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Lecture Comments (3)

2 answers

Last reply by: John Joaneh
Tue Dec 9, 2014 12:19 AM

Post by John Joaneh on November 6, 2014

I think theres something wrong here. My professor states that resource partitioning and character displacement are opposite in the way you defined them. Do you have a resource that supports your definition of the two terms?


  • A population is a group of individuals from one species living in a given area.
  • Mortality is the number of deaths per a given population or standardized population size. A survivorship curve represents how the mortality of the species varies with age.
  • Biotic potential is the maximum rate at which a given population could grow under ideal conditions. Exponential growth is the type of growth a population experiences under ideal conditions.
  • Carrying Capacity (K) is the maximum number of individuals that can occupy an area under given conditions. The logistic model shows growth rate from the time a population is introduced to an area to the time it reaches its carrying capacity.

    Growth Rate = r N (1 – N / K)

  • “r- selected” species have rapid population growth when obstacles are limited. They quickly reach carrying capacity. “K-selected” species tend to dominate in stable, established environments.


Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

  • Intro 0:00
  • Population 0:07
    • Size 'N'
    • Density
    • Dispersion
    • Measure Population: Count Individuals, Sampling, and Proxymeasure
  • Mortality 7:29
    • Mortality and Survivorship
  • Age Structure Diagrams 11:52
    • Expanding with Rapid Growth, Expanding, and Stable
  • Population Growth 15:39
    • Biotic Potential & Exponential Growth
  • Logistic Population Growth 19:07
    • Carrying Capacity (K)
    • Limiting Factors
  • Logistic Model and Oscillation 22:55
    • Logistic Model and Oscillation
  • Changes to the Carrying Capacity 24:36
    • Changes to the Carrying Capacity
  • Growth Strategies 26:07
    • 'r-selected' or 'r-strategist'
    • 'K-selected' or 'K-strategist'
  • Human Population 30:15
    • Human Population and Exponential Growth
  • Case Study - Lynx and Hare 31:54
    • Case Study - Lynx and Hare
  • Example 1: Estimating Population Size 34:35
  • Example 2: Population Growth 36:45
  • Example 3: Carrying Capacity 38:17
  • Example 4: Types of Dispersion 40:15

Transcription: Population

Welcome to

We are continuing our discussion of ecology today with the lecture on populations.0002

Recall that a population is defined as a group of individuals from one species living in a given area.0009

We are going to start out with some terms that you will be encountering as we discuss populations.0017

The size of a population is usually represented as N, and it is given as the number of individuals in a population.0023

Density is the size of the population per unit area. For example, you could state density as the number of individuals per square kilometer.0044

What is shown down here is dispersion, and what dispersion describes is how individuals are distributed across an area.0062

There are three major types of dispersion: clumped, uniform and random.0087

Clumped is the most common, and the reason that individuals may clump together is for protection. That is one reason.0092

Another is because there might be a favorable environment, so there might be a bunch of plants living in an area that has good moisture, for example.0102

If the dispersion is uniformed, it is very likely that the individuals - either plants or animals - are repelling each other in some way.0114

So, this could be plants that are secreting some sort of toxin, or it could be animal behavior,0125

animals defending their territory that do not let other individuals get within a certain distance of their territory.0132

Random dispersion occurs when there is no particular influence on the dispersion.0141

In studying populations, it is very important to be able to measure a population, and there are numerous ways that this can be done.0147

So, the methods used to measure a population, the first one is to actually count individuals.0158

And this is pretty difficult to do unless you are talking about a very localized area like the number of sea stars in a tide pool.0167

Birds can actually be counted pretty well by using photographs, but in general, it is usually not practical to count all the individuals in the population.0177

So, another way is to use samples, so sampling methods.0186

With sampling, what you could do is, one way is to count the individuals in a small area0191

or several small representative areas and then, extrapolate out to the entire area.0200

This is a good technique for trees or other plants, so count individuals in one or a few areas and then, extrapolate from that.0205

Another sampling method is sample and mark or catch and release. We will call it catch and release.0221

