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Differential Reproduction - An Exponentialist View
Malthus and Evolution

Evolution - An Exponentialist View
Malthus - An Exponentialist View

External Links:
Natural Selection and Differential Reproduction - from Replicators: Evolutionary Powerhouses

Natural selection article on Wikipedia

Malthusian Selection on Wiki Academia

Social Darwinism article on Wikipedia

Malthus, Thomas Robert, An Essay on the Principle of Population. J. Johnson. 1798. (1st edition) Library of Economics and Liberty.  

Malthus, Thomas Robert, An Essay on the Principle of Population. John Murray. 1826. (6th edition) Library of Economics and Liberty.

Natural Theology; or, Evidences of the Existence and Attributes of the Deity (Google Books) by William Paley (1802 through 1809

Reverend Malthus and Evolution

"In science the credit goes to the man who convinces the world, not the man to whom the idea first occurs."
Sir Francis Darwin, Eugenics Review, April 1914 
http://www.quotationspage.com/quotes/Sir_Francis_Darwin/

Introduction

Malthus never wrote specifically about evolution, and never proposed any theory of natural selection. Indeed, philosopher Elliot Sober noted that what Malthus wrote (Sober, 1993):

"...concerned the regulation of population numbers, not the frequency of characteristics found in a population. In fact, Malthus thought his law prevents populations from changing much."

Malthus would have read of Aristotle's scala naturae, with its ladder of life and fixity of species. This view had held sway for over 2,000 years, right up to the works of his Malthusian convert and contemporary Archdeacon William Paley (1748-1805) who wrote his Natural Theology in 1802 on the Argument To Design as proof of the existence of God. 

Malthus stated, in the Summary View at the conclusion of his great work "An Essay on The Principle Of Population" (published 1798), that his own Principle Of Population was a further proof of the existence of God - a work of natural theology. Darwin's response to Paley's designer God, and the fixity of species, came in 1859 with Origin Of Species. Today is is accepted by the scientific community that there is no scientific evidence that proves the existence of any god.

Today evolution is accepted as scientific fact, and Malthus' unintentional contribution is often regarded as nothing more than an historical curiosity. However it was Malthus that first highlighted the process of differential replication, using human populations to illustrate his point.

Malthus' Influence On Darwin and Wallace

Most books on evolution briefly note that Darwin credits Malthus' essay as critical to his theory of Natural Selection. From Darwin's "Autobiography" (Darwin & Darwin, 1958):

"In October 1838, fifteen months after I had begun my systematic inquiry, I happened to read for amusement Malthus on Population, and being prepared to appreciate the struggle for existence which everywhere goes on, from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The result would be the formation of a new species."

Some books on evolution also quote Wallace, co-founder of modern evolutionary theory. This quote noted by Professor Frey (1970) in his introduction to the Penguin Classics edition of Malthus' An Essay On The Principle Of Population is typical:

"...the most important book I read was Malthus' Principle Of Population...It was the first work I had yet read treating any of the problems of philosophical biology, and its main principles remained with me as a permanent possession, and twenty years later gave me the sought-after clue to the effective agent in the evolution of organic species."

In Francis Darwin's publication of his father's autobiography and letters (Dover edition, 1958) I came across a rarely quoted letter from Alfred Wallace to a Professor A. Newton, Dec. 3rd, 1887. This passage immediately caught my attention (Darwin & Darwin, 1958):

"The most interesting coincidence in the matter, I think, is, that I as well as Darwin, was led to the theory itself through Malthus - in my case it was his elaborate account of the action of "preventative checks" in keeping down the population of savage races to a tolerably fixed but scanty number. This had strongly impressed me, and it suddenly flashed upon me that all animals are necessarily thus kept down - "the struggle for existence" - while variations, on which I was thinking, must necessarily often be beneficial, and would then cause those varieties to increase while injurious variations diminished....I was lying on my bed (no hammocks in the East) in the hot fit of intermittent fever, when the idea suddenly came to me. I thought it almost all out before the fit was over, and the moment I got up began to write it down, and I believe finished the first draft the next day."

Despite this "most interesting coincidence", modern evolutionists are still apt to play down Malthus' unintended contribution to evolutionary theory.

