Science Buddies: "Ask an Expert"

my topic is Predicting Population Growth with Models: https://www.sciencebuddies.org/science- ... Q&from=TSW

i don't really know where to start. how to do the research, and if i have to do all the equations?. i also don't know if this is a practical choice for me since i only have about 18 days to do it...please help??

Hi kddizon,

I think this is a great project and I think you can get it done in the amount of time you have. About half way down the page there is a list of words and concepts to get you started on your research. I would start by making sure you understand what those words mean and how they fit into your project. There are some references given that should help you.

There are three equations listed. The first equation is an ideal model that assumes that everything the population needs to grow is available. This is not true in nature so this model isn’t usually used for animal populations. Can you think of some reasons why animals might be restricted in their ability to reproduce?

The second equation is another model that attempts to take into account the limitations of the habitat on the growth of the population. It requires some complex mathematics so the third equation is an approximation. The third equation is the one you will use to compare how carrying capacity affects population size.

Can you give me some more details about your assignment so I can answer some more of your questions?

-microkts

Hi kddizon,

This is a great idea for a research project. The thing about doing these types of research projects is that you'll need to know a lot of math, specifically statistics to do this type of work. Do you have a statistics background (ie have a taken a statistics course in high school?)

-Sam

hi..thank you very much for replying!!!
to microkts
i asked my teacher and he told me to choose one of the equations and then plug in different information to get different results, is the 3rd equation the best choice? also since im only choosing one, do i have to say why i didn't choose the other two equations?


to sk1
yes, i do have a background for statistics since im taking math studies and biology this year. it was the very first lesson we had and i know how it works.. but would that be sufficient?


thank you so much!!this is my very first science fair even though im already a junior..and you guys are a great help since i don't usually get what my teacher says most of the time... i was a little hesitant to do this project at first since it seemed hard but hopefully with your help i could pull this off.

Kddizon,

It sounds like you are getting a good start on your project. I think the third equation is the best for your project. The first equation doesn’t apply to real situations.

To answer your second question, yes. All three equations are related. The first calculates the population growth under ideal conditions. The second equation calculates population growth using more realistic conditions. What are the extra conditions that are included in the second equation? The problem with the second equation is that is uses complex math that can be difficult to use. So the third equation is an approximation of the second that uses simpler math.

Before you begin make sure you have a clearly defined hypothesis that you are testing. What hypothesis would you state that could be answered by the third equation?

Sam makes a great point. Most studies of this kind are further analyzed using statistics. Are you familiar with curve fitting?

-microkts

Oh ok..and well yeah,as I said, I'm taking math studies and biology this year..so I'm familiar with it since it was the first lesson we had....for my hypothesis, i was thinking of answering the statement in the objective which was: how a population grows when it is far below, at, or far above it's carrying capacity..would this be fine? And also the the logistic model has population[time] as part of its equation which means the population at the current time increment, would this be the initial population? and it also mentions that I should change the initial population as much less than the carrying capacity and much more for the 3 cases..does this mean that I'll come up with my own initial population? Thank so much again...!and sorry for the many questions

Kddizon,

Ask as many questions as you want. Your hypothesis sounds good; just make sure to state it in a way that other people will understand unfamiliar with the project will understand.

“Population [time]” is the initial population for the first iteration of your calculations. For the second iteration of your calculations “Population [time]” will be the population size you calculated in the previous iteration. Repeating these iterations you will calculate a set of populations over a span of time. You will then graph them to see how the population grows over time. For example you could graph the growth in a population of wolves over 10 years by calculating the population size every year and then graphing those numbers vs. the number of years.

You can either come up with an arbitrary initial population or look-up real numbers from a DNR (Department of Natural Resources, for example www.michigandnr.com). Scientists often times will use “made-up” numbers when they are running simulations. The thing that you are interested in is how population growth is affected by the relationship between initial population size and carrying capacity. In other words how does the population grow (or shrink) if it starts out larger (or smaller) than the carrying capacity?

Try this link http://ats.doit.wisc.edu/Biology/ec/pd/t3.htm. There is a very nice explanation of the logistic model and a tutorial on how to use it. The equation they use has different letters for the variables so see if you can figure out which variables correspond to which terms.

-microkts

oh ok thank you for the site..although the other one doesn't really work??the thing about logistic model??it says not found..

