Malthusian Memes - An Exponentialist View
Viral Replicators - An Exponentialist View
Bacterial Replicators - An Exponentialist View
Cellular Replicators - An Exponentialist View
Rabbit Replicators - An Exponentialist View
Human Replicators - An Exponentialist View
Grey Goo - An Exponentialist View
Death By Replication
Exponential Assembly - An Exponentialist View

Richard Dawkins - An Exponentialist View

Population Doubling Mechanism
New Malthusian Scale

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

SI Unit Prefixes - BIPM

Some Wikipedia Links Related to Viruses:

Bacteriophage (a Virus that infects bacteria)
Common Cold
Dengue fever
Herpes simplex (cold sore)
Influenza (flu), including Bird Flu , Spanish Flu and Swine Flu
Retrovirus (an RNA virus)
Yellow Fever
Viral Hemorrhagic Fever, including Ebola, Hantavirus and Lassa Fever

Viral Replicators - An Exponentialist View
(It is recommended that you also read Bacterial Replicators - An Exponentialist View)

Virus - "A piece of bad news wrapped up in protein." Sir Peter Medawar (Crawford, 2000, p.6)


In this article I will consider questions such as whether or not viruses are alive, whether viruses replicate faster than bacteria, and whether or not populations of viral replicators grow exponentially. I'll also criticise a concept I call cellular chauvinism. First, let's get an idea of one of the key differences between bacteria and viruses - size.

Microbes and Nanobes

Viruses are small - very, very small. They are much smaller than bacteria.

Whereas a bacteria is a microbe (1 to 10 microns in length [Crawford, 2000, p.7]), a virus might be considered a "nanobe" as the word virus means sub-microscopic (0.02 to 0.2 microns, or 20 nanometres to 200 nanometres [Mangold, 1999, p.380]). As per the SI Unit prefixes, nano (10-9) comes below micro (10-6) in size.

A bacteria can be seen with an ordinary  microscope at 200 times magnification, but a virus requires sub-microscopic magnifications up to 500 times smaller. That's a magnification of 200 x 500 =  100,000 times (Crawford, 2000, p.7)!

OK, so viruses are small. But are viruses alive?

Viruses - Are They Alive?

Referring to viruses as "Tiny Aliens", Marine biologist Karen McGhee appears to have an open mind as to whether or not viruses are alive (McGhee, 2001):

 "...that there is an ongoing debate about whether they should even be classified as 'living'".

Microbiologist Dorothy H. Crawford would agree with McGhee that the question of whether or viruses are alive is an open question (Crawford, 2000, p.19):

"...the answer to the question of whether viruses are alive or not remains a matter of opinion and personal preference."

Crawford wonders whether the question really matters as (Crawford, 2000, p.19): :

"...there is no doubt that viruses as unique and utterly unlike cells which are the building blocks of all other organisms."

However consultant physician Frank Ryan is in no doubt that viruses are alive (Ryan, 1996, p.47):

"In my opinion, a virus is very definitely a form of life. It has the same physiology and biological chemistry as all other forms of life on Earth. DNA, with its counterpart RNA, is of course the template of life and heredity."

Ryan also notes that DNA and RNA constitute a unique and extraordinary ecological niche - a "home" - for a virus (Ryan, 1996, p.47).

At the opposite end of the spectrum, biology professor Lynn Margulis and science writer Dorion Sagan boldly exclude viruses from the land of the living and claim that (Margulis, Sagan 1995, p.24):

"The cell is the smallest unit of life."

