Soc 663 Fall 2003 Lectures September 23 and 25


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Soc 663

Fall 2003

Lectures September 23 and 25

I. History of human population growth: plan

We will review basic features of human population growth from the times of Adam and Eve. The plan is the following:

(a) first, we will place human population growth in a larger context and compare it with growth among other species;

(b) we will then study the main engines of human population growth through a very simple model;

(c) we will examine the actual determinants of long trends in population growth and the main outcomes of the operation of those determinants;

(d) I will provide some examples (case of Western and Northern Europe; case of Ireland);

(e) we will suggest the existence of a simple population dynamics to explain the historical record at least up until to 1700-50.
II. The growth of human and the growth of other species.
a. Classification
According to a widely accepted schemata proposed by May and Rubinstein, most species fall in one of two groups: those that follow r-strategies of survival and those that follow K-strategies.
Equation for NRRas a measure of reproductive fitness
The r-strategy applies to populations exposed to highly unstable environments, where very high reproduction rates (TFR-equivalent) are called for to forestall uncertainty and very high levels of mortality.
These populations have short periods of gestation, short birth intervals and short generational lengths (roughly, the time between birth and peak of reproduction). They are characterized by small body size (height or weight/height)

The K-strategies applies to populations who live in more stable environments, where lower reproduction rates are compatible with reduced risk, uncertainty and lower levels of mortality. These populations have longer gestation, longer birth intervals and much longer generational lengths. They are characterized by larger body size.

There is a strong empirical relation between generational length and body size
{Graph # 1 from Livi Bacci, pp. 5, relating body length and length of maturation period}
{Graph # 2 from “Offspring”, pp141, relating body weight and length of various periods, maturation, gestation, weaning}
b. Is this classification acceptable?
If you envision the population dynamics of r-strategy populations you would probably think of the following: population size fluctuating and oscillating wildly, attaining very low and very high values within relatively short periods of time (time scale adjusted for their life expectancy).
On the other hand, the K strategy should result in minor oscillations even over long periods of time and on a relatively short distance between maximum and minimum population size.
This characterization is probably incorrect. In particular, humans--a K-strategy species--have experienced growth dynamics close to that applicable to r-strategy species. In particular, throughout most of the time humans have inhabited earth, say from 1-2 million years ago until close to 1750 years ago, population growth in just about all human settlements, including bands of hunters and gatherers in the Paleolithic, followed a dynamic that more closely resembles the r-strategy than the K-strategy. Our objective is to show precisely that.

III. A simple model for growth
In order to understand the dynamic of human growth we use a very simple model derived from stable population theory.
First of all, remember what a rate of natural increase is (when there is no migration)
but if r is constant between say year T1 and year T2
r= ln (P(T1)/P(T(2))

Remember also that in a population closed to migration that has experienced constant mortality (the rates Mx) and constant fertility (Fx) for relatively long periods of time (100 years or more), the following equality holds true:

where NRR is the net reproduction rate, r is the rate of natural increase and Tg is the “length of a generation”. Think of Tg as the mean age at childbearing. This age fluctuates but within a narrow range centered at around age 25. There are two equivalent ways of interpreting this expression:
a. Meaning of NRR ( I)
NRR is equivalent to the ratio of the size of a generation of daughters to the generation of mothers that produced them. Thus, if NRR is 2 it means that each mother produced 2 daughters during her reproductive life. If the regime is maintained the population will double every 25 years.
b. Meaning of NRR (2)
We also defined NRR as follows:
NRR~.50*∑ Fx*S(x)
where Fx are age specific fertility rates and S(x) are probabilities of surviving from birth to age x. The multiplication by .50 converts total births into female births)
Imagine now that all childbearing is concentrated at age Tg. Thus, if women in this population have a TFR of about 4 (so that their GRR is about 2.0) they will deliver 2 girls when they reach age 25. Since NRR is roughly equal to GRR multiplied by the probability of surviving up to age 25 we have:
NRR~.50*∑ Fx*S(x)~GRR*S(25) = exp(r*Tg)
(remember that exp(x)=ex where e is the base of Naperian logarithms)