Sorry about the link. Try this one, it is working on my computer:

http://ats.doit.wisc.edu/biology/ec/pd/t3_a1_a.htm

If this link is still not working you can find the page by going to www.wisc.edu adn entering "Elephant Population Growth in a Nature Reserve" in the search bar. It should be the first page on the list titled: "Conecting Concepts - Ecology"

-microkts

oh thats fine..i actually looked into that site already since its listed in the site where this project was mentioned...and so i started my research already, and it helped clear a lot of things up..but while researching i found so many versions of the logistic model and i dont know which one was right. i tried looking at them to see if they just changed the variables but they're really different from the one here in science buddies..i dont know which one is the right one..
there's an equation like this; Nt = 1 + [ (K - N0)/N0 ] * e-rt,

another one from this site; http://www.math.northwestern.edu/~mlerm ... logist.pdf

this one: Letting X(i) represent the population at the beginning of time period i the logistic model is:

X(i+1) - X(i) = r*X(i)*(1 - X(i)/K)

where * represents multiplication. ..r the growth rate

there's this one; Population[time+1] = Population[time] + GrowthRate × ( 1 - Population[time]/CarryingCapacity ) × Population[time]...its confusing..and there's more than those...and btw can the logistic model be used for predicting human population also?

Kddizon,

It looks like you are doing a really great job with your research. Some of the math you are looking at is really advanced; the kind of stuff you learn in advanced algebra and calculus.

The first two equations that you listed both contain the number e (Euler’s number). These are the same as Equation 2 in the science buddies project you have been using. These are the true Logistic model equations. But you want to use the approximation for your project. It will give you the same results in most cases. The approximation is Equation 3 in the science buddies project. This is the same equation (just written a little differently) as the second two you listed. If you add X(i) to both sides of the equation you get an identical equation to Equation 3 in the Science Buddies project. This is something that is taught in Algebra. If you haven’t taken Algebra yet then don’t worry about trying to understand it, you don’t need to for your project.

So for your project I would use whichever version of the approximation you like the most:

X(i+1) - X(i) = r*X(i)*(1 - X(i)/K)

Or

Population[time+1] = Population[time] + GrowthRate × ( 1 - Population[time]/CarryingCapacity ) × Population[time]

It is possible to use the logistic model to predict human populations. It usually work best over short periods of time (decades instead of centuries). What kinds of things would affect the carrying capacity? Birth rates and death rates are taken into account as the growth rate, r. When and why does the birth rate of the human population change?

Let me know if you have any more questions

-microkts

oh ok..thank you..im thinking of doing it on human population because i find it more interesting...would it be alright if i manipulate the carrying capacity instead of the population?.because compared to the population, there's really no known value for sure for earth's carrying capacity..the thing about that is im kinda confuse about my control group..since the population after a time period would be my dependent variable, i thought that the carrying capacity would be my independent variable since im changing it...would the experiment with the population at the level of carrying capacity be my control group then?

It's awesome that you have picked something that interests you. You can most definitely change the carrying capacity instead of the starting population. Just be aware of how that is going to change your hypothesis. You have identified your independent and dependent variables correctly. In this experiment you are not going to have a control group, you are going to have controlled variables. Can you think of the other variables that you are controlling. For example, you will be using the same equation for each carrying capacity you test. You will also be starting with the same initial population each time you change the carrying capacity. What other things will you keep the same while you change the carrying capacity? If you need some help read up on controlled variables here:

https://www.sciencebuddies.org/science- ... bles.shtml

Hmm..I was actually thinking of retaining the same hypothesis..which was answering how a population grow when it is far below,at or above...I thought it wouldn't really make much difference if I just make the carrying capacity suit my purposes..like make it bigger than the population so that the population would be far below the carrying capacity..that will be fine right???also do u know any famous reliable person who predicted the carrying capacity of earth??I saw some predictions and it only says ecologists or scientists..my teacher want me to site a real name..I found someon but he made the prediction in the 17th cent and my teacher didnt really like the idea of using his predictions for carrying capacity..again thank you for helping me go through this!!!:))

Also, since I'm changing the carrying capacity instead of pop., would that change the way I graph things the way science buddies suggested??idont think so...but I just want to make sure..and I dont really get the instructions for the graphing...I understand the part where it says population on y and time on x but idont get how I'm suppose to graph the carrying capacity and time since I'm only gonna use the same carrying capacity for each case...wouldn't it be just a straight line?..I saw some graph while researching how there's a straight line somewhere on the top of each graph to serve as carrion capacity and the pop would go over it..is that what the instruction meant??if so then that means I have to do them on the same graph right???like two lines in one graph??