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

Cellular Chauvinism

To Lynn Margulis and Dorian Sagan (1995, What Is Life?):

"The cell is the smallest unit of life."

Amongst other things, I hope to prove in this article that Margulis and Sagan are guilty of a chauvinistic attitude towards cellular life, and unduly dismissive of the idea that DNA or a virus are alive. To them, both bacteria and cells are autopoeitic. Autopoeisis (or self-poetry) is deemed to refer to life's self-maintenance, or metabolism. Hence, DNA can be dismissed as not alive:

"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 autopoietic. Replication is not nearly as fundamental characteristic of life as is autopoeisis."

Here are their views on whether viruses are alive:

"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."

Margulis and Sagan thus reserve the term replication for the (presumably lifeless) process of a non-autopoietic entity producing another copy "...exactly like itself." Reproduction is thus the term they reverently reserve for when an autopoietic entity produces "...altered offspring...". 

This distinction seems unnecessary and confusing. Neither DNA, nor viruses, produce only replicas. There are mutations. Thus, these replicators also evolve over time. Indeed, they are the basis of all evolution. As Dawkins (1976, 1989) explains it in The Selfish Gene:

"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."

Hence, the definitions used by Margulis and Sagan are false. 

However, whether you prefer the word replication or reproduction, the result is the same - more copies. So, replication (used synonymously with reproduction) is a fundamental characteristic of life. In fact replication is more fundamental than autopoeisis as autopoeisis does not apply to all life. 

It is precisely the ability to replicate which defines life. Yet Margulis and Sagan rightly point to the example of the mule (the result of a union between a horse and a donkey). The mule is alive, but sterile. In fact, if reprogenetic and cloning technologies fulfil their promise, the mule need no longer even be considered sterile (it could become artificially fertile).

Life - an exponentialist definition

OK then, ignoring artificial fertility for the moment, 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 cannot replicate is still alive. In fact, something which chooses not to replicate, or is killed before it can replicate, is also alive (or was alive, for those that are killed). Note that this definition 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.

By my definition, artificial life ("A-life") or a computer virus is life, in the broadest sense. If Eric Drexler's 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.

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

When it comes to viruses, confusion reigns. Issue 5 (May-June 2001) of the graphic science magazine "Newton" featured an article called "The enemy strikes back - Virus" by marine biologist Karen McGhee. In a section of her article on viruses entitled "Tiny Aliens", McGhee notes (as we have seen):

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

One section of the article was called "Building Viral Armies" and attempted to explain the difference between how populations of viruses and bacteria grow. Accompanied by some very nice graphics, McGhee notes that "The Viral Multiplier" invades a cell and takes it over, and the cell thus produces new virus particles. The cell becomes:

"...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, the confusion comes in when McGhee claims that although bacteria can thus grow fast "...(exponentially in powers of 2)..." she states that:

"...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 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. 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:

• Replication Rate: 18 per 1,000 and Death Rate: 8 per 1,000 = growth rate 10 per 1,000 (1%)

• Replication Rate: 38 per 1,000 and Death Rate: 28 per 1,000  = growth rate 10 per 1,000 (1%)

• Replication Rate: 23 per 1,000 and Death Rate: 13 per 1,000  = growth rate 10 per 1,000 (1%)

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:

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" (see Darwin - An Exponentialist View for more) :

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

One such species was smallpox, which once took advantage of our steadily increasing human population to increase its own numbers. Then, in 1798, Jenner invented vaccination. The subsequent demise of the smallpox virus is just one factor which has lead to an increase in human growth rates. 

In 1918 over 40 million people worldwide died of the Spanish Flu virus, far more than died in World War I which preceded the pandemic. 

Another viral replicator which is now on the rise is HIV / AIDS. It is estimated that in the next 10 years more people will die of HIV / AIDS that died in all the wars of the 20th century.

But long before humans came along, viruses were doing what comes naturally to all life - replicating. 

Bibliography

What Is Life? - Lynn Margulis & Dorian Sagan

Newton Graphic Science Issue 5 (May-Jun 2001)- Australian Geographic

Flu The Story of the Great Influenza Pandemic of 1918 and the Search for the Virus that Caused it - Gina Kolata (1999)

Future Plagues Biohazard, Disease and Pestilence Mankind's battle for survival - Peter Brookesmith (Brown Packaging Books Ltd, 1997)

Plague, Pox & Pestilence Disease In History - editor Kenneth  F. Kiple (Weidenfield & Nicolson, 1997)

Virus X Understanding the real threat of the new pandemic plagues - Frank Ryan

Plague Wars - A true story of biological warfare - Tom Mangold and Jeff Goldberg (1999)

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Copyright © 2001 David A. Coutts

Last modified: 17 December, 2005