And I am going to talk in more detail here about this sample or mark type method catch and release way of measuring the numbers in a population.0231

So, what happens is individuals, animals are caught. They are marked in some way.0242

They are released, and then, you wait a period of time until they have spread back out among the rest of the population.0250

And then, you capture a bunch of individuals from that population and count how many marked individuals there are in your second catch.0257

And a formula, then, can be used to determine N, the number of individuals in the population, so N = MxC/r.0268

So, what do these terms mean? N is what we are looking for, the total number of individuals in this population, and M is number of marked individuals.0278

So, these were the individuals who were caught the first time, marked in some way and then, released.0292

C are the number captured the second time, and then, R are the number of recaptures. These are marked and caught again.0300

The best way to understand this is through an example.0320

Imagine that there are researchers trying to figure out how many gazelles are in a given area, in a given population.0323

So, the researcher captures and marks 20 gazelles.0330

The researcher, then, lets the gazelles back out in the wild, waits a week, waits two weeks, waits five days, waits an amount of time0337

that these gazelles will mix back into the population and then, captures a hundred gazelles and checks them for markings.0344

Let's say one week later, one week later captures a hundred gazelles.0354

The researcher, then, looks and counts five of these captured gazelles are marked.0361

And the researcher wants to know how many gazelles are in the population, so what is N?0369

Using this formula the original number marked was 20. The number caught that second time was 100 gazelles, and out of those 5 were marked.0375

So, five were recaptures. If you do the math, you will find out that this works out to 400.0390

OK, so, this is an excellent method of sampling and trying to determine measure of population where it is not practical to count each individual.0398

Proxy measures can also be used. Hunting statistics, sightings, other statistics, these can give you an estimate.0407

These are not great for an exact count.0424

But, they can give you an estimate or help you develop a trend that "Oh, there has been more sightings of bears lately".0426

Perhaps, the population is increasing. That is possible, so just general trends or estimates.0431

Regardless of the method used, appropriate statistical techniques need to be used0437

to ensure that the sample is adequate and to determine confidence in the results.0443

Mortality is a very important statistic in studying populations.0451

Mortality is the number of deaths per a given population or standardized population size, and each species has a different pattern of mortality as they age.0455

This can be demonstrated using a survivorship curve.0468

A survivorship curve shows the individual's age, the member's age on the X axis and the number of the remaining individuals or survivors on the Y axis.0471

Typically, the Y axis is the logarithmic scale, and it goes up to a standard number of individuals.0489

Here, it is 10,000. It could max out at 1000.0494

Now, when multiple species are being plotted like right here, what is usually done is that the X axis, instead of being in age two years,0498

three years, four years and on up, it is plotted from 0 to 100% of maximum lifespan.0508

So, the animal being studied here may have 100 year lifespan, and this one may only have a 20 year life span.0513

But, at any point, I could still plot 50% of the maximum lifespan, which would be a different absolute number for this species and that one.0519

But, I could still plot them all in the same curve using this method.0527

There are three general types of survivorship curves that you should be familiar with.0531

Here, we have type I survivorship. As you can see what happens here, there is a relatively low death rate at first.0535

So, we start out with 10,000 individuals, and it drops off pretty slowly until older age; and then, it drops off quickly.0543

So, in type I survivorship curves, what you see is a low death rate at young age relative to others species.0551

And individuals in this population mostly die of age-related diseases/age-related causes.0564

This is typical of large mammals who have few young and who provide significant parenting to the young,0578

so large mammals with few young and a lot of good parental care, so the offspring have a good rate of survival.0586

This includes contemporary humans living in developed countries.0605

They have a good survival rate among the young and then, much of death is due to age-related causes, so my example here is going to be humans.0609

Now, this is not necessarily the case for human beings who lived hundreds or thousands of years ago0620

or in some underdeveloped countries where there is a much higher infant mortality rate.0626

The second type of survivorship curve, type II, shows a species that has a fairly constant death rate0632

meaning an individual is equally likely to die at any age, any particular age, so a relatively constant death rate.0639

Examples would be reptiles and rodents, and this curve is characterized by just this straight line.0653

