POPULATION ECOLOGY

[Click here to jump to notes concerning Netting's Törbel study for Oct 12th class]

Intro

Population is important focus in two distinct areas of ecological anthro:

1) issues concerning population regulation (carrying capacity, variation in fertility & mortality, etc.)
2) theories proposing that "population pressure" on resources leads to cultural innovations which serve to reduce this pressure

I'll address these issues below, but begin by discussing principles that underlie theory of population ecol. and reproductive strategies

Population growth

Rev. Thomas Malthus (in An Essay on the Principle of Population, 1798) was the first to make clear that population growth is what he termed "multiplicative" rather than "additive"

That is, whenever births exceed deaths (even slightly), population will grow exponentially (like money in a bank account earning compounding interest)

This because each addition to population also reproduces, and the compounding effect on population size means that the rate of increase in population size itself increases (causing accelerating, not just constant growth)

Exponential growth equation in simplest form is dN/dt = rN, which is shorthand (in differential calculus) for "Change in population size N per unit time t is a product of r (the per capita reproductive rate) and N (population size)"

The simple mathematics of exponential growth tells us that, no matter how small the initial population, or how slight the excess of births over deaths, any growth rate >0 will lead to exponential increase, meaning N will grow at an increasingly faster rate (like a bank balance earning compounding interest)

Simple as it is, exponential growth leads to some rather counter-intuitive results

For example, E. coli bacteria reproduce every 20 minutes under ideal conditions; if this rate of growth were to persist unchecked, after 36 hours the descendants of a single bacterium would cover the entire surface of the earth one foot deep, in the next hour be over our heads, and within a few days weigh as much as the visible universe and be expanding outward at the speed of light

If that seems unrealistic to point of absurdity, consider a hunter-gatherer band colonizing a new area (e.g., the first Americans, migrating from Siberia); if we assume an initial population of only 100 people, and a growth rate of 1% per annum (hence doubling every 70 yrs), after 12,000 yrs (the most recent possible date for colonization of the Americas) the resulting population would = 5.99x10⁵³ (that is, approximately 6 followed by 53 zeroes; by comparison, present world population is <7x10⁹; the estimated population of the Americas in 1492 was roughly 6 x 10⁷)

So exponential model with an annual growth rate (AGR) of 1% overestimates actual Amerindian population by ~46 orders of magnitude! (again, for the mathematically challenged, 46 orders of magnitude = 1 followed by 46 zeroes, not the much smaller 46 times)

You might object that an AGR of 1% is unrealistic, and it certainly is over any sustained length of time (which is one of my points here), but in the short run many expanding human populations have achieved growth rates of 4% or 5%; in fact, the current global AGR is about 1.5%, and the AGR of many countries or areas is far higher than that

Indeed, a 1% AGR only requires that the average person produce 2.4 surviving (and reproducing) offspring over their lifetime; and keep in mind that a sustained average of <2 surviving offspring ® population extinction

As Maltlhus realized, it is a well-established fact that all species, humans included, have the physiological capacity to reproduce far above replacement rates

Obviously the exponential model is highly unrealistic, since no population can reach infinite size or expand at infinite rate -- or even sustain 1% AGR indefinitely

Long before this occurs, something must intervene to make growth rate zero or negative (by making births £ deaths), resulting in population stability or decline

So a key question for population ecology is, what factors prevent exponential population growth from occurring unchecked?
 

Population Regulation

Malthus argued that as population got too dense, further growth was limited by factors causing increased mortality (which he termed "positive checks," such as war, famine, and disease), as well as factors decreasing fertility (the so-called "preventative checks," such as late marriage, sexual abstinence, etc.)