Cellular Chauvinism

Amongst other things, I hope to prove in this article that Margulis and Sagan are guilty of an illogical chauvinistic attitude towards cellular life, and unduly dismissive of the idea that DNA or viruses are alive. I refer to their position as cellular chauvinism. To them, both bacteria and cells are autopoeitic (Margulis, Sagan 1995, pp. 23-28). Autopoeisis (or "self-poetry") is deemed to refer to life's self-maintenance, or metabolism. Hence, Margulis and Sagan feel that DNA can be dismissed as not alive (Margulis, Sagan, 1995, p.23):

"DNA is an unquestioningly important molecule for life on Earth, but the molecule is not alive. DNA molecules replicate but they don't metabolise and they are not autopoeitic. Replication is not nearly as fundamental characteristic of life as is autopoeisis. Consider: the mule, offspring of a donkey and a horse, cannot "replicate." It is sterile, but it metabolizes with as much vigor as either of its parents; autopoietic, it is alive. Closer to home, humans who no longer, never could, or simply chose not to reproduce can not be relegated, by the strained tidiness of biological definition, to the realm of the non-living. They too are alive."

Having dismissed DNA because they do not metabolise it's then a simple matter to repeat the process using the same criterion for viruses (Margulis, Sagan, 1995):

"In our view, viruses are not. They are not autopoeitic. Too small to self-maintain, they do not metabolise. Viruses do nothing until they enter an autopoietic entity: a bacterial cell, the cell of an animal, or another live organism. Biological viruses reproduce within their hosts in the same way that digital viruses reproduce within computers. Without an autopoietic organic being, a biological virus is a mere mixture of chemicals; without a computer, a digital virus is a mere program."

Applying the logic of critical thinking to the definition of life, the question is what are the necessary defining attributes of living creatures, and what are the sufficient attribute defining attributes of living creatures?

Is the cell a necessary defining attribute of living creatures (must life be based on cells) or is it merely a sufficient attribute (may life be based on cells, or on something else such as molecular nanotechnology)? Similarly, is DNA a necessary defining attribute of living creatures (must life be based on DNA) or is it merely a sufficient attribute (may life be based on DNA, or on something else such as molecular nanotechnology)? From the quotation regarding DNA above it is unclear whether Margulis and Sagan feel that DNA is a necessary or sufficient attribute of living creatures, even though it is considered an "unquestionably important" criterion. Still, given their reductionist view that the cell represents the smallest unit of life then they must feel that DNA is a necessary attribute of all living creatures as all cells are based on DNA.

To an extent then Margulis and Sagan have contradicted themselves in the quote regarding viruses. Given that viruses are also based on DNA (or its cousin RNA) then by their own logic viruses must be alive too! However I disagree that DNA is a necessary attribute for life, as "life" based on molecular nanotechnology  - with no cells in sight - could potentially both replicate and metabolise. Sure, it would be not life as we know it today, but that does not excuse a parochial Earth-based definition of life. After all, life on other planets may not be based on DNA or cells. Therefore DNA and cells are only sufficient attributes of life (but especially so on Earth).

Is replication a necessary attribute of life (must life be based on replication) or is it merely a sufficient attribute of life (may life be based on replication, or could a living creature not be based on replication in any way)? From the examples of the sterile mule, the infertile human, or the celibate human, Margulis and Sagan appear to think that it is either the ability to replicate or the willingness to replicate is relevant here. However, a counter-consideration is whether or not any of these living creatures would be alive if they were not the result of one or more replication events.

The fact is that each was born - but birth is just one type of replication event and viral replication is another. How a replication event occurs is much less important than if it happens, as both lead to replicator populations. Whether you prefer the word replication or reproduction, the result is the same - more copies. The fact is that each of these example living creatures grew in a womb and then grew after birth via cell division - cell division is another type of replication event. Hence, all living creatures including viruses are the result of one or more replication events. Without replication none of us would be alive - therefore it is precisely the ability to replicate which defines life. The same would be true of life based on molecular nanotechnology, or any alien life form. So, replication is a fundamental characteristic of life. Therefore replication is a necessary attribute of life.