Population Thinking

As noted by evolutionist Ernst Mayr, one of those most generous in giving Malthus the nod, Darwin initiated "an entirely new way of thinking" (Mayr, 2001):

"Darwin's new way of thinking, being based on the study of populations, is now referred to as population thinking....Population thinking is one of the most important concepts in biology: It is the foundation of modern evolutionary theory..."

Later Mayr examines Darwin's explanatory model of Natural Selection, which is based on 5 facts and 3 inferences. What's interesting is the influence of Malthus on Facts 1 and 3 (Mayr, 2001):

"Fact 1: Every population has such a high fertility that its size would increase exponentially if not constrained. (Source: Paley and Malthus)...

...Fact 3: The resources available to every species are limited. (Source: observation, reinforced by Malthus)

Inference 1: There is intense competition (struggle for existence) among the members of a species. (Source: Malthus)..."

With regards to Fact 1, William Paley's Natural Theology (originally published in 1802, 4 years after Malthus' essay) is simply repeating Malthus' own argument, so I'm not convinced of Mayr's assertion Paley was a source of this fact along with Malthus (Paley, 1802):

"The order of generation proceeds by something like a geometrical progression. The increase of provision, under circumstances even the most advantageous, can only assume the form of an arithmetic series. Whence it follows, that the population will always overtake the provision, will pass beyond the line of plenty, and will continue to increase till checked by the difficulty of procuring subsistence (Note: See a statement of this subject, in a late treatise upon population.)"

Paley's note appears be a reference to Malthus' essay. Indeed, in the introduction to the Penguin Classics edition of Malthus' essay, Professor Flew (1970) states:

"Among his first distinguished converts Malthus was proud to number both William Paley and the younger Pitt."

However, I guess the main thing to note with regards to Fact 1 is that Darwin was influenced by Paley (who appears to have been influenced by Malthus), and by Malthus directly, so the source of this fact is basically Malthus alone. 

Thus, it was Malthus' original thinking on population which was pivotal to the creation of modern evolutionary theory. Not Paley, not Wallace, and not Darwin.

Malthusian Parameter of population increase

The term Malthusian Parameter was first coined by evolutionist R. A. Fisher in 1930 in discussing the population growth rate m (Fisher, 1930):

"The number m in which satisfies this equation is thus implicit in any given system of rates of death and reproduction, and measures the relative rate of increase or decrease of a population when in the steady state appropriate to any such system. In view of the emphasis laid by Malthus upon the 'law of geometric increase' m may appropriately be termed the Malthusian parameter of population increase. It evidently supplies in its negative values an equally good measure of population decrease, and so covers cases to which, in respect to mankind, Malthus paid too little attention."

I agree with Fisher's criticism of Malthus here - the lack of negative rate cases in Malthus' arguments is very clear and this absence does need to be formerly addressed. I have accommodated the negative cases into a Malthusian Growth Model in my article Scales of 70. Fisher goes on to examine the "close analogy" of population increase via the law of geometric increase with the growth of capital invested at compound interest, noting the absence of commercial products that use negative rates of interest. I have explored the relationship between compound interest and geometric increase in my article Compound Growth vs. Exponential Growth.

Fisher explains that the Malthusian Parameter effectively measures the fitness of a genotype relative to its environment. For example, comparing the growth rates of England and the United States of America Benjamin Franklin noted in his 1751 essay "Observations concerning the Increase of Mankind, peopling of Countries, etc.,"  (assuming the current population in the USA to be 1 million):

"This Million doubling, suppose but once in 25 Years, will, in another Century, be more than the People of England, and the greatest Number of Englishmen will be on this Side the Water."

Franklin was right, as the population of the USA now far exceeds that of England, and of the whole of the United Kingdom. This is an example of the differential reproduction of two discrete human populations through intraspecies competition. The key to understanding population doubling is the Malthusian Parameter, or population growth rate. Population doubling is a topic I explore further in my article The Mechanism Of Population Doubling.

From an Exponentialist perspective, the main issue with defining the population growth rate as the measure of fitness is that it ignores limits to growth. Although the Malthusian Parameter does indicate which populations of which species are "winning" the struggle for existence (or the survival of the fittest), such populations are inevitably impelled towards a point at which they have exhausted their resource supply.

Intraspecies Competition

Noted by Sober is the influence of Malthus on Darwin's thinking is the shift from interspecies competition to intraspecies competition (Sober, 1993):

"...the Malthusian paradigm pictures competition between organisms of the same species as an important force. Attention was shifted from the struggle between the lion and the lamb to that between the lamb and the lamb."