Because we are assuming that Tg is fixed --a convenient though not entirely accurate fiction--we can think of the quantity r as determined by S(25) and GRR only. Once you fix these two quantities, there must be only one possible (real number) rate of increase, r, that is compatible with them. Fixing S(25) means fixing the mortality level of the population. Fixing GRR means fixing fertility or reproduction level of the population.

c. Values of r
What are plausible values for r?
We can play with possible ranges for S(25) and GRR to determine plausible ranges for r. One extreme would be to have S(25) be equal to 1.0, that is, there is no mortality before age 25. This can now be combined with two possible scenarios for GRR: one where GRR attains a maximum observed (about 4.5-5.0) and another where it attains a minimum observed (about .85). We then have the following possibilities:
1 x 4.75=exp(r x 25) implies that r=.0623

1 x .85=exp(r x 25) implies that r= -.0065

Now, think of a population exposed to very high mortality so that S(25)=.30, a perversely high level of mortality. This would now yield:
.30*4.75=exp(r x 25) implies that r=.0142

.30 x .85=exp(r x 25) implies that r=-.0547

So, the range for r is between -.0547 and .0623
R expresses number of added persons per person years of exposure. Thus, if r=.0623 we are adding 6.23 persons per 100 persons (in the middle of the year). If r=-.0547 we are taking out 5.47 persons per 100 persons (in the middle of the year).
To see it in a different light, think of the doubling times of a population: if r remains constant the population will double during an interval that depends only on r and a constant. In particular, if the rate of natural increase is r then the doubling time is approximately .69/r. Thus, if r= .0623 the doubling time is 11.08 years. If r = -0.0547 the ‘halving’ time is about 12.6 years.
d. Growth spaces

Since a value of r depends only on S(25) and GRR, we could construct all possible combinations of values for S(25) and GRR that produce the SAME value of r, say r=.010. Then you can plot the resulting points in a graph having GRR in the y-axis and S(25) in the x-axis. The result will be a curve that resembles a hyperbola on the xy plane

If one increases the value of r to be, say, .020, we will produce another hyperbola only that this time it will be located at a higher level than the first one. Suppose we repeat for all values of r we consider plausible (see above). The result will be a graph such as the following:
(Graph # 3a on growth spaces here; from pp 23 Livi Bacci)

(Graph 3b on growth spaces here; from pp22 Livi Bacci)

IV. A tour of the growth space
Livi-Bacci suggests that we should think of population growth as governed by two forces: (a) constraints and (b) choice. The forces of constraints can emanate from biology (the relation of fertility and mortality to biological conditions) and from the environment including those that limit space, production of food and environmental resources. The forces of choice influence preferences and behavior so that population dynamic is consistent with the constraints. Some of these choices may be conscious, but some of them may not be altogether understood by actors. For example, lengthy breastfeeding periods are socially enforced in some societies but their rational is not that they protect the health status of the infant
Livi Bacci thinks of these forces as if they acted in tandem and sometimes one was dominant over the other.

I prefer to think that human populations always evolve under constraints and that sometimes these constraints force adaptation in physiological or biological characteristics and others instead they impose boundaries reflected in choices or behaviors

=Examples of constraints affecting physical and biological characteristics

a. Body size adaptation (small body size in areas with frequent food shortages) may have operated but over very long periods of time. In order for it to work it needs time: adjusting body size is not a very useful strategy to avoid sudden onsets of crop failures.