Is metabolism (or autopoeisis) a necessary attribute of life (must a living creature be able to metabolise) or is it merely a sufficient definition (may a living creature be able to metabolise, or not metabolise)? Margulis and Sagan clearly feel that replication is merely a sufficient attribute, not a necessary one - but why? I suggest it is because they failed to consider the true significance of replication to life. Having ruled out replication  - incorrectly, as it turn out - then according to Margulis and Sagan metabolism must be the defining attribute of life. In fact replication is more fundamental than metabolism as metabolism does not apply to all life. Therefore metabolism is only a sufficient attribute of life.

Margulis and Sagan reserve the term replication for the "lifeless" process of a non-autopoietic entity producing another copy "...exactly like itself." (Margulis,  Sagan 1995, p.24). Reproduction is thus the term they reverently reserve for an autopoietic entity that produces "...altered forms... (Margulis,  Sagan 1995, p.24)". This distinction seems unnecessary and confusing. Neither DNA, nor viruses, produce only replicas. There are mutations. As Dawkins explains (Dawkins, 1976):

"We do not know how accurately the original replicator molecules made their copies. Their modern descendants, the DNA molecules, are astonishingly faithful compared with the most high-fidelity human copying process, but even they occasionally make mistakes, and it is these mistakes that make evolution possible."

All replicators evolve over time. Indeed, imperfect replication is the basis of all evolution. Hence, the argument used by Margulis and Sagan is a straw man fallacy (an argument based on misrepresentation). In fact, in yet another contradiction, Margulis and Sagan freely admit that  - just like DNA - "...viruses mutate and evolve..." (Margulis,  Sagan 1995, p.24).

For some reason Margulis and Sagan feel the desperate need to resort to ad hominem attacks. An ad hominem attack is a logical fallacy in which the person is attacked, rather than addressing the argument. Margulis and Sagan refer to viruses as "a mere mixture of chemicals" and  "...at best chemical zombies" as if this justifies their exclsuion of viruses from the living (Margulis,  Sagan 1995, p.24). Obviously no virus will be offended by such slurs so the target of their attacks must be those readers who might disagree with them. Yet viruses replicate, they mutate and they evolve. According to Nobel prize winner Joshua Lederberg viruses may even represent the greatest threat to the future of humanity (Crawford, 2000, p.2):

"The single biggest threat to man's continued dominance on the planet is the virus."

Ok, so viruses are unique in that they do not metabolise. Point taken. They are unique in their ecological niche. Point taken. But all populations of all species  interact with viruses, often to deadly effect. Even bacteria are affected by viruses, through bacteriophages. Our fates are so intertwined with viruses that it would be foolish and dangerous to relegate them from the exclusive members club that we call life just because they do not metabolise. 

Life - an exponentialist definition

So replication is the overriding attribute of life - a necessary attribute. However, metabolism is still a sufficient attribute for life. OK then, let's define a living entity as follows:

A living entity is the result of a replication event by one or more replicators, and is encoded with the instructions of its own assembly. A living entity can either metabolise or replicate, or it can do both.

Hence, something which does not replicate due to infertility, sterility or celibacy is still alive, and still metabolises. But every single metabolising living creature would not exist without replication. Note that my definition of a living entity does not require self-assembly. Hence viruses are encoded with the instructions of their own assembly, but they use cells to actually produce more copies of themselves.

By my definition, artificial life ("A-life") or a computer virus is life, in the broadest sense. If Eric Drexler's molecular nanotechnology replicators and assemblers become reality, then we will have a new form of life altogether - but one which still conforms to the above definition (see Drexler - An Exponentialist View for more). Wherever populations of replicators compete for resources you have differential replication, and evolution. Such replicators do not even need to be the result of Natural Selection or Artificial Selection, though so far most are. However, the authors of Kinematic Self-Replicating Machines claim that artificial self-replicating systems have existed since the 1950s and are therefore no longer the exclusive preserve of living systems (Freitas, Merkle, 2004, p1). Hence, whether or not replication is a fundamental feature of living systems  - with or without DNA - is no longer just a theoretical question. In time, self-replicating systems may rival viruses in the threat they pose to Earth's cell-based life forms.

