Second International Conference on Sociocybernetics

Panticosa, Spain - June 2000

"The Aggregate Female Fecundity Interval (AFFI)"

The Origin of the Periodicity of "Lösch" Birth Waves

DRAFT January 20, 1999

Copyright © May 9, 2000, James T. Corredine
All rights reserved. Permission granted to make one copy for noncommercial use.

(Figures not included in Web Site Version)

Author’s Note: I would like to express gratitude to Professor John R. Weeks for his personal suggestions, to Professor Tessaleno Devezas for special help in pinpointing the source of the Lösch Axiom in the original German and physicist Nick LaRocca for his help and counsel.


This paper investigates August Lösch’s population cycle analysis using modern population and demographic concepts to propose a system of biological time constraints that underlie Lösch’s axiomatic ~33-year repetitive time interval on which he based his predictions. The primary time constant is identified as "The Female Fecundity Interval" which taken collectively becomes "The Aggregate Female Fecundity Interval." This "Aggregate Female Fecundity Interval," determined by the ages of first fecundity and menopause at extreme opposed ends of the fecundity range as a subset of a normative life span becomes the foundation for further mitigated constraints that ultimately result in the periodicity, broadening and flattening of the birth waves. These waves are basic elements of recurrent socioeconomic phenomena, such as Kuznets cycles and Kondratieff Long Waves


Lösch (1) in 1936 has stated: "We find quite clearly great [centennial] waves, the main cause of which are the great wars. The deficit of births during a war and the surplus of births in the immediate postwar period repeat themselves about thirty-three years later, when the new generations are at their time of highest fertility (author’s brackets and italics). For the same reason thirty-three years later a third wave occurs. Of course these subsequent waves become broader and broader, flatter and flatter, and after a hundred years entirely interfere with each other,…"

At this observation of an approximate ~33-year biological periodicity, we must make our inquiry.

Analyzing the fecundity concept Weeks (2) recently stated: "The physical ability to reproduce is usually called fecundity by demographers. A fecund person can produce children; an infecund (sterile) person cannot. The term fertility is typically reserved to describe reproductive performance, that is, the actual birth of children, rather than the mere capacity to do so …. For most people, fecundity is not an all-or-none proposition and varies according to age. Among women it tends to increase from menarche (the onset of menstruation, which usually occurs in the early teens), peaks in the twenties, and then declines to menopause (the end of menstruation).… If we assume that an average woman can bear a child during a 35-year span between the ages 15 and 49…" (my italics).

Here Weeks helps us understand the periodicity of Lösch Population Waves. The 35-year span he describes should have a name. In this work it is proposed to call it the "Female Fecundity Interval." Taking together all women in a population, the collective "Female Fecundity Interval" should be called, "The Aggregate Female Fecundity Interval", or AFFI for short.

This 35-year time-constant, "The Female Fecundity Interval," taken in the aggregate is the foundation of the periodicity of the recurring "Lösch ~33-year Birth Waves." It is the discreteness of the fecundity interval in relation to the normative life span that sets up the conditions and limits for the aggregation, periodicity and repetition of fertility and birth waves which in consequence create the changing age distribution dynamics of populations.

The midpoint of the average 35-year maximum "Female Fecundity Interval" is half of 35 years or17.5 years into the interval. Since the average age of first fecundity is 15 years, adding 15 to 17.5 yields 32.5 years old as the average age in a woman's life when she is at the midpoint in time of her potential ability to bear a child.

When the number of total births in a population peak for whatever cause, speculation might suggest the peak should take place around the approximate mathematical midpoint of an "Aggregate Female Fecundity Interval." Even if this is not exactly the case, once the baby boom is established, because of the biological periodicity of "The Aggregate Female Fecundity Interval," the next peak should occur, one might suspect, about 32.5 years later, somewhere around the midpoint in time of the succeeding "Aggregate Female Fecundity Interval." This coincides closely with what Lösch calls "new generations…at their time of highest fertility."

However, as Weeks (2) points out, fecundity is not uniformly spread over the reproductive years (Fig. 1) – it is stacked up in the earlier years. For this reason, the average age of childbearing occurs earlier in the interval, rather than at the mathematical midpoint. The calculation of this age, which demographers call the "mean length of generation" or "mean reproductive age of females," is shown below (Table 1). For the U.S. in 1995, as shown, it was 26.79 and not 32.5.

