Help Me Calculate Wooly Mammoth Populations

Ya’ll, I’m sorry, but I need you to put on your calculating hats and help a woman defeat creationists. I have numbers, but no higher math skills to work ’em out*. Any of you care to calculate?

Here’s what I need to know: how many wooly mammoths can we expect 900 years after the Food?

Let’s give creationists the benefit of the doubt, and pretend Noah kept two wooly mammoths aboard. Let’s further say they were of breeding age when they got off the boat, and there was lots of forage, and they got it on right away. Here are the relevant stats, pulled from their closest living relatives, the Asian elephant.

Breeding age: 10-15 years until around 50-55

Gestation: around 18-22 months

Weaning: around 3 years

Which gives us a birth interval of about 4-5 years.

Life expectancy: roughly 60-70 years.

So, if our wooly mammoths pump out bebbies on the regular, and all is ideal, and we even let ’em all live to ripe old ages, how many mammoths will we have after 900 years?

Herd of wooly mammoths. Painting by Charles R. Knight, image courtesy Wikimedia Commons.
Herd of wooly mammoths. Painting by Charles R. Knight, image courtesy Wikimedia Commons.

I’ve got plenty of other ways to show that the creationist crap being spouted about wooly mammoths in this textbook is utter bunk, but it would be nice to hoist them by their own petard, while we’re at it. Thanks for your help, my more numerate darlings!

*Gawds, I can’t math. Up until pre-algebra, I was actually pretty good at the stuff, but I got jumped ahead before I had the proper foundation, then had a string of truly awful math teachers and never recovered. I shoulda kept up on the tutorials I was doing back in the early aughts, but I let my skillz atrophy because hey writers don’t need math right?

Let this be a cautionary tale to all aspiring authors: keep your math skills polished. Otherwise, you’ll end up on the intertoobz at three in the ay-em begging your readers to do the math for you and feeling a right nitwit.

Help Me Calculate Wooly Mammoth Populations

18 thoughts on “Help Me Calculate Wooly Mammoth Populations

  1. 1

    You aren’t a nitwit. Math is hard!
    The answer I got is between 5400 ~ 5600 mammoths after 900 years. Here’s how I got that estimate:
    We assume that mammoths are not class Artiodactyla, so they would not be “clean” animals. Therefore, they would be taken by twos into the Ark, one male and one female. We will assume basic gender parity throughout the course of this thought experiment.
    If we are very nice to the creationists, we can assume 45 breeding years per female, at 4 years between babies, giving us 11 babies per female. Let’s round that up to a nice even 12 babies per female to account for possible twins or breakthrough pregnancies. Assuming gender parity, that gives us 6 females per generation per breeding female. We have 900 years before extinction, and our females start breeding at age 10, so we have 90 generations. 90 generations with 6 females times 12 babies per female gives us 5600 maximum population.
    Just for fun, if Noah took 2 females on the ark and artificially inseminated them, we could possibly get up to 11200 mammoths by extinction.
    Someone else might want to check my math, but that’s my back-of-the-envelope calculations. Have fun with your creationist.

  2. 3

    I’m really not following the math you’re using. Any unrestricted population growth should be exponential, right?

    I mean, even if I take something like… the population doubles every 45 years, 900 years gives you 20 doublings, which puts you on the order of a million.

  3. 4

    If we’re assuming unlimited growth, with (say) 1 new mammoth for every 20 in the population per year (an underestimate given your numbers, and data I found on elephants)

    Year 0: 2
    Year 50: 58
    Year 100: 1,735
    Year 150: 51,120
    Year 200: 1,505,863

    Year 900: 5.5 x 10^26

    Obviously exponential growth doesn’t continue over those kinds of time periods. 900 years is plenty of time for populations to become resource-limited, even slow-breeding ones like mammoths.