Of course, the species that Malthus focussed on was man. As Darwin put it in his notebook (Ridley, 1997):

"Malthus on man should be studied;"

Refer Human Replicators - An Exponentialist View for more on that topic.

Differential Replication

Many evolutionists stress the importance of differential replication (though they may use the phrase differential reproduction). Refer Differential Reproduction - An Exponentialist View for more.

Here Dawkins compares biology with physics (Dawkins, 1976):

"The laws of physics are supposed to be true all over the accessible universe. Are there any principles of biology that are likely to have similar universal validity?

...will there still be any general principle that is true of all life?

Dawkins states that he doesn't know, but is prepared to put his money on the following universal law (Dawkins, 1976):

"This is the law that all life evolves by the differential survival of replicating entities."

 I call this Dawkins' Law.

Even a cursory look through Malthus' essay, most especially from the second edition on, should convince anyone that Malthus was intrigued by this very point, especially in how it related to discrete populations of man. In A Summary View, Malthus makes his case for the differential replication of human populations plain (Malthus, 1830)

"It may be safely asserted, therefore, that population, when unchecked, increases in a geometrical progression of such nature as to double itself every twenty-five years. This statement, of course, refers to the general result, and not to each intermediate step of the progress. Practically, it would sometimes be slower, and sometimes faster."

And here in 1798 Malthus (well before Darwin or Wallace) extends the law of differential survival that Dawkins seeks to plants and animals (Malthus, 1798):

"The greatest check to the increase of plants and animals, we know from experience, is the want of room and nourishment; and this experience would direct us to look for the greatest actual increase of them in those situations where room and nourishment were the most abundant."

How is this possible if Malthus believed in the fixity of species? In An Essay On The Principle Of Population Malthus argues that human populations grow at different rates for specific reasons (Malthus, 1798):

"Taking countries in general, there will necessarily be differences as to the natural healthiness in all gradations, from the most marshy habitable situations to the most pure and salubrious air. These differences will be further increased by the employments of the people, their habits of cleanliness, and their care in preventing the spread of epidemics. If in no country was there any difficulty in obtaining the means of subsistence, these different degrees of healthiness would make great difference in the progress of population;"

Throughout the later editions of his essay Malthus gathered extensive evidence to prove that this was, in fact, the case. Malthus did such a thorough job of studying human populations (which grew at varying rates overtime) that he is today regarded by some as the founder of the field of demography (Peterson, 1979, 1999).

See Reverend Thomas Robert Malthus - An Exponentialist View and Malthusian Memes - An Exponentialist View for more.

Malthusian Selection

The theory of Natural Selection introduces the principle of differential reproduction (which I refer to as differential replication), which is typically explained as entirely the result of genetic variation within a species, including the effect of the genotype on the phenotype (Mayr, 2001):

"Owing to unequal survival and reproductive success of its individuals, there is a continuing genetic turnover in each population as a result of chance and natural selection."

However, this statement discusses the genetic make-up of a population. Chance is acknowledged to play a part, but how much of a part? (Mayr, 2001):

"Much of the differential survival and reproduction in a population are not the result of selection, but rather of chance.

This statement is the clincher. Differential survival and reproduction are largely due to chance. Yet, if populations are growing and shrinking at differential rates, then some are being selected for and some are being selected against. So, Mayr does not see chance as a selective force, only "selection" (meaning natural selection).

In discussing Herbert Spencer's famous phrase "the survival of the fittest", Mayr explains what it means to be fit (Mayr, 2001):

"To be fit means to possess certain properties that increase the probability of survival."

Elsewhere in his book, Mayr makes it clear that it is random genetic variation caused through mutation and sexual recombination which makes non-random Natural Selection possible. 

Sober doesn't think much of Malthusianism when it comes to selection (Sober, 1993, pp.194-195):

"Malthusianism is not a proper starting point for the theory of natural selection for reasons made abundantly clear by Fisher (1930, pp.46-47)."