Throughout time our global human population has grown exponentially despite the failure of some individuals (for whatever reason) to replicate. All of these individuals are part of that population, and their failure to replicate should be seen in the context of the population to which they belong. Populations of all replicators tend towards exponential growth within limits to growth - this is a universal and fundamental law of life. It was not Darwin who discovered this law, but Malthus (see Malthus - An Exponentialist View).

Viral Populations

Viral populations are a popular example of exponential growth (Kelly, 2002):

"Most people have an intuitive understanding of what it means to have exponential growth. Basically, it means that things are increasing in an out-of-control way, like a virus in a horror movie. One infected person spreads the illness to another person, then those two each spread it to another. Two infected people becomes four, four becomes eight, eight becomes sixteen, until it's an epidemic and Jackie Chan has to come in and save the day, possibly with karate kicks."

I find Kelly's approach of counting the infected people interesting and useful in its simplicity (the same approach could be used for memetic replication into human brains), but what is the viral population itself and how fast do they replicate?

Crawford mentions that after a virus invades a living creature and turns their cells into "...factories for viral production..." then a day or two later "...thousands of new viruses emerge..." (Crawford, 2000, p.9) and the factories then go on producing "...thousands of offspring every one or two days..." (Crawford, 2000, p.35).

McGhee notes that "The Viral Multiplier" invades a cell and takes it over, and the cell thus produces new virus particles such that the cell becomes (McGhee, 2001):

"...a viral photocopier that produces hundreds or thousands of offspring viruses."

Then, for "The Bacterial Divider" McGhee explains the nature of mitosis for cellular life - a cell divides in two. So far, so good. However, confusion arises when McGhee compares fast bacterial growth "...(exponentially in powers of 2)..."  - with the growth of viral populations (McGhee, 2001):

"...viral infections can take off faster because each infected cell produces hundreds or thousands of offspring virus which then turn other cells into multipliers and so on."

Before I continue, I am happy to concede that McGhee is probably right that viral infections often spread quicker. However, what does it mean to say that something grows faster than something else (which grows exponentially to powers of 2)? This is an important question, and should not be dismissed lightly.

Human Populations

In the first place, it may surprise you to know that humans also grow exponentially to powers of 2. So do viruses! Yet humans do not divide in two, and nor do viruses. In a nutshell, although cell division may be a sufficient cause of exponential growth (cell division does lead to exponential growth) it is not a necessary condition of all exponential growth (other replication events such as birth, budding and viral replication also lead to exponential growth).

The problem with the generational approach to population modelling is that, enticing and easy as it may be, it is flawed. See Cell Replicators - An Exponentialist View for more. In short, you cannot realistically extend the exponential doubling series for generations of cells (1, 2, 4, 8 etc) without unrealistically assuming immortal cells.

However, it is still possible to use the exponential doubling series for bacteria, viruses, DNA or humans. The exponentialist approach is to turn to Malthus. If you know the replication rate and the death rate for a given period, then you know the population doubling rate for a population. This ignores immigration and emigration, though they can be easily factored in if need be. 

For humans, the replication and death rates are expressed per thousand individuals in the population. The time period of measurement is normally a year. Thus, each of the following gives precisely the same growth rate:

At this rate, a human population will double roughly every 70 years. If the rate was 2% then the population will double every 35 years. These crude doubling rates are based on the Rule Of 70, but they will be good enough to prove the exponentialist case.

Of course, it should be noted that a constant growth rate is unlikely in reality - but neither is it necessary. Variable growth rates still produce exponential growth. So, for example, a population with a growth rate that varies between 1 and 2 % will double somewhere between 70 and 35 years. This is proven by the last global doubling of our human population from 3 billion in 1960 to 6 billion in 1999 - in just 39 years. Our annual rate of growth peaked  at 2.1% and fell to 1.29%.

