Population Growth

by Jason Amores Sumpter
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per capita just means per individual in a population, So the per capita birth rate is the number of offspring produced by the average member of population per unit time. Because it's a rate, remember, so the mortality rate is going to be the average number of deaths per unit time in a population. Well, look at these two factors to see how population sizes fluctuate. Now, if the birth rate is equal to the death rate, your population size won't change. However, if your birth rate is higher than your death rate, your population is going to increase in size. Whereas if your death rate is higher than your birth rate, your population is going to decrease in size now. The difference between the birth rate in the death rate or the mortality rate, I should say, is the per capita rate of increase our now when R equals zero like we saw at that midpoint, you have zero population growth, and again, that's because the birth and mortality rates are equal. When you have an are, that's greater than one, meaning your birth rate exceeds your mortality rate. You get exponential population growth and this is a J shaped curve. You can see it right down here. This is what exponential growth looks like. And basically, uh, this is a density, independent type of growth, meaning that it does not depend on the number of individuals in the population. And if the birth rate isas highest possible and the death rate isas low is possible, you can have an intrinsic rate of increase or our max the maximum rate of increase. So exponential growth does occur in nature sometimes, but it can't occur indefinitely. Basically, resource is our finite space is finite. Everything is finite in nature. And that's why even though you might have a period of exponential growth for a population, eventually that's gonna burn itself out. And what we will often see is logistic population growth. So basically, there's a new upper limit to, uh, the population size that an area can sustain. And this is ah, limit due to the number of resource is available, how much space is available and because individuals they're going to compete for those resource is and that space, and there's going to be, in fact, other species competing for that. Those resource is in that space. Additionally, and this doesn't always apply, but the amount of waste produced by the individuals can lead Thio limits on population size. For example, you know, if you take a look at yeast which produce alcohol, you know, they they produce ethanol which is waste to them as a byproduct of their metabolism and eventually that waste can kill them. So you know it. Z not always relevant, but it can be relevant. So carrying capacity is just this maximum population size. It's the limit on the population that the area can sustain and we represent it with letter K. So here you can see that in this particular chart, the carrying capacity is reached due to limit on the food supply. However, it could be other factors as well, you know, in actual real life scenarios. Now, here we can see the characteristic s shaped curve of the logistic growth curve and couple of things that I want you to take note of is that the population size will increase and our will go up and then our will go down. So here are is increasing, and then here are is decreasing. Actually, in the second part of the curve are is approaching zero, and one thing that I want you to take note of is that our is going to be at its greatest when n equals one half K. So if this is our carrying capacity, the half way marker there is going to represent the greatest our value, right, let's turn the page.