b. Similarly, genetic changes of disease agents and simultaneous development of the immune system are feasible adaptations in co-evolution but they too require a long time.
c. Another example is the evolution of a thrifty gene that enables people exposed to frequent crises to store fat in periods of abundance. This ‘thrifty’ gene is thought to be behind the explosion of obesity and diabetes among some people
d. Other adaptations are more likely in a smaller time scale (they are more ‘time-efficient’). For example, improvements in diet may simultaneously increase fertility and reduce mortality. This occurs even if actors do not realize it and pursue improvements in nutrition for some other reasons.
=Examples of effects on choices
More interesting for social scientists are those adaptations that work through changes of behavior regulating birth intervals, and the duration women spend in unions within which reproduction is socially sanctioned.
a. Some societies practice infanticide when they face strong stress from environmental forces (like hunters and gatherers facing depletion of game or agriculturalists facing droughts)

b. We will see that an important mechanism for controlling the magnitude of GRR is the regulation of marriage and remarriage, a regulation that is intimately associated with patterns of land tenure systems and the social class system associated with the property system.

c. Another example is the choice of length of breastfeeding which modulates with some efficacy the length of inter-birth intervals. The post-partum taboo period in Africa has the unintended consequence of prolonging breastfeeding and bonding between mother and child.

d. A final example is the regulation of divorce and remarriage through which time spent in unions is regulated at least partially. In Africa for example, brothers in law acquire rights over their siblings spouses (levirate).

Choice and constraints have dictated the pattern of growth of populations over the very long run. One can place human societies (as averages) in the above graph: those in the Paleolithic period (before 10000BC) were located near the y-axis with GRR hovering around 3.0. The Neolithic period (roughly after 8,000-9,000BC) displaces societies upwards along the y axis (toward levels of GRR hovering around 4.0) but also moves them closer to the y-axis (meaning that mortality increased).

(See graph with space of growth above)

From 8,000BC up until 1700-50 there is a slow displacement toward the right (along the x-axis) as mortality decreases, but a more marked movement downward along the y-axis as fertility is constrained somewhat.
The period after 1700-50 sees two developments: first, in the western world there is a sharp increase in survival beginning in 1700 or so. This is followed by a lagged decrease in fertility lasting until 2000. Second, in developing countries, there is an even sharper decrease in mortality beginning in 1940-50 but no fertility decline until after 1970-80 when they experience sharp drops.
These various population phases can be translated in at least three different stages of growth, as portrayed by Deevey
(Graph 4a from Livi Bacci adapted from Deevey, pp.29. Also in Cohen)
Although there are appear to be three stages the reality is that the last period can be broken down in three, one from 1750-1800 until 1950 with relatively mild growth; another from 1950-60 until 1990 with very rapid growth and a third from 1990-2000 with mild growth again.
V. Population numbers and rates of increase.

What is it that these patterns meant in terms of population size and rates of natural increase? What forces actually kept populations in a particular location or displaced them along the xy-plane?

a. Numbers
First, let us agree on a time scale: the earth is about 4-5 billion years old. First cells (eukaryotes) may have appeared between 3 and 4 billion years ago. Human ancestors may have started to appear between 1 and 4 million years ago. But humans with modern anatomy date back to 130,000 to 150,000 years ago ONLY.
Second, let us use some very rough estimates of population counts. The population estimates we have are simple guesses and should not be taken too seriously unless one attaches to these numbers large standard errors. To at least consider these errors, I give ranges rather than point estimates:
Population around 10,000BC (end of the Paleolithic period) ~ 2-20 million

Population around 1AD ~ 170-300 million

Population around 1750 ~ 650-850 million

Population around 1950~ 2,200million

Population around 2000~ 6,000million
The implied rates of increase between each period are as follows ( I am using the midpoint of ranges for all calculations):
Paleolithic period (from a small band of 500 guys to about 11 million) between 140,000 and 10,000 BC): r is of the order of .00007691 or .007691 per hundred persons. This implies a doubling time of about 8,971 years.
Neolithic period (from 11 million to about 235 million in about 10,000 years): r is of the order of .00030617, ten times higher than during the Neolithic period. The doubling time is reduced from 8,971 years to about 2,250
From 1AD until 1750 r is of the order of .00066314 twice as large as during the previous period. The doubling time stands now at 1,045 years