  4. rq

    I wonder how inbreeding would affect population viability?
    Anyway, I’m going to work on this next break. I’m going to assume a bunch of stuff, like not all mammoths born are females (that there’s more than one breeding male per generation), and that turnaround time is 5 years, etc. I know there’s a formula out there, but I’m just going to play around with excel because it’s more fun that way.
    Also, math isn’t hard. Just takes a little practice. :)

  5. 6

    BTW, I found some data on elephants in the Kruger National Park. Starting with 10 elephants in 1905, the population reached 7500 in 1996, and were then at or beyond the Park’s carrying capacity. In 1946, the Park had 3750 elephants, and had a growth rate of 282 more elephants a year, a growth rate of 1 for every 13 elephants, not the conservative 1 in 20 I used above.

  6. 7

    At a 5% growth rate per year, every fifty years your population should increase by about 11.5 times, not 29 times.

    I mean, I’d use the same approach – maybe assume a 2% death rate, for a total of 3% population growth per year. Say… 23 years to double, round up to 25 – 36 doublings puts you at about 130ish billion or so.

  7. rq

    Ok. I got about 5.015×10^23 mammoths in 900 years.
    I can show my work.
    I feel like that’s a bit excessive. But Excel calculated it for me, so it can’t be wrong (as long as I entered all formulae and initial numbers correctly). Can it?

    (Assumptions: breeding starts at 8, due to ease of calculation – I could probably raise that to 13 easily; where there is an odd number of breeding-aged females, more females are born (i.e., if 3 females, then 2 new females and 1 new male); where there is an even number of breeding-aged females, both sexes are born equally; all mammoths die of old age at 60; all mammoths stop breeding of old age at 55; all female mammoths produce a baby mammoth every five years (* gestation + weaning); probably a bunch of other stuff that I’m forgetting right now.)

    That’s a lot of mammoths.

  8. 9

    Ok. I got about 5.015×10^23 mammoths in 900 years.

    So, almost a mole of mammoths then! Or something.

    But let’s not forget the creationist concept of “kinds”. They’re quite happy to use it to reduce the required capacity of the ark. So mammoths (of all varieties), mastodons, and modern elephants are all “elephant-kind” and came from one original pair. The differentiation is just “micro-evolution” so it doesn’t count.

  9. 11

    OK, let’s throw the creationists a few bones…

    Assume 15 years to one mammoth generation, the time it takes a female to reach sexual maturity.

    Assume each female gives birth every 5 years.

    So, each female (1/2 of the population) produces 3 offspring during that 15 year period. Thus, starting with 2 mammoths in year 0 there would be 5 mammoths in year 15. The population would have increased by a factor of 2.5 .

    The 2.5 figure is an ideal. But let’s grant the creationists that there will be some mishaps and say it is smaller.

    Let’s use a smaller figure than 2.5. Say…2. That is, 2 mammoths produce 2 offspring that reach maturity during a 15 year span (more or less since old mammoths stop breeding and even older mammoths die), with population doubling every generation. In 900 years = 60 generations, we get 2^60, or roughly 1,500,000,000,000,000,000 mammoths. Oops.

    OK, a still smaller figure. 1.5. More mishaps, more dead mammoths. That is making the assumption that 2 mammoths produce 3 offspring in 15 years, but 2 of the 5 mammoths die during that time. (1.5)^60, or roughly 37 billion mammoths. Again, oops.

    Or maybe Noah just screwed up and brought two male mammoths on board by mistake. Oops.

  10. 12

    All of the math above assumes that all births of females results in females that live a) to breeding age; and 2) live long healthy lives continuing to produce calves. That is just silly. Consider the Hispid Cotton Rat (Sigmodon hispidus), the cutest native Texas rat. A single female, in the conditions you are describing (lots of food, no early deaths) can produce 12,000 descendants by the time of her 1st birthday. Yet, we here in South Texas are not up to our nipples in Cotton Rats. In extraordinarily favorable environments, like after the major drought in the early 50s when all the vegetation came back in the increased rainfall, cotton rats had a major population explosion, with an estimated 100 rats per hectare in the very favorable environments. That means that even in a good environment, those females were not producing 12,000 descendants per year. Now, it is true that rats are r-selected (that is they produce large number of offspring in a short amount of time) and elephants are k-selected (they have much fewer offspring but take care of them to increase the chance an individual calf will survive to adulthood). But in the real world, elephants are not going to have anything like complete success. Many calves will die before they can breed. Many more will live only a short time as breeding adults.

