Absolute limits to population growth III – imagine death

To identify the ridiculous and impossible from the improbable but possible, I begun a series of simple calculations.

We imagined someone claiming that a closed population of 1000 feral horses or burros (asses) is increasing by 30% each year. I showed how we can use these values to estimate the size and age-structure of the population, especially the population of breeding mares and their foals.

We now continue by incorporating death into our calculations of biology’s absolute limits.

For every 1% of our population, or 10 horses, that die before the next breeding season, 10 more foals than the 300 already expected (j) will need to be born to maintain a 30% annual growth rate (o). If 5% die, 50 more foals must be produced (p).

Deaths, therefore, lift the number of mares that must foal and the foaling rate required. A 5% annual death rate would mean that 350 of our 385 mares (91%) need to foal, or about 9 out of every 10 mares (q). This increases the minimum number of 2-year-old mares required to foal for the first time from 93 (m) or 52% (n) of 2-year-olds to 143 (r) or 80% (s).

Text box 3Maximum deaths possible

There is a biological limit to how many deaths a population can sustain and still increase at an extraordinary rate.

As the number of deaths increases the reproductive demand on mares to maintain a 30% growth rate becomes increasingly implausible. The largest number of deaths that our population can support but still increase by 30% this year is 85 (t) because our breeding-mare population is 385 (i). Eighty-five deaths would be an 8.5% death rate for the population (u).

But an 8.5% annual death rate would require that ALL mares 1 year old and older became pregnant and carried that pregnancy to successfully foal. It is improbable that our population could support death rates approaching 8.5% and still grow by 30% a year.

How many die?

Our calculations, therefore, have identified a second critical piece of information required to corroborate claims of extreme population growth – evidence for very low death rates. Almost all individuals, even the vulnerable because they are young (foals in their first days of life), inexperienced (breeding and defending themselves for the first time), and old, must survive for extraordinary population growth rates to be maintained.

Nevertheless, so far the values for survival, when combined with values for mare reproduction, for a population growing by 30% each year appear possible, albeit improbable.

We have not yet, however, factored in year-to-year variation in reproduction and survival.

There will be good years and bad years

Population growth must vary from year to year. No population grows constantly, consistently.

In my next post I will reveal why the variation inherent in every biological system, and imposed on every population, makes an average 30% increase per year biologically impossible.

  1. Dear Wayne,
    Nice blog!! I agree with you about 30% population growth is not possible with high population size.
    But in small, females biased, with high adult proportion, recently introduced feral horse populations it is…If we have 15 horses, 10 of them adult females and 0.70 of them have foals (7 foals), and supposing 10-15% mortality, so 2-3 horses die, at t+1 we have 20. 20/15=1.30
    This is r at very low population density, theorically maximum attainable rate…(Grange et al. 2009; Scorolli & Lopez cazorla, 2010).
    All the best
    Alberto Scorolli

    • Hi Alberto,
      Thank you for your comment. It is good to hear from you. I have followed and enjoyed reading your work.

      The critical item to focus on in your comment is the adult sex ratio. One can elevate or depress potential population growth rates by manipulating adult sex ratio. A female-biased sex ratio will elevate, and male-biased sex ratio depress, population growth.

      This is why the recent National Academy of Sciences report recommended against the practice of removing disproportionately more males than females – it increases population growth potential.

      I will address the influence of sex ratio and its implications for population management in a future post. For the moment, however, I am establishing the baseline that can be expected in unmanaged, un-manipulated populations. So far I am being careful to stipulate that the imagined population is closed and at even sex ratio.

      I am in Colorado at present and today I visited Rocky Mountain National Park. I saw pika, marmots and coyote. Fantastic.

      All the best,


      • Dear Wayne,
        Happy to know that you enjoy my work.
        This blog looks like a good oportunity to share ideas and comments. I hope to keep in touch!!
        In 2012 I began a blog about feral horse ecology and management in Argentina (in spanish at the moment, in english in the future I hope!!) http://caballoscimarrones.blogspot.com.ar/
        Enjoy your Rocky trip!! It is surely nice!!
        All the best

      • Thank you Alberto for the link to you blog. I am sorry I cannot read Spanish but some of my readers will be able to.
        All the best,

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