Sober notes the following quote from Fisher (Sober, 1993):

"There is something like a relic of creationist philosophy in arguing from the observation, let us say, that a cod spawns a million eggs, that therefore its offspring are subject to Natural Selection; and it has the disadvantage of excluding fecundity from the class of characteristics of which we may attempt to appreciate the aptitude... The historical fact that both Darwin and Wallace were led through reading Malthus's essay on population to appreciate the efficacy of selection, thought extremely instructive as to the philosophy of their age, should no longer confuse the consequences of that principle with its foundations."

Sober is considering whether exponential population growth forces Natural Selection or whether Natural Selection forces exponential population growth. I think the point that Darwin and Wallace understood, but Sober does not, is that the "struggle for existence" between populations of the same and different species is forced upon us by, as Darwin put it (Darwin, 1859):

"...a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection..."

This Malthusian struggle for existence is a zero sum game, with a net gain for one population balanced by an equivalent net loss by another population (Darwin, 1859):

"In looking at Nature, it is most necessary to keep the foregoing considerations in mind - never to forget that every single organic being around us may be said to be striving to the utmost to increase in numbers; that each lives by a struggle at some period of its life; that heavy destruction inevitably falls either on the young or old, during each generation or at recurrent intervals. Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount. The face of Nature may be compared to a yielding surface, with ten thousand sharp wedges packed close together and driven inwards by incessant blows, sometimes one wedge being struck, and then another with greater force."

The "incessant blows" are struck with a Malthusian force. As discussed later in this article, Malthusianism also explains how a small founding population becomes a full-blown one (Zimmer, 2001). This is because the speed and relentless power of the exponential Malthusian forces (population growth) works as a much faster pace than Natural Selection and Darwinian evolution.

The exponentialist view is that Natural Selection, Artificial Selection, Malthusian Selection and Unnatural Selection all contribute to the rate of growth for a population  - the Malthusian Parameter - and thus each influences differential replication.

The Malthusian Parameter, as Fisher argued, measures genotype fitness relative to an environment. Hence, according to Fisher, differential replication is the result of differences in the Malthusian Parameter between competing populations (intraspecies and interspecies), depending upon the environment in which they find themselves. However, I believe that Fisher has missed something which Malthus did not - human cultural factors. I would also add that human cultural factors (for example, civilized societies compared to hunter gatherer societies) will also affect the Malthusian Parameter, as evidenced (for example) by the relative populations of pre-colonial Australia and the USA compared to their population sizes post European colonisation.

Malthus and Fisher would both agree that environment influences the growth rate, and so their two views intersect in the Venn diagram below. However, Malthus would argue that cultural factors are the other main factor that determines the growth rate whereas Fisher would argue that it is the genome which is the other main contributing factor. The Exponentialist view is that only the combination of these two views is correct - the genome and environment through Natural Selection, and culture and environment through Malthusian Selection.

Artificial Selection is a special case in which human cultural factors indirectly affect the genome of other species (through animal husbandry, hybridisation, and other farming and gardening techniques) and thus represent a union of the two views, rather than an intersection. Unnatural Selection is another special case in which human cultural factors directly affect the genome of other species (through genetic engineering) or directly affect any other mechanism for self-replication (for example, molecular nanotechnology).

Overall, I refer to this hypothesis as Malthusian Selection. Malthusian Selection is an Exponentialist hypothesis which explains how environment and non-instinctive behaviour (culture) affect the rate of growth for a population and thus influences differential replication, in conjunction with Natural Selection, Artificial Selection and Unnatural Selection.

Sober argues against Malthusian influences in relation to theories of selection (Sober, 1993):

"Malthusianism survives in contemporary selection theory, but not because Malthus identified natural tendencies of population and food that guarantee that the grim reaper of mortality selection will always be with us."

I fundamentally disagree with Sober here, though perhaps because he is asking what drives Natural Selection as if Natural Selection was evolution, in its totality. It is not, as noted by Fisher in his great synthesis of Darwinian natural selection and Mendelian genetics which ironically is Fisher's attempt to have natural selection discussed for the first time in its own right (Fisher, 1930):

"Natural Selection is not Evolution."

Natural Selection is a part of evolutionary theory, but does not represent the entire theory. Similarly, Natural Selection is just one contributing factor to a population's growth rate.

Furthermore Sober, like Fisher, fails to consider how cultural factors can also affect the Malthusian Parameter. Malthus wrote extensively on this subject, and Malthusianism does have something original to say on the subject of selection.