A century and more later, population ecologists refined Malthus' basic argument and constructed a theory of population regulation

One key element of this theory is a distinction btwn 2 kinds of population regulation, density-independent vs. density-dependent

Characteristics of density-independent population dynamics:

• mortality or fertility rates unaffected by population density
• caused by factors such as climate, natural catastrophes, etc.
• typical of insects
• leads to essentially random fluctuations

Density-dependent population regulation involves:

• mortality or fertility rates (b&d) correlated w/ population density
• due to such factors as competition, predation, resource limitations
• typical of vertebrates
• leads to cyclic or stable population size (i.e., population equilibrium)

Many arguments in the scholarly literature about which of these is most prevalent in nature, but for large, long-lived, and slowly-reproducing animals like ourselves, the general consensus is that density-dependent dynamics are more important

Density dependence could be result of any of the classic kinds of Malthusian checks

Population ecologists modified exponential model to incorporate density-dependent checks on population growth

Simplest version of this is termed the logistic model of population growth:

dN/dt = rN (K-N/K)

Note that the only new variable added to the exponential model is K = "carrying capacity," defined as the equilibrium population size achieved when births = deaths, and hence dN/dt = 0 [zero]

Logistic simply formalizes idea that as N increases, fertility decreases and/or mortality increases

Thus, logistic model says that when N is very small (i.e., low population density, an "empty" habitat), population growth rate is highest

As N increases, (K-N)/K becomes smaller, hence population growth rate slows

Finally, when N = K, (K-N)/K = 0, hence growth rate (dN/dt) = 0, and N equilibrates (population stops growing, births = deaths)

Logistic model produces "sigmoid" (S-shaped) growth curve; if K declines, it will produce "backwards S" as N drops to new value of K

Although logistic is more realistic than exponential model, it is still full of simplifications (like any model)

Nevertheless, logistic model gives reasonably good fit to many experimental and natural data on various species expanding into unoccupied habitat

More complicated (but still relatively simple) models in population ecology produce limit cycles, overshoot with damped oscillations, chaotic behavior, or overshoot and crash (see Cohen 1995 reading)
 

Logistic Growth In Human Populations

Historical demography and archaeology indicate that whenever humans develop a new energy source, eliminate a major disease, or colonize unoccupied environments, we observe rapid population growth (up to 3% AGR = doubling each generation) for a period of time, followed by slowdown and approach towards equilibrium

Precise demonstration of logistic growth in humans is elusive, because long-term demographic records not available except in situations where too many other variables intervene (e.g., emigration, rapid technological change, etc.)

But some archaeological records give reasonably strong support for basic model

For example, Hawaiian Islands colonized approx. 1500 years ago, probably by small founding population of <1,000 people who came from Marquesas in several voyages

• First 700 yrs characterized by slow, steady growth (doubling ca. every 200 yrs), to population of ca. 15,000

• Then a reorganization of settlement pattern, production system, & social organization led to rapid population growth

• This lasted for 400 years, followed by 200 years of little growth but much warfare, intensive competition for land

• At contact (1778), Hawaiian population = approx 225,000

• Thus estimated annual growth rate averaged over entire period was less than 0.5% (.0425%)

• If AGR had been just a little higher (i.e., 0.7%), population at contact would have been 7.5 million (= entire population of No. America in 1780); but of course, there are good ecological reasons (not least of which is limited amount of arable land) why such a population density was not possible

Global long-term population trends subject to lots of guesswork, but some reasonable estimates are:

a) a few thousand or tens of thousand at outset of hominid lineage (ca. 5 million yrs ago)

b) approx. 8 million worldwide at beginning of Neolithic (10,000 B.P.)

c) world population increased 160x (5 mill. to 800 mill.) from 10,000 B.P. to A.D. 1750, doubling every 1,000 years (mean AGR = 0.1%)

d) total AGR now ~1.7% (= doubling every 44 yrs)

e) big question is whether it will level off in sigmoid fashion (Cohen 1995: Fig. 4), or perhaps "overshoot" K resulting in crash or oscillations
 

Carrying Capacity

Concept of carrying capacity takes several forms in both biology and anthropology

As Dewar reading explains, in bioecology concept usually refers to K = equilibrium population size (regardless of the factors producing this eqilibrium)

In anthropology, by contrast, carrying capacity usually refers to ability of environment to support human population on sustained basis (Dewar's "Cc")