From 1750 up to 1950 r is approximately equal to .00358. The doubling time is now 193 years

From 1950 up to 2000 r attains a value close to .02. The doubling time is at a minimum: 35 years.
A few remarks about these numbers:
i. They are approximations and different people could, justifiably, assign different numbers to the various periods. However, the statements I make below based on these numbers would not differ appreciably, irrespective of who produces the estimates.
ii. These numbers are averages and conceal an enormous amount of variation if one uses as unit of analysis entire countries or even large geographic areas.
b. Important statements derived from these numbers
i. rapid population grow (r>.010) is a very recent phenomenon. If populations had been growing at the same rate as they were growing during the last period (r=.02), the starting point would have been not more distant than 1930.

If one accepts than human populations started when they did and had grown at the same rate as during the most recent period, there would not be enough matter in the universe to produce the bodies we would have.

Inference No 1: Something very special happened very recently (200 years ago) to sustain these rates of increase.
ii. A graph of population size over the entire period surveyed here shows a very flat curve for most of the time interval with a sudden increase and take off around 1700-50. This is difficult to model: it cannot be captured by a known function unless you break the entire interval into smaller periods
(Graph # 4b, 4c, 4d from Cohen, p.55)

iii. If we concentrate our attention on the period past 1AD then we see what appears to be a hyper exponential curve: population was not growing at a constant rate but at an increasing rate of increase; the rate of growth may itself have been growing exponentially. But even this model does not fit very well the data we have.

So, what’s going on?
An important regularity that accompanies population growth is the growth in the production of energy. Indeed, if you graph estimates of absolute magnitude of kilowatts produced per person over time (and these estimates are even more inaccurate than those of population) you will obtain a curve that resembles that of population: thus, energy production, a reflection of our ability to domesticate nature, appears to be behind population growth. But is it energy that sustains growth or is it growth that pushes the invention of technology to extract energy?

(Graph # 4e from Cohen Table on energy output}

Another regularity is that populations have grown is height and weight: parallel to the growth of energy there has been an increase of BMI and, independently, of body weight and height. In general a growth of BMI (Body Mass Index=weight (kgs)/[height(mts)]2
Inference No 2: Growth of the population is related in one way or another to energy production and size adaptation.

VI. A tour of some important periods

For this part I am adopting Cohen’s periodization of population history. This is slightly different from the one adopted by Deevey or by Livi-Bacci for it breaks down both the agricultural and industrialization periods into two subperiods.

a. Hunters and gatherers
For all we know life expectancy must have been around 20 years with a great deal of mortality occurring early in life and during young adulthood. Fertility was not at a maximum but may have been of the order of 5 to 6 children per women.

Birth intervals were very long and they were maintained so by long periods of breastfeeding. Fecundity at young ages was low and a number of social rules and behaviors reduced drastically the fecundity of young adult women. These populations were highly vulnerable and many which did not adhere to the pattern we now recognize as typical of H&G went extinct.

Their absolute size (of hunting -gatherers bands) is likely to have been harshly pressed against a ceiling since the bands could not move around in large numbers without generating food shortages
An important point is that high mortality was a product of violent deaths (among young adults) and of mortality at early ages (perhaps below 5). It is unlikely that infectious diseases had any appreciable effect. Lack of food and outright starvation may have been more likely killers.
b. Agriculture
The establishment of agriculture took place in several places simultaneously at very different times. It surely spread from one settlement to another. Its origins are believed to be a response to shortages produced by extinction of game at the end of the last glacial era. This is one of the first pieces of evidence we have regarding effects of population on environment. Domestication of animals was an important part of early agriculture and this is perhaps the first quantum leap in terms of energy production.
{Table-Graph #5 from Jere Diamond about here}
Population dynamics changed dramatically as the ceilings applicable to hunters and gatherers were lifted. First, fertility is likely to have increased substantially for sedentary life styles did not require lengthy birth intervals. Duration in unions--within which reproduction took place--may have also increased substantially (early marriage was now possible).
Finally, numbers also mattered as the strength of a clan or a group and their ability to defend a settled territory was a function of sheer numbers.

