Some Fun Nonesense
Growth Curves - Only The Curviest
Here are some logarithmic growth curves I cooked up using the equation we learned on Tuesday:
As you can see, these curves all have different values for r and for K. All of the populations start with just two individuals. All of the values are rounded to the nearest integer for that extra bit of realism, since you can't have half a beluga.
Here is logarithmic growth curve responding to changes in the value of K:
The magenta 'curve' is the changing carrying capacity and the dark blue curve is the population as it responds. As the value of K increases we see an exaggerated growth phase. When the value of K falls back down the populations hugs it pretty closely. This is all mathematically good of course, but I wonder, do populations actually respond to changing carrying capacitance in this fashion? Does carrying capacity go up and down linearly, as I've simulated, or does it tend to be sharper in nature?
Finally, as a biotechnologist, I couldn't help but be reminded of this, the real time PCR (Polymerase Chain Reaction) curve:
I'm sure there's more than one sort of sigmasoidal curve that our population growth curves could be compared to, this is just my favorite and the one I know best. PCR is the thing you do when you want to amplify a sample of DNA - you put your sample of DNA in a tube with some phosphorolated bases, DNA polymerase from a bacterium that lives in hot springs (so that the DNApoly won't get denatured), you sprinkle in a little bit of LSD to pay homage to Kary Mullis, and then you heat it up and cool it down and heat it up and cool it down etc. When you're doing real time PCR, you also measure the florescence of the new double stranded DNA every heating cycle. You do that by using some sort of intercalating agent that only fluoresces when it intercalates with the DNA,
This method gives you an idea of how quickly your DNA strands are replicating, which allows you to estimate how much DNA you started with. During the 1st phase, the relative growth is very small because even though you're doubling your DNA concentration each cycle, double of almost nothing is still almost nothing. Then, at some point, you enter the second phase. No matter if you literally started with only one DNA strand, doubling and doubling and doubling will eventually result in an amount of DNA which rises above the background fluorescence. Pretty close to that point, the doubling gets really significant and you enter the third phase, called the growth phase, where the fluorescence greatly increases each cycle. Then, finally, you enter the fourth phase, called the plateau phase, where the growth slows and finally stops. This is because, at some point, you run out of phosphorolated bases and there's no more resources to make new DNA strands with.
Lots of parallels, eh? Anyway, that's all I've got. Cheers!



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