Nevertheless, recent United States demographic history supports Lösch’s 1936 observations of an approximate ~33-year birth wave periodicity as was manifest in the German case last century (Fig.2) and is now manifest in the U.S. case as shown by Dent(3) (Fig. 3). Post-war Baby Boom births peaked in 1957 and Baby Boom Echo births peaked in 1990, ~33 years later. This is the same ~33-year periodicity observed by Lösch 63 years ago.

The 35-year biological time constant "Aggregate Female Fecundity Interval" helps to explain the causality of the periodicity of the birth waves. In the U.S. Baby Boom mothers in the aggregate gave birth to the most Baby Boom daughters in or around 1957. Their daughters have now given birth to the most Baby Boom Echo daughters in 1990, at or around the midpoint of the succeeding "The Aggregate Female Fecundity Interval." But, this time periodicity does not appear to match the "mean length of generation." One would assume that if most daughters were born in 1957, and a mean length of generation of approximately 27 years is normative, then the next peak in births would have occurred about 1984. THIS IS NOT THE CASE. Instead the peak is indeed 33 years later, as Lösch would predict, based on his axiom that births "repeat themselves about thirty-three years later, when the new generations are at their time of highest fertility."

It is now evident in the U.S. case this century, as it was in the German case last century that a ~33-year birth wave is manifest. The 33-year wave is not explained by the demographic convention called the "mean length of generation," (normative at about 27 years as we see in fig 1.) Certainly, however, the origin of this ~33-year birth wave, when manifest, must be biological as Lösch states. Further logical explanation of his axiom "when the new generations are at their time of highest fertility" had not been available to us in his writings in English. But this is the heart of the matter and the only elemental time-constant that can work as a regulatory mechanism and serve as the origin of the birth wave is the 35-year "Aggregate Female Fecundity Interval."

Lösch in his original German text Bevolkerungswellen und Wechsellagen (4, p.3) states: "Für solche breiten Wellen ist nicht nur (wie auch für die übrigen) der Abstand der Wendepunkte, sondern auch der Abstand von Hoch zu Hoch, oder von Tief zu Tief, eine Generationslänge (rund 33 Jahre, vgl. Anm. I S.I)." This translates closely into English as: "For such broad waves (as also for the remaining) not only the distance of the turning points, but also the distance from peak to peak, or from trough to through are, a generation length (approximately 33 years, viz. note I S.I)." (Author’s translation).

Viz. Note 1 S. 1 refers to footnote one on Page one of Bevolkerungswellen und Wechsellagen that reads: "Das mittlere Alter Mütter bei der Geburt war in Schweden 1750-1900 ungefähr 32 Jahre, die Ehemänner waren rund 3 Jahre älter, das mittlere Alter der Eltern betrug demnach 33.5 Jahre. Für Deutschland mag wegen der früheren Eheschließung die Zahl um a Jahre zu vermindern sein. Die 30-35 jährigen Ehefrauen liefern unter allen Altersklassen absolut die meisten Geburten.". This translates closely into English as: "The average age of mothers giving birth in Sweden during the years 1750-1900 was approximately 32 years, the husbands were approximately 3 years older, the average age of parents amounted therefore to 33.5 years. For Germany the number may have to be reduced somewhat because of earlier marriages. However, of all age groups, it is without question the 30-35 year-old wives who give most births." (Author’s translation).

This footnote is the foundation for Lösch’s axiom that the births "repeat themselves about thirty-three years later, when the new generations are at their time of highest fertility." Lösch, for his convenience, simply added 32 and 35 then divided by 2 to yield 33.5 years as the average periodicity on which to make projections. Note that Lösch himself was not specific about the exact timing of the repetitions. He used the superior Swedish data to arrive at his axiomatic number of 33.5 and then noted that the number may have to be reduced somewhat for his German projections, perhaps the reason he uses the phrase "about thirty-three years later."