Main uses of carrying capacity concept in ecol. anthro:

a) to determine if population and resources are in balance

b) to predict equilibrium or prehistoric population size

c) to explain cultural features as adaptations that maintain equilibrium (population "self-regulation")

d) to explain cultural features as adaptations allowing or responding to increase in population size ("population pressure")

Note that a) and b) are descriptive, while c) and d) are explanatory

Two basic problems in using carrying capacity concept:

1) limiting factors (climate, food resources, etc.) subject to rapid & unpredictable fluctuations

2) human populations can alter their own carrying capacity

First problem is complex, but its clear that given our long generation length and offspring dependency, humans can't track short-term fluctuations in limiting factors; at best, we are adapted to some medium-term minimum

Second problem relates to choice and flexibility, and capacity for behavioral and cultural change: alterations of technology, economic organization, rules of land use, even religious beliefs can significantly alter equilibrium population size in a given area

This means that K is niche-specific, not set by environment per se; according to Joel Cohen (1995:343), this is a uniquely human attribute

However, some would argue this is a matter of degree, since non-human species also respond to population pressure (N approaching K) with niche shifts and other behavioral and/or physiological changes that in turn alter K
 

Calculating Carrying Capacity

Several equations have been developed for calculating Cc

For H-G, these include measures of staple food density, sustainable yield, caloric value, seasonal variations, etc.

Sometimes Cc is estimated directly from net primary production (NPP) of habitat, but have to guess at percent of NPP utilized by humans (which depends on trophic level, resource choices, technology, and so on)

For agricultural populations, Cc estimated using land area, fallow period, productivity/area

These estimates are typically 30-50% higher than observed population, suggesting either

1) population regulated below subsistence max. (self-regulating equilibrium view)

2) population limited by other factors (e.g., protein, disease) (Malthusian view)

Despite failure to predict N with any precision, comparative data on human populations indicates pretty good correlation btwn Cc and observed N

Graph shows data on 13 subsistence-agric. populations

Note that all but 1 population fall below estimated Cc, and none exceed it

Furthermore, the data exhibit a very strong linear relationship btwn observed & predicted population (correlation coefficient = 0.993, which means >98% of variance in N can be predicted from Cc, even though N≠Cc)

This suggests that basic notion of populations being limited by resource base (Cc) is at least partially correct; otherwise we would expect as many populations to fall above diagonal line as below it, and a far more "noisy" relationship between N and Cc

We can also surmise that something in addition to arable land is acting to limit population density among these agric. groups; otherwise more would show N=Cc rather than N<Cc

While aggregate data like this are illuminating, to really understand population regulation must examine particular cases in detail -- as in Netting's analysis of Törbel

Case Study: Swiss Peasants (Netting)

Robert Netting's (1981) study is example of an ecological approach to historical demography

Netting focused on single parish centered around Swiss alpine village of Törbel; census records & other data cover 3 centuries

Thus, Netting's study examines historic shifts in demography & subsistence over long time spans and at a local level (vs. national or regional aggregation usually employed in historical demography)

Some basic findings of study:

1. Fertility rose and fell in rough balance with mortality rates (Netting, Fig. 6.1)

(see footnote 7 on p. 245 re rapid recovery from epidemics: "When an epidemic is past, those who remain alive are more vigorous; the dead have opened up new places and left behind their inheritances, and for this reason everyone marries who can." -- Waser, 1700s)

2. Overall, varying but positive levels of population growth most of the time; "excess" population emigrates, so resident population remains relatively constant for long periods

3. Fertility limitation is primarily via restriction on marriage:

a. Linked to inheritance of agricultural estate (common pattern in Europe)
b. Land scarcity ® delay in age at marriage, even lifelong celibacy (notes on p 135 that when density increases, celibacy is as high as 33%!).  Is this an example of density-dependent population regulation?

4. Netting concludes that increase in population growth rate in 19th century due more to increases in fertility than declines in mortality

a. Presents data that rule out various possible causes (age at marriage, marriage duration, deliberate fertility control, etc.)
b. Attributes this primarily to better nutrition ® shorter inter-birth intervals
c. Suggests proximate cause was introduction of potato