Type III survivorship curve: this shows species that has a very high mortality rate for the young, high mortality rate at young ages.0665

So, this would be a species that has many offspring but few survived to maturity. Examples are fish as well as many invertebrates.0683

So, what you see here is a very steep curve, very high mortality rate early on. Those that do survive, then, it flattens out.0699

Another way to represent this data is in what is called age structure diagrams.0712

And what an age structure diagram shows is the percent of a given population that is a particular age,0719

so the percent of a given populations as a particular age.0726

The vertical axis is arranged into equal blocks of ages. This could be, for example, representing 0 to age 4 .0732

Then, this could be individuals who are ages 5 to 9, then, 10 to 14 and so on, so that is along the vertical axis.0742

Then, here on the X axis, the horizontal axis, what we see is the percent of population at that age.0763

Frequently, males and females are shown separately because they may have different age distributions in the population.0771

For a given species in the same environment, what an age structure diagram can help us0780

visualize is if a population is expanding, expanding rapidly, expanding slowly, stable or even diminishing.0786

Right here, what we see is a high percent of the population at younger ages.0797

This population maybe growing rapidly if mortality at a younger age is not high because you can have a high percent of the population0803

whose under the age of ten, but if there is also high mortality rate for that age, the population is not going to expand.0811

And this also does not take into account immigration and emigration. We are just talking strictly here about birth rate, death rate, mortality.0816

So, this is ignoring immigration and emigration, individuals moving into or out of a population.0825

But, looking at this diagram, this would be typical of a population that is expanding with rapid growth.0832

A large proportion of the individuals in the population are young.0840

If the population is expanding but more slowly, you are going to see a more even age distribution.0846

And then, finally, in a stable population you are going to see survivorship - excuse me - age structure diagram that looks0856

similar to the one shown here, much more even distribution rather than bottom-heavy like the one shown over here.0864

This would be where you see relatively even proportion of individuals and then, drops off towards the older age.0873

This is going to be more like a type I curve.0880

Now, if this population ends up having a high infant mortality and childhood mortality rate,0883

this would be more similar to a type III survivorship curve that we just saw where there is many offspring, but there is a high mortality rate.0891

And then, the mortality rate decreases after childhood.0900

This is more like the type I that we talked about in developed countries where there is fewer offspring but good survival.0903

So, the age structure diagrams that we are seeing represent similar numbers to what we saw in survivorship curves but in different ways.0913

And what the age structure diagrams are typically used for is to compare different populations of the same species.0922

For example, we might compare population growth in different countries or different times in the same country.0929

Now, patterns of population growth, one type of growth is exponential.0937

Biotic potential is the maximum rate at which a population can grow under ideal conditions, ideal conditions meaning there is no limit on space or food.0944

There are no diseases. There are no predators.0956

This does not occur in nature. You can get fairly close in a lab with certain species, but this is just an ideal.0959

It is a maximum.0966

The biotic potential is the function of various parameters. What is a species' biotic potential?0969

Well, it depends on things like age that reproduction begins. It depends on the number of offspring per reproductive period.0974

It depends on the length of the reproductive period and the lifespan during which the species is capable of reproducing.1005

An organism that starts reproducing early ends late. It has a lot of offspring during a reproductive period.1019

Many years during which it can reproduce is going to have a larger biotic potential than a species that reproduces only a few offspring infrequently.1025

Exponential growth is the type of growth that you see when a species is introduced to a new area that is favorable to survival,1035

an area that has little or no disease, predators or competition.1044

So, what you are going to see is unrestricted growth, and it is going to be represented by a J-shaped curve.1050

The formula is shown here: N at time T = AxBT.1060

N is the number in the population, number of individuals in the population at time T. A and B are constants.1069

A is the initial population, so it is the population at time 0.1089

B is a growth factor, and B is going to be different depending on the particular species and the environment it is in.1099

So, as I said, this curve is J-shaped. It is introduced into the environment and then, grows at an exponential rate.1110

This is normally a very short-lived type of growth because the species is quickly going to outgrow its resources. Food or space will be a limiting resource.1117