It may be that there was an element of choice playing here, albeit unintentionally, in that the cost of childbearing was reduced significantly whereas the value of children (as labor) was increased.

Second, the archeological evidence plus our inferences from the nature of the transformation suggest that life expectancy must have decreased. Two elements are important here.

The first is that the quality and variety of the diet must have declined. Unlike H&G, the first agriculturalist relied on monocultivation and in the absence of commerce, a diet based on one product --even potatoes-- would surely lead to chronic malnutrition. The second is that the increased density of settlements must have made the exposure to and transmission of infectious diseases much easier. In addition, animal domestication for all its pluses, leads to increased contact with infectious diseases that are harbored by animal populations
(Some of the contrasts between H&G and agriculturalists can be observed today, albeit crudely, by comparing, for example, tribes in the Amazons or Papua New Guinea with people practicing primitive agriculture. We also know for example that !Kung fertility increased as they settled. And so did their mortality levels)
As Cohen suggests, it is probably useful to separate agriculturalism before say 1AD and after. The transformations of agriculture technology and the establishment of property systems dictated very different conditions in the more modern period. Indeed, it is during the period following the collapse of the Roman Empire when we begin to see the makings of a population dynamic that is the closest we get to a homeostatic or Malthusian balance. Not that the other periods did not witness such dynamic. Only that in the post-Roman empire years, it became more clearly delineated. The operation of the system required the existence of social classes or of a hierarchy. And social classes and hierarchies were the product of the first agricultural revolution.

But before I go into that, I want to identify some characteristics of the post-Roman Empire period. At around 1000AD The European population was increasing, and this lasted for over 300 years. This may have reflected renewed impetus in agriculture, new crops, new techniques, new land brought under cultivation. But toward the end of this period it was clear that the process was being hampered by more frequent crises (caused by harvest failure, weather related conditions, and also frequent wars).

Increased frequencies of crises simply reflect the vulnerability of the population to the agricultural mode of production, a vulnerability that did not exist among H&G. It may well be that given the level of technology the population engine was losing steam, reaching a ceiling so to speak.
A pertinent question at this point (but one that we will try to answer later) is the following: was agriculture a spontaneous invention or did it emerge mostly as a response to population growth that could not be handled by a H&G mode of production? Some historians and archeologists have interpreted the rise of agriculture as a natural response to the extinction of animal resources due to intense hunting. If so, population growth may have preceded full adoption of agriculture and the population growth that followed adoption was simply sustained by agricultural production.
Then, the plague struck (circa 1350). The entire population of Europe subsequently shrank by about 1/3 in the course of the next 200 years.
What is the plague? It is caused by a bacillus (yersinia pestis) that lives very happily in mice and is transmitted by fleas. Humans became a good mode of transportation due to their close vicinity to mice. The plague had struck before (200AD and then again in 400-500 AD) but had had limited effects, perhaps because of the low density of populations. This time it came and went several times before being finished. And, just as suddenly as it appeared, it disappeared (circa 1660).
Why was the plague so virulent?