Viral and Bacterial Populations Compared

Exactly the same population growth model applies to bacteria, DNA or viruses. In fact, this model is universal for all populations of all replicators. So, it is meaningless to assert that one population can grow faster than another population (which grows exponentially at a power of 2). They both grow exponentially at a power of 2! They can both been shown to grow exponentially at a power of 3, if you like. Again though, that too would be meaningless. 

If you want to compare the growth rates of populations then you need to talk in terms of actual growth rates, and this forces the key inclusion of time. McGhee does not mention time. Growth rates also require you to consider death rates - something else not mentioned in the McGhee exploration of exponential growth. McGhee only considers replication rates, which is not enough. 

Once you have the growth rate, you have the population doubling time.  Doubling times will allow you to compare the speed of exponential growth for viral and bacterial populations. In this example, I show a bacterial population growing faster than a viral population:

Doubling time =
25 minutes
0 25 50 75 100
Virus (Millions) 1 2 4 8 16
Doubling time = 
20 minutes
0 20 40 60 80
Bacteria (Millions) 1 2 4 8 16

Table A. Malthusian growth model showing bacterial population
growing faster than viral population.

To get a population doubling time of 20 minutes, the bacteria would have to have a growth rate of about 3.5% per minute. By comparison, a viral population doubling every 25 minutes would have a growth rate of about 2.8%. As with the example of human population growth rates, it is possible to arrive at the same growth rate using many different replication rates and death rates. Hence, I could provide countless possibilities to arrive at a bacterial growth rate of 3.5%, or a viral growth rate of 2.8%. Hopefully by now you are getting the point, so that should not be necessary.

There are lots of ways this atypical situation could arise. Perhaps an individual infected with the bacteria has received no treatment, whilst the virus has been recently vaccinated against in another individual. Hence, although the virus undeniably produces more offspring (100s or 1000s per infected cell), a higher proportion are dying. Most people are familiar with the concept of boom and bust population growth. Perhaps our bacterial population is in the boom phase, and the viral population (for whatever reason) is approaching its bust phase and its growth has begun to slow. Or perhaps we just compared a particularly virulent bacteria and a relatively inactive virus. 

So, whilst each individual virus has a very real advantage in individual fecundity over the individual bacteria, this is not enough information to conclude that viral populations grow faster. Apart from the replication rate, you must know the death rate for the same period. Only then do you have enough information to make any conclusions regarding the speed of growth.

The above example, whilst perhaps atypical of the actual supremacy of viruses over bacteria (in terms of rates of growth), goes to show that all life is united by the inherent tendency of all population of replicators towards exponential growth. Not all populations succeed, but all are capable of staggering exponential growth. As Darwin said in "Origin Of Species" (Darwin, 1859):

"Lighten any check, mitigate the destruction ever so little, and the number of the species will almost instantaneously increase to any amount."

See Darwin - An Exponentialist View for more




Crawford, Dorothy H., The Invisible Enemy - A Natural History Of Viruses. Oxford University Press. 2000

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

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

Freitas, Robert, A., Merkle, Ralph, C., Kinematic Self-Replicating Machines. Landes Bioscience. 2004.

Kelly , W. Michael, The Complete Idiot's Guide To Calculus. Alpha (A Pearson Education Company). 2002.

Mangold, Tom; Goldberg, Jeff; Plague Wars - A True Story of Biological Warfare. Macmillan. 1999.

Margulis, Lynn; Sagan, Dorion, What Is Life? Simon & Schuster. 1995

McGhee, Karen, Building Viral Armies, Newton - Graphic Science (Issue 5). Australian Geographic. May-Jun 2001

Ryan, Frank, Virus X - Understanding The Real Threat Of The Pandemic Plagues. Harper Collins. 1996.

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Copyright 2001 David A. Coutts
Last modified: 08 November, 2009