Witting notes that it is Fisher's idea of natural selection and not Darwin's which underpins most of the predictions of classical theory of evolution (Witting, 1997, p.19):

"Where Darwin defined natural selection from the competitive interactions that arise from Malthusian increase, Fisher disregarded these interactions, and defined natural selection from Malthusian growth in itself."

Witting poses the question of who is right, Darwin or Fisher, and concludes that (Witting, 1997, p.20):

"...Darwin was right in the sense that selection by density dependent competitive interactions is essential for our understanding of evolution by natural selection."

Thus I believe Sober should consider the effect of the Malthusian Parameter as a force for selection at the level of the population via differential replication. Competing populations growing at different rates are either being selected for or against, whether or not they actually evolve. Differential replication is an idea that is in some ways bigger than natural selection, and bigger than the theory of evolution (and the origin of species). The thing to bear in mind though with differential replication is that it is a population theory, intertwined with evolution and natural selection theories, but not the same thing.

Natural Selection Versus Malthusian Selection

Consider the pace of Natural Selection, and all the classical evolutionary processes. They are generally agreed to be slow, though they speed up significantly with short-lived creatures such as insects or microbes. Now consider the rate of population doubling of all species. Compared to the pace of evolution, population numbers change dramatically in short fashion. 

Take Mankind, as Malthus did. We are capable of doubling a population every 25 years. But just how quickly do we evolve? So, if Malthusianism is "a consequence, not a foundation, of the theory of natural selection." (Sober, 1993, quoting Fisher again), just what it is that drives the differential replication of the human species?

In examining Darwin's thought processes, Zimmer considers the question from the point of view of a founding population destined to evolve into a new species (Zimmer, 2001):

"How could an incipient species become a full-blown one? Here Darwin brought Malthus into the argument. Even a slow-breeding species like a human or a condor can double its numbers in 20 or 30 years, easily overrunning the planet in a few millennia."

So population increase occurs on a very short time scale, whereas when Zimmer considers Natural Selection he identifies the much more gradual process of Natural Selection (Zimmer, 2001):

"If natural selection worked on a variety long enough, it would turn it into a new species of its own. After a thousand generations, a single species of bird made of two varieties might end up as two distinct species."

So if Natural Selection is the pretender to the throne of differential replication in explaining the survival of the fittest, I'd say that the evolutionists have their work cut out for them.

Common Ground - Creationism and Evolution

A useful thought experiment (Coutts, 2004) is to consider a world in which species did not evolve - a Creationist world with species fixed and non-evolving since creation. In fact, given that evolution is a gradual process that may take millennia to make its mark on a species such as Homo sapiens sapiens, it is easy to imagine a lack of evolution in the short-term (geologically speaking) for our species.

In such a world, if we go with the logic that nothing evolves, we must logically find that the Malthusian Parameter still drives the differential replication of competing populations. After all, we can see that populations grow at different rates. Thus, creationists (including Malthus) would have to concede that the concept of the survival of the fittest would still have meaning in their world. It is ironic then that Creationists argue repeatedly against the concept of the survival of fittest when this is actually common ground they inevitably share with the evolutionary theory.

Franklin's example of the differential replication of English and American people is a fine example. The fitness of each population over time does not require any superiority in the genome of either population. Instead, as Fisher noted, the Malthusian Parameter denotes the relative fitness of a population to its environment. Hence, with the genome being irrelevant, it is the difference in environment (e.g. size, rainfall, soil, existing population density etc) between England and the USA that explains the Malthusian Selection of the American population over the English population. That, and the fact people migrated from England (and elsewhere) to America, and not the other way round. However, the USA has sustained high natural rates of domestic population increase well in excess of that which could be explained solely through immigration.

I should stress that this is just a thought experiment, and that I do believe that species evolve via Darwinian evolution though natural selection. However, I do not believe that the theory of evolution together with natural selection suffices to explain the survival of the fittest through the differential reproduction based on different values of the Malthusian Parameters of competing populations.

Malthusian Growth Model

The Malthusian Growth Model is perhaps the key contribution made by Malthus to population thinking and the law of differential survival. Malthus again, A Summary View (Malthus, 1830):

"The immediate cause of the increase of population is the excess of the births above deaths; and the rate of increase, or the period of doubling, depends upon the proportion which the excess of the births above the deaths bears to the population."