Partly because it was a new form (mostly pneumonic). Partly because there were very favorable conditions for re-infection (crowding) . Partly because improved immunity after contact strengthened defenses only marginally. Partly because during this period other conditions were weakening populations (other diseases as well as wars and continued famines and malnutrition)

Why did it disappear?
The reasons for the disappearance of plague are fairly mysterious. One explanation is that the bacillus lost steam and became more benign or that immune responses finally kicked in after nearly six to seven generations of exposure. Another is that there was revolution in hygiene practices not the least of which is that the mice population may have become more isolated from the human host due to different housing construction techniques.
An interpretation: Livi Bacci, page 48 suggests that it was a totally exogenous event.
Read paragraph starting with “ The plague constitutes ……”
(read text by Livi-Bacci)
This may be too radical a conclusion. If the plague settled well in Europe it was because population density, living conditions, means of communications, and population flows did facilitate transmission. This is not something to be interpreted as ‘exogenous’. Livi Bacci statement implies that if you consider history as a repeatable experiment, it is very unlikely that plague would have emerged when it did, keeping everything else constant. This is a not a provable counterfactual but the factors that appear to explain the appearance of the plague do not suggest that it was a totally exogenous event.
This is important to keep in mind since it is an example of the controversies that are generated when people make statements about whether or not population is related to environments (in this case we are speaking of a “disease” environment)

Be that as it may, the truth is that the period of the plague was the last that saw the population of the continent dwindle seriously. From then on populations recovered handsomely and then grew some, albeit under a regime with frequent setbacks and recoveries. This is the period characterized by frequent population crises followed by robust rebounds. This system is what is known as the Malthusian or homeostatic population regime.

VII. Homeostasis

The main statement we made before is that the population regime established on the shoulders of the new agricultural mode of production led to higher rates of increase. But, over the long run the prevalence of frequent crises and important adaptive behaviors kept populations within check, that is, not exceeding limits imposed by the ability to produce food. This system was in place for a long time but nowhere is made clearer than in Europe during the period 1000-1700/50.

{Graph # 6 from Wrigley, pp 83; Colyton}
First, I will show you a few graphs for Egypt that reveal how the population regime worked.
Second, I will give you an example of this regime using Ireland as an illustration. Finally we will try to introduce a model that captures the essential features of the population regime.
a. An illustration from Egypt
The graph show comes from Cohen’s page 39 and it is derived from data from a study by the historian Hollingsworth. It reflects what one would observe were we able to put a microscope on population trends over the European or Eurasian continent. A few remarks will suffice to draw some lessons from this:
First, population size fluctuated wildly. Note that the range in a period of about 2,500 years is 2.5-28.5 millions.
Second, the peaks and valleys in the picture reflect declines followed by recoveries. As soon as decline takes place--say after an epidemic--there is a quick recovery that oftentimes overshoots the mark.
Third, this picture negates the imagery of a species regulated by a K-strategy. This is certainly not a reflection of a population not exposed to large fluctuations.

Fourth, the question that one may pose at this point is the following: was the population system regulated by mechanisms that forced it to have a close-to-zero population growth?

It certainly looks that way for Egypt (over the long run), and it definitely fits with what occurred empirically in Western and Eastern Europe. But then, what were these mechanisms? And how did they operate? Were they dependent on conscious choices or did they take place and function independently of men’s will?
b. An illustration from Ireland: the role of potatoes.
Livi-Bacci provides four illustrations of population adjustments (population regimes). The first is the case of the Amerindian population that, due to facts associated with the conquest, declined rapidly and in some cases ended in outright extinction. The second is the case of French Canadians and the population explosion after migration. The third and fourth illustrations, Ireland and Japan, represent cases of populations that somehow adapted and survived though the strategies used were markedly different. We should study the case of Ireland in some depth because it highlights the role that human behavior played to adapt to constraints imposed by environment and by the ability, or lack thereof, of populations to render these constraints less harmful.
b.1. The potato
Potatoes have been virtually the only staple sustaining populations in the high Andes for centuries. It is a food/staple that has three very important properties and several drawbacks:
-nutritional content: potatoes are almost a complete food. They contain all the basic minerals and vitamins. They are especially loaded with vitamin C particularly when not overcooked. However, they lack vitamins A and D and Calcium. Potatoes and milk products, however, provide a fairly complete meal. Even with the deficit in calcium and vitamins, weight for weight, potatoes can provide more than enough calories.

