Absolute limits to population growth IV – imagine variation

In our imaginary population growing 30% per year, less than 8.5% of the population can die and more than 78% of mares, and at least 52% of 2-year-old mares, must foal every year.

Although extraordinary, these rates are not inconceivable, at least for short periods of time. Nevertheless, we have not yet considered that there will be year-to-year variation in reproduction and survival. No population grows constantly, consistently. Low population growth in some years must translate into higher population growth in other years to maintain an extraordinary average.

There will be good years and bad years

Population growth must vary from year to year. For every year when the population grows by just 29% there must be another year when it grows 31% to maintain the average of 30% per year. But environments and populations are still more variable than that. For example, the weather and diseases can extract a periodic toll on wildlife.

Extremely heavy snows falls have been reported to trap and kill bands at high altitude. Photo source: http://www.wildhorsesofalberta.com

– the weather

Climates impose irregular cycles on wild animals’ resources because they are quasi-periodic. Some of those climate cycles occur over relatively short time periods of 5 to 10 years and are responsible for large fluctuations in rainfall and temperature. They influence the chances of severe weather events too, like massive snowfalls.

The Pacific Ocean’s El Nino-La Nina oscillation, for example, imposes warm dry winters on the northwest, mid-west and eastern USA during El Nino, and below average rainfalls in the south during La Nina. During a decade there is a shift from La Nina to El Nino weather and back again. There are many other climate cycles with major effects on wildlife.

– the sicknesses

Diseases can also impose death events on populations and some can return as quasi-periodic epidemics – called sporadic or endemic diseases. After an epidemic a larger proportion of the remaining population is immune – they survived, or avoided, infection. Disease infection rates decline until it persists only in a few individuals, or other populations or species (called the reservoir).

With each breeding season after an epidemic, in the absence of substantial transmission and reinfection, the proportion of the population that is immune declines until a disease can once again spread rapidly through the population and, once again, kill those without immunity.

Quasi-periodic death events

We know that extreme weather extracts a toll on populations. Unusually heavy snowfalls can entrap and kill whole bands of horses at high altitude [1, 2]. Violent rain storms accompanied by lightning strikes and high winds can also capture horses away from shelter [3].

Mare and foal at waterhole, Placitas, New Mexico. Source: http://bigstory.ap.org

Drought kills too. Adults succumb to food and water lack [4], and foals die in the quagmire of over-used water-holes [1, 2].

Extreme weather and weather events are common, especially in the environments at continents’ centers, and can be catastrophic, especially for the more vulnerable young and old. Nevertheless, deaths can also be greatest amongst healthy adults, even mares and impose limits on the populations capacity to recover [3].

There are many disease of horses that might be endemic in populations or sporadically cause death events.

The few studies that are detailed enough and long enough, tell us how variable survival and reproduction, and population growth can be from year to year. They also reveal the importance of periodic death events from extreme weather and disease.

Tornquist Park, Argentina

In Argentina during the early years of this century, around 700 horses were free-ranging in an approximately 20 square kilometre section of Tornquist Park. The population had grown rapidly during the previous eight years from about 450 [5] to 700 [3] in 2002. A once-in-a-hundred-year rain storm on the night of the 12 November 2002, at the height of the foaling season killed 193 horses – 28% of the population. It killed 12 foals, 49 yearlings, 46 2-year-olds and 74 adults. Most of the adults killed were females (62), some in good condition [3]. Although researchers reported an extraordinary population growth averaging about 39% per year for the eight years to 31 October, 2002, the storm returned the number of breeding females to levels prior to 1997 – setting the population back five years.

Cumberland Island, Georgia

During 1990-91 an epidemic of Eastern equine encephalitis killed 40 horses of the Cumberland Island population, Georgia USA – an approximately 18% decline in population size [6]. The population had been increasing steadily since 1981 at a modest average of 4.3% per year before the epidemic.

Pryor Mountain, Montana-Wyoming

The Pryor Mountain horse population is reported to have increased by as much as 23% in some years but decrease by 41% in others over the 11-year period, 1976-1986 [7]. A severe winter in 1977 killed around half the population such that the population multiplier (λ) for that year was 0.593*. The winter of 1983 too depressed population growth to 5.2%.

Horses of the Pryor Mountains – one of the few populations where a study [4] provided reliable records over enough years to report year-to-year variation in population growth. Photo source: http://www.nps.gov

The Pryor Mountain record illustrates that, even in populations with ordinarily low death rates and high reproductive rates, growth can be substantially depressed and reversed in some years for reasons unrelated to the size of the population, like typical extremes in seasonal climate**.

We can use values of annual variation like these to test the credibility of a 30% average annual growth per year over time periods that are desirable for planning the management and conservation of wildlife, like 10 years…

… in my next post.


* The Pryor Mountain population had a female-biased sex ratio and horses were removed (a male-biased harvest) which elevate population growth rates.

** Ecologists call this type of variation ‘density-independent’ because it occurs in all populations regardless of how well resourced they are. Even populations with plenty of food and shelter will suffer in extreme weather. The opposite of density-independence is density-dependence where the variation from year-to-year is primarily caused by how well the population is resourced. When the availability of food, water and shelter causes population growth to vary it is said to be density-dependent. Density-dependence and –independence will be the subject of a future post. The concepts are important to understanding population growth and decline.


1. Berger, J. 1986. Wild horses of the Great Basin. Chicago: University of Chicago Press.

2. Berger, J. 1983. Ecology and catastrophic mortality in wild horses: Implications for interpreting fossil assemblages. Science, 220, 1403-1404.

3. Scorolli A, Cazorla A, Tejera L. 2006. Unusual mass mortality of feral horses during a violent rainstorm in Parque Provincial Tornquist, Argentina. Mastozoologia Neotropical, 13, 255-258.

4. Greger, P. D. & Romney, E. M. 1999. High foal mortality limits growth of a desert feral horse population in Nevada. Great Basin Naturalist, 59, 374-379.

5. Scorolli AL, Cazorla ACL, 2010. Demography of feral horses (Equus caballus): a long-term study in Tornquist Park, Argentina. Wildlife Research 2010, 37:207-214.

6. Goodloe RB, Warren RJ, Osborn DA, Hall C. 2000. Population characteristics of feral horses on Cumberland Island, Georgia and their management implications. Journal of Wildlife Management, 64:114-121.

7. Garrott, R. & Taylor, L. 1990. Dynamics of a feral horse population in Montana. Journal of Wildlife Management, 54, 603-612.


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