Population Ecology Explained: Growth Models, Strategies, and Survivorship

[Music] hi it's Mr Anderson and this is environmental science video 12 it's on

population ecology one of the greatest conservation stories in biology is the story of the whooping crane they used to

number 10,000 in the US but by 1938 their numbers had dropped to only 15 individuals so scientists had to figure

out where are they where are they breeding how do we protect those areas and you can see the population is

starting to rebound but the health of the population is dependent upon the size of the population how do we

increase the size of a population through births and immigration new individuals coming into the population

likewise how do we decrease it through deaths and immigration these things contribute to What's called the

intrinsic growth rate is it increasing or is it decreasing it's not the only characteristic we also have the density

and distribution we have the sex ratio and the age structure as well but what other factors outside of this intrinsic

growth rate can affect their growth well we break that into two groups density dependent and independent density

dependent factors are factors that limit growth based on the density of the population so if you think about it as

the population's density increases if there's not enough food or water or shelter we call those limiting resources

and what happens to the population it'll eventually level off it hits something called a carrying capacity or k it's the

maximum number of individuals and area can support we also have density depend independent and those are going to be

things just related to change so a flood or a fire could be examples that limit the size of the population so in

population ecology we're studying these factors and scientists come up with models that help to describe what's

going on in a population so a famous model is the exponential growth model what we're looking at is this growth

rate and how it's increasing the population over time and then we have a logistic model it's also showing

exponential growth but eventually it's reaching what's called a carrying capacity or this limit uh of population

growth scientists also study strategies that species have some are what are called K selected that means their

population size will increase until it gradually hits a carrying capacity and those who live more of a boomer bus

cycle that are are selected and we can look at how long individuals survive and that tells us a little bit about which

strategy they're using and so the population size is incredibly important so if we have these rabbits so we have

nine rabbits then their n value at this point would be nine if we lose two of them our NV value is seven if we gain

three now our n value is going to be 10 it's the set number we have but also density is important that's the number

of individuals we have in a given area and so we could call this one density but we would call this greater density

we could also look at their distribution I would say that these rabbits are now randomly distributed but they could be

distributed uniformly or they could just be clumped in their distribution and we could also look at their sex ratio so

how many of are males and how many of them are going to be females and we could expand that to look at what's

called their age structure not only what is their gender but also how old are they so we could organize them like this

where this is going to be our first year female rabbits second year and third year and we can do the same thing with

males but when it comes to the health the population size is incredibly important it's dictated by births deaths

immigration and immigration and so we have a formula that allows us to to look at that and the calculations are very

simple you can do them just in your head and so let's say we have a population of 10 so our n knot is going to be 10

that's our initial population here's our equation so it's really simple the change in N is going to be the births

minus the deaths plus the immigration minus the immigration so let's look at this population over here and see what

happens so this rabbit gave birth to three other rabbits and so if we write this out what's our births going to be

it's going to be three now let's watch the watch the population again so you can see one of the rabbits died and so

we're going to put a one here in the deaths we could look at immigration how many come in looks like just one so we

would put a one right here and then how many emigrate it looks like two left and so we would put a two right here and so

the Delta n or the change in N is simply going to be 3 - 1 + 1 - 2 or 1 that's the change or we've seen an increase in

one now what's the growth rate the growth rate is going to be the change divided by the initial population so 1

divided by 10 gives us us a 10% growth rate or 0.1 is our growth rate we call that the intrinsic growth rate and as

long as we have no other factors outside that population that will remain constant over time and you could solve a

really hard problem if we have a million people in an area a 100,000 are born 10,000 die if you're given the

immigration and immigration you should be able to calculate R for that population so if we study a group of

rabbits over time their population will increase but it'll eventually level out at some point now that leveling out

point is called the carrying capacity or the K now why is a population going to level out it's because they're running

out of something they're running out of food or water or shelter and so we all call all of those things limiting

resources disease could be another limiting resource the more rabbits we have the more disease and so it's

eventually going to level it off now it won't look perfect like that in a normal population it's going to have overshoots

and it's going to have a lot of die off but we're going to have that average that we eventually hit these are density

dependent factors because they're based on the density of the population we can also have density independent so imagine

that these rabbits over on this side are killed in a forest fire that's just chance it's just chance taking over and

so it's not based on the density of rabbits that we had so if we start to use models to explain how this works a

really important model is the exponential growth model and so the equation looks like this it's a little

scary but it's really not that bad n subt is going to be the population at any time into the future and sub o is

going to be the initial population so let's say we start with a population of 10 R is going to be the growth rate

that's that intrinsic growth rate and T is going to be time so the only thing that you really don't know in this

equation is e e is going to be e the mathematical constant so it's a number it's just like Pi it's going to be