-yield: potatoes are very adaptable and can grow even in the most adverse climatic conditions (such as those of the high Andes). They thrive in wet weather and mild

temperatures, conditions that were and are still widespread in Ireland, among other places. They require relatively low amounts of labor and minimal technology. Most importantly, the yield per acre is high which means that a peasant does not need vast amount of land to produce what he/she needs to consume. Under normal conditions, small plots result in suitable yields at least for subsistence.

-secondary benefit: they can be fed to some animals with ease and constitute a good diet for some domesticated species such as pigs. Thus, peasants can combine the care of some domesticated animals (the Irish used pigs) and cultivation of potatoes without having to choose between one and the other (as is the case for example with animals that need vast spaces to graze and the cultivation of oats or wheat)

-storage: although potatoes do not last very long before going bad, they can be transformed into a flour that retains nutritional values and can be preserved for long periods of time (“chuno”). As far as I know this was not something Irish people adopted.

And this may have led to the famine we will describe later
Drawbacks of potato cultivation are several:
-they are difficult to transport so bartering them is rarely an option in areas with low levels of energy for transportation;
-although robust, they tend to be affected by a number of pests against which there is little safeguards (except variety)
-without complementing them with some other foods, the persistent deficiency of calcium and vitamins A and D can lead to nutritional deficiencies of some importance.
b.2. The Irish

Prior to the adoption of potatoes as the only staple (monocultivation) in Ireland, the main meal courses were oatmeal, salted fish, milk and milk products and some meats, particularly pork. Potatoes entered via England sometime during the middle of the 1600th and after some resistance, its cultivation spread to the entire island but mostly to lower classes. It is estimated that at some point around 1800 about 50% of the average Irish population’s diet depended solely on the ingestion of vast amounts of potatoes (about 5.5 lbs per person per day or the equivalent of several tons per year per person). Initially it was combined with consumption of milk and milk products as well as oats. But, as the dominance of the root increased, cultivation of other staples became more difficult and the tenure and grazing of animals impossible. As a consequence monocultivation led to ‘monoconsumption’. This created one condition important to keep in mind: high vulnerability. If a crop failed there were no backups to speak of.

Now, let us look at some numbers before we go on. The following are estimated population figures for Ireland:
1732----2.2 million

1791----4.8 million

1841----8.2 million

1901----4.5 million

There is at least one thing clear: population declined after the potato famine around 1845-49. The decline was due to: (a) migration, (b) mortality and (c) decline in birth rates.
Two issues are NOT clear:
(i) was the population increase prior to 1841 directly related to the adoption of the potato as a staple? And if so, what exactly were the mechanisms?
(ii) how exactly did the failure of the potato in 1845-49 depleted the population of Ireland?
Let us address the first issue first. The evidence available indicates that, if Ireland was like England or other countries in Western Europe, population was increasing before the widespread diffusion of the potato. The evidence is not really numerical but based on individual historical accounts. But the reasons for this phenomenon are still unclear. The following are two possibilities:
-even in the absence of technological improvements, expansion of land cultivated (to marginal lands) and adoption of marginally better techniques could have increased caloric intake.
-the disappearance of some scourges such as the plague and attenuation of virulence of other diseases may have had beneficial effects on mortality levels.

-the age structure effects of the plague were powerful: remember that with a more favorable age distribution (fewer people in adult ages) pressure on resources may have been lower, employment levels higher, and overall levels of well being may have been on the increase. This could have had positive effects on fertility