To complete the picture, one must also state the complimentary law (I have turned Malthus' phrase on its head):

"The immediate cause of the decrease of population is the excess of the deaths above births; and the rate of decrease, or the period of halving, depends upon the proportion which the excess of the deaths above the births bears to the population."

Together these statements form the basis of the Malthusian Growth Model, an exponential law of population growth (Turchin, 2000). All exponential growth is inherently compound growth by nature, whether you use a constant rate or variable rates. However, as demonstrated in The Scales Of 70, the real-world population growth is based on variable rates of compound interest. Given the universal belief that exponential growth is defined by a constant rate of compound interest, I have given the name Couttsian Growth Model to the population growth we see in the real world, which is based on Couttsian Growth and Couttsian Shrinkage. Thus I have reached the entirely opposite view of Sober and Fisher, and declare that Malthusianism is precisely the right point for the study of Natural Selection. To that I would add Artificial Selection, Unnatural Selection and Malthusian Selection.

Social Darwinism Versus Malthusian Selection

In case you think Malthusian Selection sounds like Social Darwinism I hasten to add that Malthusian Selection is not proposed to further any world view of European (or British) racial superiority. I do not support racism in any form. Social Darwinism is a theory of social progress based on Natural Selection. Social Darwinists included people such as Herbert Spencer (who coined the phrase survival of the fittest) and Sir Francis Galton (Darwin's cousin, who promoted the highly controversial concept of eugenics), but not Darwin himself.  Malthusian Selection, on the other hand, is proposed as a force for selection at the level of populations in addition to Natural Selection.

Unlike Social Darwinism, or even the Australian History Wars, Malthusian Selection is a neutral scientific hypothesis that does not seek to favour any one human population over another. Because Natural Selection is unable to explain how the European population was able to grow and sustain a much larger population in Australia than the indigenous Aboriginals, some other selective force must apply. That selective force is what I call Malthusian Selection which, in the case of Australian colonial history, shows that differential replication still occurs even when Natural Selection does not. Hence Malthusian Selection reveals that  - from a population perspective - differential replication encompasses Natural Selection and not the other way around. This is why the concept of Malthusian Selection is important.

Conclusion

Malthus revealed the basic mathematical growth model which forces Natural Selection upon all populations. Together with Artificial Selection  and Unnatural Selection, Natural Selection works through the differential replication of populations (both intraspecies and interspecies). Small founding populations, during their slow evolution of millennia, can actually increase in numbers very rapidly - again, the Malthusian Growth Model can be used to model such growth (which lead directly to the Couttsian Growth Model, a scientific law of population growth).

It can also be proven that Malthus had already extended his Principle Of Population to all populations of all species (though he did focus on human populations), and that he considered the effect of the environment and behaviour upon the differential growth of populations (through what I call Malthusian Selection). 

Not bad for someone who wasn't even writing about evolution.

References

Coutts, David. Common Ground - Creationism and Evolution. Australian Humanist. No .76 Summer 2004.

Darwin, Charles. Origin Of Species The Illustrated Edition*. Sterling Publishing Co. 1859, 2008*.

Darwin, Charles & Darwin, Francis (ed). Autobiography and Selected Letters. Dover. 1958.

Dawkins, Richard, A River Out Of Eden. Phoenix. 1995

Dawkins, Richard, The Selfish Gene. Oxford University Press. 1976, 1989.

Fisher, R. A. The Genetical Theory of Natural Selection (1930, 1958) A Complete Variorum Edition - Oxford University Press. (1999, 2003).

Malthus, Thomas Robert. A Summary View. 1830. (included with Penguin Classics 1983 edition of the 1st edition of Malthus' essay).

Mayr, Ernst.  What Evolution Is. Basic Books. 2001

Paley, William. Natural Theology; or, Evidences of the Existence and Attributes of the Deity (Google Books).1802 through 1809

Peterson, William. The Founder Of Modern Demography: Malthus. Transaction Publishers (1979, 1999)

Ridley, Mark. Evolution. Oxford University Press. 1997

Sober, Elliot.  The Nature Of Selection - Evolutionary Theory in Philosophical Focus. University of Chicago Press. 1993

Witting, Lars. A General Theory of Evolution By Means of Selection by Density Dependant Competitive Interactions. Peregrine. 1997

Zimmer, Carl. Evolution The Triumph Of An Idea. Harper. 2001

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Last modified: 08 August, 2012