An example of when you would see this would be in a lab or even in an outside new environment.1126

But, you would more commonly see this like among microorganisms.1133

So, if you took some bacteria, plated it out on the Petri dish, at first,1136

it is going to undergo exponential growth until crowding takes over and limitations on space and resources.1140

The second model for growth or type of population growth is logistic population growth.1148

In reality, there are limits on resources such as food, water and physical space.1154

The carrying capacity is the maximum number of individuals that can occupy an area under given conditions.1160

The logistic model shows the growth rate from the time that a population is introduced to an area until it reaches its carrying capacity.1170

Here, we see time versus the size of the population, N, and it is introduced.1182

And at first, the species may - if there is not a lot of competition, and there is plenty of food and space - undergo this exponential growth.1190

But then, it is going to reach its carrying capacity because of these limits imposed by space and food and resources and other factors.1200

So, the growth rate according to the logistic model can be plotted as rNx1-N/K.1211

Now, you know what N is, the number of individuals in a population, so what is r? r is the maximum or is also called the intrinsic growth rate.1220

Again, this equation models growth from the time a population is introduced to an area to when it reaches carrying capacity.1238

And it has this classic S-shaped curve contrasted with the J-shaped curve that we saw with the exponential model of growth.1245

Now, I talked about carrying capacity and limiting factors, so factors that establish the carrying capacity that limit the1255

population that is going to be reached can be divided into density-dependent factors and density-independent factors.1264

Density-dependent factors are factors that impact population growth or mortality rates that are dependent on the density of the population.1278

These include things like disease because when there is more organisms together, diseases are more likely to be spread.1288

An increase in predators because if you have a lot of a particular animal or plant, other animals that feed on those are maybe attracted to the area.1295

Food shortages: if there are too many individuals, food will run short; a build-up of waste.1306

So, these limit the carrying capacity.1315

The second type of factors are density-independent. These are unrelated to the population size or density, and these are things such as drought.1317

So, it does not matter if there are two individuals there or a thousand. Drought could have an effect.1335

It is more complicated than that because drought will make food scarce and if there is more individuals that will affect it.1341

But, just to keep it fairly simple, density-independent factors are things like drought, fire, other weather events, eruption of a volcano.1346

These are all going to occur regardless of how dense the population is, and both of these affect carrying capacity.1357

Now, to make this more complex, we are going to look at this model in terms of oscillation around carrying capacity.1367

Because the reality is an actual population is not necessarily constant at the carrying capacity as1377

shown by that simple S-shaped curve of just getting the carrying capacity and sticking right there.1383

In reality, there are often natural oscillations in variances due to disturbances.1389

So, a disturbance could be something like excess predators, or it could be a drought occurs and drops the population; and then, it needs to recover.1396

So, a lot of predators come into the area. The population drops.1411

The predators leave as their food supply goes away. The population comes back up.1415

Or the population is doing well and then, there is a flood that wipes out some of the population.1420

So, the population often oscillates around carrying capacity.1424

So, here is a scenario of what this graph could represent.1430

Let's say a species is introduced into a new region.1435

Initially, growth is exponential until competition for food and other resources limits its growth.1438

It may even overshoot its carrying capacity initially. It does not respond quickly enough as a population, so it overshoots.1446

There is not enough food around. There is a die off among the population.1455

It drops below carrying capacity and then, another surge in this oscillation.1461

The sequence can repeat itself. It could be a result of predators, of food shortages, of parasitic diseases that creates this pattern.1466

Another scenario is that instead of oscillating around at the carrying capacity, a disturbance can actually change the carrying capacity.1478

So, a disturbance may change carrying capacity.1487

For example, at some point, let's say a disease destroys a type of plant that is a food source for the species.1500

So, here is the species. It was introduced.1509

There is plenty of the plant that it feeds on. It undergoes exponential growth.1511

It gets up to carrying capacity, maybe overshoots it and then, oscillates around where its carrying capacity is.1517

Then, a disease destroys the plant that this animal feeds on. This could initially create a big drop in the population of this animal that feeds on this plant.1524