Higher nutritional levels and higher levels of well-being are favorable to higher marital fertility and may have increased marriage rates and the time spent within marriages. Mortality levels may have been coming down as a result of less damage produced by a handful of strategic diseases. Thus, the natural rate of increase went up.
But this could not have been all there is to tell about this story. It is impossible that such rapid rates of growth could have been sustained given the existing land tenure system and prevailing levels of technology. The adoption of the potato must have sustained persistent growth. It may not have caused it but it surely would not have gone for so long without the spread of potato cultivation.
So, how did potato cultivation sustain relatively high rates of increase?
Imagine the following scenario:
-what a laborer produces, O, is a function of two inputs: land and labor. There was no capital to speak of. If one increases labor on a fixed plot of land, the yield per laborer will be reduced. This is the so-called law of diminishing returns:
product per worker=A x (labor)b
where b is less than 1.0 and A depends on the amount and quality of land as well as of minimum technological inputs
-the property system is characterized by landowners who simply did not invest in land and were not at all interested in increasing production. Land was a status symbol. Property was highly concentrated. Somebody had to pay rent and these were the tenants who leased land and then subleased it to those who actually cultivated it.

-to exploit the land one needed arrangement so that production was organized in some fashion. The Irish used the so-called ‘rundale’ system. Through this a group of families would lease and then subdivide a piece of land and would appropriate what they could produce, using part of the product to pay rents and the remainder to consume. In the absence of technological inputs and in the absence of marginal lands, subdivision leads to lower yields per person. Thus, this system works well only if the population remains stable or grows very slowly.

{text from Zuckerman page 38}

-a further stimulus had to do with the system called cornacre whereby a tenant would rent prepared land for cultivation and would not have to pay rent until the crop was in. This amounted to a loan with no interest. Since rent could be paid by the sale of a pig, the crop could be consumed. This arrangement was far LESS risky than an equivalent arrangement: search for a low wage job and buy potatoes.

{Zuckerman’s text page 149}
-continuous subdivision of land would drive down yields on any crop except potatoes (remember that potatoes are a high yield crop).
-cultivation of potatoes was compatible with:
possibility of wage labor somewhere else;

domestication of pigs;

-Thus, adoption of potato cultivation essentially enabled Irish farmers to maintain subdivision of land without affecting standards of living. This had two important consequences: it did not put pressure on (a) the marriage regime and (b) on fertility within marriage. Males could seek partners since they would be endowed with some land at some point in their lives and that would be enough to sustain a traditionally large family.
{text Zuckerman page 42; 43-44}
-Continuous subdivision of land impaired the production of other products (milk, meat, other cereals) and rendered the population totally dependent on the single staple. Further, subsistence must have been at the margin: that is, nutritional levels were volatile.
-Result: vulnerability of the population. In fact, there were several famines prior to the Great Famine of 1845-49. But population was able to recover.

Imagine the following counterfactual scenario: the potato was not as gracious as it actually was. Say that it was a more labor-intensive crop, with low nutritional value and requiring higher acreage per weight of product. Then one of three things (or all three or combinations thereof) would have occurred:

marriage system would have changed

marital fertility would have declined

mortality would have increased

So this much is clear: relaxation of fertility and marriage norms was only possible under a land tenure system that permitted subdivision without driving down the production value of the land. But it did lead to a negative outcome: high dependency on one crop only.

b.3. The Irish, the potato and population decline.
So, a pest arrives and destroys the entire crop for several years in a row. Then the whole system collapses: migration becomes a tide, mortality shoots up since malnutrition takes a toll among infants and the elderly already on the verge of being deficient in a number of nutrients, and younger people are unable to marry, time for reproduction is lost and fertility is driven down.
The key question here is the following: was it population increase that led to the crisis? Or was the crisis unrelated to population? (remember main issue raised above by Livi Bacci regarding the Black Death)
The answer it seems to me must be a qualified YES (as it was in the case of the Black Death). The pest imported into England arrived by chance. It was a truly exogenous event. But what took place after its arrival was closely dependent on the population growth regime and what sustained it, the property system. Given a sudden tightening of environmental conditions (introduction of the potato virus) the population growth mechanisms reacted and led to a different equilibrium.

{Epilogue: Zuckerman page 228}

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