2.718 it just keeps going like that so for our purposes we just think of it as 2.71 and so let's say we want to figure

out what's going to happen to the population in year one so if we want to figure out we started at 10 what's going

be the population probably at year 1 we just use this equation so E's going to be the same so what's going to be our r

value our r value will always be 0.5 that's that intrinsic growth rate what's our T value our T value is going to be

time what's our initial population it's going to be 10 so if I expand that a little bit we're simply multiplying 1

time 0.5 one year times that growth rate and so that's going to be 10 * 2.71 again that's e raised to the 0.5 power

so that's really like taking the square root of 2.71 and so that's 1.64 so if we work that out that's going to be around

16 rabbits after one year so let me graph that and let's go to the year two so same thing we're going to plug in our

value of 0.5 but now our T value is going to be two still have that same initial population and so now it's going

to be 2.71 raised to the 1 power so what's that that's simply 2.71 so if we work this out now we're going to have 27

rabbits in that next year you can see the population is increasing we're starting to see that exponential growth

let's go for year three so if we figure out year three again our intrinsic growth rate is still 0.5 three is going

to be the year we're at still have that same initial and so this is going to be 2.71 raised to the 1.5 power you'd

probably need a calculator to do this we now get 44.6 or let's say 45 rabbits so if we

graph it you can see that the population is increasing like that we have what's called a j-shaped curve and it's going

to increase rapidly over time we're going to the whole world would be filled with rabbits if we keep following this

model and so we know that's not what occurs and so not only intrinsic growth rate is important but K that carrying

capacity so if you're given a problem like this could you graph what's going to happen over time if K is 70 well

you're going to get something that looks like this it's going to be J for a while but it's eventually going to curve off

and we're going to have a s-shaped curve this is a logistic growth model there's also a mathematical model we w't won't

work through I'll put a link to another video where I do that down below and so scientists now that they have models

they can start to apply that to Nature so what we found is that species kind of fall into one of two camps we have what

are called K selected species those are going to be species that their population increases and then it'll

eventually hit a carrying capacity and it stays there what are some character istics of species like that they're

going to give a lot of Parental care to their offspring they're just going to have a few Offspring and so the whooping

crane would be an example of that humans are example of that we don't just go up and down in our population our selected

are going to do that so an Arctic hair is an example of that a famous study was looking at the pelts that were collected

by the Hudson Bay Company and they found from 1850 to 1930 that the population of Arctic hair just went up and down and up

and down and so hairs are going to be groups of individual that have lots of Offspring they don't give tons of

Parental care and their population is going to increase and then it'll crash so we have this boom and bust cycle now

what's interesting is that there's another species and so the Arctic are fed on by the Canada links and if we

look at their population their population goes through a boom and bust as well we have what's called a predator

prey relationship where as the Arctic care population increases then we can have more links feeding on it but as

they crash then the links are going to crash as well now a way to look at which strategy speci are using is figuring out

their survivorship so we have time on the bottom and then we have the survivors on the side so if we look at

humans as a type one survivorship curve what that means is when we're born almost all of the humans survive and

then throughout their lifetime they all die right at the end and so we give a lot of Parental care to our Offspring

almost all of them survive and then when we get into our 80s 90s then we all die off we could also have a type two

survivorship curve song birds are an example of that from the moment moment they're born they're dying off at a

constant rate or we could look at type three those are individuals like the acorns from a tree almost all of them

die but a few of those survive and those make up the plants that we have and so could you link that to K or R selected

species well type one individuals are generally going to be those K selected species and then type three are

generally going to be those R selected species but there are so many examples that are in the middle so if you think

about a sea turtle for example they have lots of Offspring they don't give much parental care but they live a long time

and so it's not as simple as are you are or R you K it's somewhere in the middle but they are applying these different

strategies in life and so did you learn the following could you pause the video at this point and fill in the blanks if

not population size is determined by immigration and birth that increases it decreased by immigration and deaths

we've got other characteristics density distribution sex ratio and age structure there are density independent and

dependent factors density independent remember are related to chance density dependent lead to what's called a

carrying capacity or k we use models to study it exponential models are built on the growth rate logistic models also

built on the growth rate but include carrying capacity and then we have different strategies in species K

selected R selected remember we're K selected and then we have survivorship curves that we can study to get that

that's a lot I hope it made sense and I hope that was helpful [Music]

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