So then, it is not just the mean reproductive age of females or mean length of generation based on female reproduction (which is current demographic convention in measuring generations), 32 years in Lösch’s Swedish case and 27 years in Weeks’ American case that determines the periodicity of the birth waves. What also must be considered is mean reproductive age of the husbands, 35 years in Lösch’s Swedish case and undetermined in the American case. This obscure insight is the key to understanding the dampening of the Lösch birth waves.

Indeed, the descriptions of a generation length in the literature are unclear. Malthus in "An Essay on the Principle of Population" (5) from observation of the unchecked population growth in the early United States, took a twenty-five year interval as his rule for a natural length of generation. Lee (6) notes: "a tendency for human populations to move in cycles of one generation, or twenty-five to thirty-three years; we will call these ‘generational cycles’ or ‘echoes."

We can see from our discussion that the "length of a generation" or "generational cycle or wave" may range from 25 to 33-years varying from time to time and place to place according to these different authors and that of course they must have their origin in the 35-year AFFI time constant.

To help clear up thinking in this area, we should continue to identify and name biological time periodicities. Here are some suggestions. The demographers’ "mean reproductive age of females" or "mean length of generation" could be called The Aggregate Female Fertility Wave. The "mean reproductive age of the husbands" could be called The Aggregate Male Virility Wave. These two phenomena together could make up the Mean Reproductive Age of Parents, Parental Mean Length of Generation or simply the Parental Wave.

Now we can see more clearly the fundamental biological reasons Lösch’s subsequent waves become broader and broader and flatter and flatter. Following the initial baby boom, the first parental echo wave is itself composed of two waves that make it up, a Female fertility wave and a Male virility wave, each of different duration. This causes this parental wave to broaden and flatten. The second parental echo wave (Lösch’s last wave before a new centennial baby boom) is composed of four waves, even broader and flatter, two Female fertility echo waves, each of a typical duration, but born of separate preceding Male and Female waves, each with their own typical duration and two Male virility echo waves, each of typical duration, both the product of separate preceding Male and Female waves and their typical duration. Not only is the periodicity of the waves fundamentally biological in origin but the broadening and flattening characteristics as well.

While we have not exactly solved the mystery of why the ~33 year waves now manifest in the United States this century do not match up with the demographer’s mean length of generation in this paper, this discussion and the suggestions made will lead to a better understanding of biologically originated population wave dynamics.

In summary, the ~35-Year Aggregate Female Fecundity Interval (AFFI) time constant, a subset of the normative human life cycle, is the mother of "generational" waves or cycles that vary within narrow limits of 25 to 33-years. The overall generational cycle can be named The Parental Wave, consisting of The Aggregate Female Fertility Wave and The Aggregate Male Virility Wave each of different duration. The Parental Wave duration is the foundation of general population wave repetitions. The consisting disparate Male and Female wavelengths echoing over time cause the broadening and flattening of the overall waves.

The origin of the periodicity and dampening of Lösch Birth Waves is fundamentally biological in nature, founded in "The Aggregate Female Fecundity Interval." Furthermore, these generational cycles and intensities as mitigated by other control parameters form the foundation for the causality and timing of recurrent socioeconomic phenomena, such as Kuznets cycles and Kondratieff Long Waves (7).



  1. Lösch, August. Population Cycles as a Cause of Business Cycles, Annual meeting of the Econometric Society in Chicago, December 1936, (published in the Quarterly Journal of Economics 1936-7, 51, 649-62)

  2. Weeks, John R. Population, An Introduction to Concepts and Issues, Seventh Edition, Wadsworth Publishing Company, Belmont, CA, 1999

  3. Dent, Harry S., Jr. The Great Boom Ahead, Hyperion Press, New York, 1993

  4. Lösch, August , Bevolkerungswellen und Wechsellagen, Jena, 1936

  5. Malthus, Thomas Robert. An Essay on the Principle of Population, London, Printed for J. Johnson, in St. Paul’s Church-Yard, 1798
  6. Lee, Ronald, The Formal Dynamics of Controlled Populations and the Echo, The Boom and the Bust, Demography Vol 11, No 4, November 1974 pp. 563 –585.

  7. Devezas, T., and Corredine, J.: The Biological Determinants of Long Wave Behavior in Socioeconomic Growth and Development. Paper to be presented at the World Congress of the Systems Sciences, Toronto, July 16-22, 2000.