters needed per day

How many sea otters could one killer whale eat in six years?

365 days x 6 years x 4.6 sea otters per day = 10,074 sea otters

How many killer whales would be needed to eat 40,000 sea otters, if they ate nothing but sea ottters?

40,000 otters/10,074 otters per killer whale = about 4 killer whales

What is the estimated number of killer whales in the area that eat marine mammals?

90% eat only fish, so 10% of the 4000 killer whales, or 400 killer whales might eat sea otters

If there were 400 killer whales eating otters as part of their diet, what is the average number of otters that each would have to eat, in order for 40,000 sea otters to disappear?

40,000 sea otters/400 killer whales = 100 otters per whale in six years

or 100/6 = 16.6 otters per year per killer whale

That would be about one otter every (365/16.6) 22 days.

How many male or female sea otters could a pod of one male and four female killer whales eat in one year?

A male killer whale would need to eat 5 (4.66) male sea otters or 7 (6.9) females per day.

A female killer whale would need to eat 3 (3.1) male sea otters or 5 (4.6) females per day

1 male killer whale could eat 1825 males per year or 2555 females per year

+ 4 females could eat 4380 males per year or 7300 females per year = 6205-9855 otters per year

How long would it take them to eat 40,000 sea otters?

One pod could eat 40,000 sea otters in 4 to 6.5 years

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