Empirical growth curve data!
marvin chester
Saturday, 10 October 2009 18:11 UTC
Looking for empirical findings on population dynamics.
In his very stimulating ‘General unified theory’ thread, Tim Coulson wrote, rather insightfully, I thought:
“… the phrase ‘general unified theory of population dynamics’ or similar has been used. I am not sure what this unified theory will explain.”
Berryman, in his answer, writes:
“the best thing is to first look at populations that are not, or only superficially, affected by man.”
What about elemental populations? Say, single celled organisms on a petri dish? Vary nutrients and competitive species and record populations.
I am wondering whether there are elemental petri dish experiments in which one takes note of population growth as a function of nutrient. In this case the totality of environmental effects on the population effectively amounts to only one thing: its nutrient supply. One might examine growth in a flow of nutrients. The nutrient concentration is an experimental parameter of the steady flow over the colony.
I would not expect to see exponential growth in the colony because the nutrient supply limits growth. I would expect to see a population oscillation with a frequency that may be independent of the nutient concentration in the flow. Ultimately growth is always limited by the environment. It seems to me that the birth-death mechanism is merely the agency by which biological population is governed by the environment.
This line of reasoning leads to some equations which could be compared to data for elemental biological situations. I would love to compare my results to experiment. Can someone cite experiments?
I’ll post the equations if someone is interested and I figure out how to post equations. (Have managed to post greek letters. Here’s omega: ω. The code is ω)
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Replies
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The sort of experiments have been done, using chemostats. I must admit, it’s not a literature I’m terribly familiar with but there’s quite a bit of modelling work as well.
The only way I can see to embed equations is to upload them as a gif or png somewhere, and then link to them here as an image.
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Thanks for the suggestion, Bob. I will track down chemostats. Seems like a technological tool rather than a research effort but maybe there are some leads there.
Equation images is the only way that I know to present them also.
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Hi Marvin and welcome to the Forum.
I posted a brief introduction to writing equations here, but Nature seemed to change their online formatting after. It’s worth looking and trying out some of them to check, e.g.
Nt+1 = Nt er (1 – Nt/K)
still comes out reasonably legibly. Trial and error spaces and square brackets is required. Many greek characters translate/format directly from the keyboard, e.g. Ω ß π come from ‘alt’ + ‘w’, ‘p’ or ‘s’ keys on the Mac. Presumably Windows or Unix systems can do the same.
And I’d echo Bob’s thoughts: chemostat experiments have been popular for testing these ideas for some time now, starting with (or before) the classic work by Gause 1932. One ‘drawback’ of microcosm experiments is rapid evolution. Adaptation is rarely incorporated in mathematical models of population growth, however population biologists are starting to integrate these in eco-evolutionary models – check out the theme issue in Philosophical Transations B.
In terms of natural populations, there’s a nice paper by Sæther et al 2002 which examines some important ideas about difficulties in identifying the shape of population growth.
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October 13, 2009
Dear Mike:
Thanks for your kind welcome. I did, indeed, take note of your post on writing equations. And it is useful. But on my mac, alt+w produces capital sigma not omega. And, as you say, that trick will not work universally.
Some time ago – before blogging tools became available – I gathered the info for producing some mathematics using HTML. HTML works almost universally on any web posting. And any keyboard can produce it. My list is at:
http://www.physics.ucla.edu/~chester/KEYS/index.html
Thanks so much for the Gause reference. It is very close to what I was looking for albeit more complicated than necessary. I am going to study it further but I get the impression that the experiment is too imprecise to see population oscillations if they were there and the theory seems to be constructed to fit the data without a basic driving idea. Maybe I am wrong though.
I am certainly going to explore all your leads in more detail. Thanks, so much, Mike, for putting me on to them.
Perhaps you can comment on the central principle upon which my computations are based. It is this: The effect on the environment of evolutionary success is always to alter that environment in a way that opposes the success.
Expressing this thought mathematically allows one to make some very testable predictions. The idea seems so simple and so evidently true that I suppose it is common currency. Is it? Seems like you would know.
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Hi Marvin.
Apologies for the delay, I’m in the middle of preparing to move between jobs and countries at the moment.
The effect on the environment of evolutionary success is always to alter that environment in a way that opposes the success.
This is an interesting statement, and I’d be even more interested to see how you’d frame it mathematically. Verbal “theories” often end up being a little too vague or poorly defined to robustly test logically or empirically!
As a quick example, how would you define ‘evolutionary success’? We generally use ‘relative fitness’ to compare geno/phenotypes in evolutionary ecology, but success here does not exclude extinction. You may be fitter than your conspecifics, but with a per-capita reproductive rate < 1, are unlikely to be successful in the long-term.
There’s also been discussion on this Forum of the concept of hyper-exponential growth which you may find stimulating in this respect.
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Dear Mike:
Are you now established in Mallorca? I know the place well. Stopped there many times using the ferry boat from Barcelona on my way to Ibiza where my sister used to live. Finland to Mallorca is quite a change.
Thanks so much for your interest and your very perceptive challenge to caste my principle mathematically in a testable way. Exactly what any good scientist should demand. I take it that my ‘opposition principle’ is at least original in your experience. That gives me good motivation. I will prepare the thesis for you.
The preparation is unfortunately getting slowed down by a heart problem that arose last week. I’ve got various arhythmias. Give me a few days or maybe a week to post the whole idea. I work between medical appointments.
Marvin
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