And then, it may come back up around this new carrying capacity because this disease is limiting the number of plants to a lower level than initially.1543

So, overall, food availability is lower. Even though the species may have other food sources, overall, food availability is lower.1554

And the carrying capacity has dropped to the lower level.1560

Growth strategies for organisms can be classified in two general ways:1569

those that are r-selected or r-strategist species; and those that are K-selected or K-strategist species, so let's talk about these two general types.1574

r-selected species take advantage of less dense ecological niches.1587

They produce many offspring, tend to provide little parenting and the population will grow rapidly when few limits are present.1612

So, if there is plenty of food and space, this population will expand very rapidly. They also respond quickly to disruptions.1638

A typical organism like this would be small in size and have a high reproductive rate, although, there are some variations.1648

But, examples would be bacteria, smaller fish, insects, weeds, and rodents.1656

Contrast this with a K-selected species, and one way to help you remember this is the K here stands for carrying capacity.1669

And K-selected species or K-strategist species tend to do well when competition for limited resources is required.1676

They have a more favorable strategy for conditions that are close to carrying capacity.1688

So, In general, this is a better strategy when conditions are close to carrying capacity, which is K.1694

So, when there is a stable established environment, when there are limits on resources,1712

these are individuals that tend to have long lives, extended parenting, fewer offspring.1725

Elephants are an example of this as are humans.1739

Looking at examples, let's say a fire destroys a section of the forest.1748

That area will quickly be taken over by r-strategists, small weed-typed plants, also, insects and rodents.1753

After some time though, larger plants and trees as well as larger mammals will become established in the area.1762

The weeds and smaller animals may not survive as well in this mature forest.1771

But, they will quickly take advantage of any opportunities within the forest that do arise due to changes in condition.1776

This division, like many divisions in biology, is somewhat arbitrary, and there is a continuum.1785

If you look at trees, they have long lives like r-strategists - excuse me - long lives like K-strategists.1792

They cannot respond very quickly to changes, but they do generate large number of seeds and/or offspring that have low survival rates like an r-strategist.1802

So, it is not a clean division.1813

We are going to focus just a little bit now on human population growth.1817

The human population has been growing exponentially for about the last 400 years or perhaps even longer according to some estimates.1822

Exponential growth, we will say around 400 years, and this is very unusual because as I discussed, exponential growth in a population is usually short-lived.1833

This has been an extremely extended period of exponential growth.1845

However, the rate of growth of the human population has been slowing since about 2000, slower rate of growth since approximately 2000.1849

And actually, the rate of growth slowed earlier in more industrialized countries.1864

The rate of growth is expected, so the rate of growth is expected to reach 0 and then, become negative around the year 2050, approximately 2050.1869

It is believed that the world population will peak at 9 or 10 billion people around the year 2050.1899

The lynx and the hare represent a classic case study in the predator-prey relationship. The hare is the prey, and the lynx is the predator.1916

And the Hudson's Bay Company collected almost 100 years of data on the number of pelts of the hare and the lynx that were sold.1927

Assuming that the pelts or trapped animals is proportional to the overall lynx and hare populations,1935

this data could be used to analyze the relationship between the lynx and the hare.1942

The graph here shows the number of pelts, which is a proxy for the population,1947

of the lynx in red here and the hare in blue between the years 1840 and 1930.1954

And what you will find if you analyze this graph is there is an approximately 14-year-cycle that these two populations undergo.1961

Looking at the hare, the hare peaks, and then, you will notice a little bit later the lynx population will peak- hare peaks, lynx peaks.1970

In general, there is somewhat of a lag between the lynx population cycle and the hare population, so links cycle lags behind the hare.1986

What this indicates is that the lynx population is at least partly dependent on the hare population.2005

Detailed studies that were done on the food web in the Boreal forest suggest that the lynx population is actually highly dependent on the hare population.2014

In other words, predators of the lynx do not play a major role in lynx mortality, and the hare is the primary population of the lynx.2024

Studies show that the hare population is dependent on both the food availability and predation by several species.2037