    Elephants depend pretty heavily on knowing their range well, passing that information from mother to young adults. To get from Ararat to Texas will require that they travel the roughly 11,000 miles (I took the least mountainous route) in 900 years. I use Texas because I have personally excavated elephant bones in San Antonio. They would have had to average 12 miles a year. That is 12 miles going in the right direction, including crossing vast stretches of land that was undergoing massive environmental changes. Hell, it assumes that the first two elephants didn’t die of starvation in the first few months because there wasn’t much in the way of vegetation for them to eat. Elephants eat A LOT. The plant life coming back to life after the flood would have been a tad on the sparse side, even with herbivore populations as low as they would have been immediately after the Flood.

    Oh, hell, it’s fun to play with but the absurdity of the whole notion is so extreme that I knew it was bullshit when my Sunday school teacher started telling the story when I was 8.

  11. 13

    Female 1 in year 1 makes a single offspring. Let’s be generous and say it’s a girl.

    In year 5, she has another single offspring, a male 2. Female 2 is still too young to breed. Total population = 4. (Male 1, Female 1, Male 2, Female 2)

    In year 9, being generous, Female 1 has a single offspring, female 3. and Female 2 breeds for the first time in year 10. Total population after 10 years = 5.

    Year 12, Female 2 (generousity) gives birth to female 4. Year 13, Female 1 has male 3. Total population by year 13 = 7.

    Year 16, Female 2 gives birth to male 4. Year 17, Female 1 gives birth to female 5. Year 19 female 3 breeds for the first time. Population = 9.

    Year 20, Female 2 gives birth to female 6. Year 21 Female 1 births Male 5 and Female 3 births Female 7. Population year 21 = 12.

    Year 23, Female 4 births Female 8. Year 24, Female2 births Male 6. Year 25 Female 1 births Female 9, Female 3 births Male 7.

    Total population year 25 = 16.

    etc etc. Exponential doesn’t work because breeding is only possible for 45 years for each female, so you have some dropping out. Each female is only making 6 more females over her lifetime. Each of those females takes at least 10 years to mature. They are only making another female once every 8 years.

  12. 15

    This might be breaking the rules, but I’m going to skip the math and say zero.

    There wouldn’t have been anything for them to eat. The creationists like to claim that the rainwaters of this flood carved out the grand canyon (before it deposited the layers it cut through… :( ), and chucked rocks into the moon hard enough to crater it. And then hung around long enough to kill everything off before draining off to… (I don’t think I’ve heard the creationist explanation for this, but then again, I may have just ignored it off-hand because I didn’t want to deal with the ensuing arguments about… everything.)

    There wouldn’t have been anything to eat. Let alone to sustain a pair of elephants (or mammoths).

    Also, wasn’t there some creationist bullshit about the flood that was trying to explain frozen mammoth corpses in siberia? Like, since they couldn’t get on the ark, they just froze (cause: weird understandings of the bible).

  13. 16

    Breeding age: 10-15 yrs (12.5 yrs) to 50-55 yrs (52.5 yrs). That gives an average age on breeding of about 32.5 years.
    Fertile years: 12.5 yrs to 52.5 yrs or 40 yrs.
    Pregnancy (2 years) + nursing (3 years) gives 5 years. This is for one baby at a time. Elephants sometimes have twins, but that is very rare.
    This means that each female mammoth can have as many as 8 babies over her fertile life, and counting a male mammoth with her gives 4 babies per each sex of mammoth. Continuous pregnancy would give 20 babies per female mammoth, or 10 babies per each sex of mammoth.
    So each generation of mammoths gets succeeded by another one about 32.5 years later with 4 times to 10 times as many individuals in it. That’s one out of 23 to one out of 14 mammoths per year.
    Extrapolating over 900 years, that’s 10^17 to 10^28 mammoths. So they’d run into their ecological carrying capacity long before then.

  14. JCB

    Since I’m a programmer, I decided to write a simulation. It starts with two mammoths (one each male and female); each female mammoth produces one child every four years from ages 12 to 55; and all mammoths die at age 70. This produces about 10^26 mammoths after 900 years.

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