An interesting side note is that the periodic cycling of the hare population appears to coincide with sunspot activity.2045

And it is believed that the sunspot activity causes chemical changes in the preferred plants that the hare feeds on.2054

So, that affects the hare population. Then, the hare population, in turn, affects the lynx population.2062

Notice also that there are periods of exponential growth among the populations.2067

Now, to do some examples on population ecology, example one:2077

in order to study the population's size of the endangered American burying beetle,2083

researchers set up traps throughout the beetle's range and captured a total of 200 individual beetles.2089

So, they captured 200 beetles, and each beetle was marked.2095

Each beetle was marked with a small dot of pink and released, so they are using the capture-release method.2106

One day later, the traps were reset, and a total of 240 individuals were captured.2113

So, then, they went and they captured 240 beetles one day later of which 40 had red paint marks.2121

So, they recaptured forty marked beetles. Of the 240 caught, 40 were marked.2137

What is the estimated population size of the American burying beetle?2150

Remember the equation, N, which will give us the number of individuals in the population equals the number who were originally marked,2154

times the number captured, divided by those that were marked the second time or recaptured.2161

Here, we have marked, M equals 200 times 240 that were captured all over 40 that were captures.2171

200 times 240 gives 48000 divided by 40 gives N is 1200 beetles.2184

So, this is an example of how this capture and release method can be used to determine a population.2197

Example two: a particular fly species lays eggs in the carcasses of large mammals. Describe the initial population growth in the fly larva population.2206

So, flies lay many eggs. They have many offspring.2217

And initially, when the fly populates in animal carcass, there is going to be a lot of room and nutrients and little competition.2222

So, I would expect the initial growth in a small organism with many offspring that is likely an r-strategist to be exponential.2233

Would the fly be classified as an r-strategist or K-strategist? So, as I said this is an r-strategist.2243

It is a small animal, many offspring, and it takes advantage of opportunities for rapid growth.2253

What type of survivorship curve would you expect for the fly?2262

Well, recall that an r-strategist like this is likely to have many offspring, and therefore,2266

a high and little parenting or no parenting and then, a very high mortality rate at first and then, drop off.2277

And this is typical of a type III survivorship curve: high mortality rates in young ages. A lot of young but only few survived to maturity.2284

Example three: what is the correct statement about carrying capacity K?2298

Is a fixed constant for each species- that is not true.2304

Remember that carrying capacity can be changed, droughts, floods, parasites, predators- a change in those things.2309

A change could affect the carrying capacity in a population, so this is not a true statement.2320

Is not a factor in the growth rate of a given population- no, it actually is a factor.2337

Remember that we talked about the logistic model where rate of growth is rN = 1-N/K, and carrying capacity is part of this equation.2345

So, that is not true. It is a factor.2360

Is dependent on the availability of food- yes, carrying capacity is dependent on the availability of food.2362

If there are more resources available, the carrying capacity in an area will increase.2368

If there is less food availability, for example a plant ends up getting a parasitic infection and dying off,2373

the carrying capacity for animals dependent on that plant for food is going to decrease, so this is a true statement.2382

Does K remain constant over time? No, remember disturbances affect K.2389

Is not affected by long-term climate change- that is incorrect.2397

If a climate becomes warmer of cooler, that could affect a population's survival and the carrying capacity for that population.2401

So, the only true statement here is that carrying capacity is dependent on the availability of food.2410

Example four: a sea bird species is very territorial. What type of dispersion would you expect for its nest in a nesting colony?2416

Remember, we see several dispersion patterns: clumping, random and uniform.2425

Well, clumping means the organisms, sort of, stick together, and this is a territorial species that is not going to occur.2432

Random means there is no effect either way on the dispersion, so I would not expect that.2439

What would I expect is uniform, and in fact, spacing of nest can be very exact among birds.2446

If there are a lot of birds heavily populating an area, each nest might be located just out of range of pecking,2454

just out of pecking range from the bird in the adjacent nest.2463

So, that concludes this lesson of population ecology at

Thank you for visiting.2475