Free Learning! Additional Ecology Content

Because the goal of the MS Squared program is to integrate math and science, this Ecology course contains less ecological content than it would it ecology was the sole focus of the course. I develop course blogs for many of my courses and these blogs contain many lessons that might prove useful or interesting to you. Enjoy

The Rio Grande Class http://riograndeclass.blogspot.com/

I teach this course through the Honors College at Tech for students majoring in Environment and the Humanities degree program. This class focuses on the ecology of the Rio Grande River and the surrounding land. The highlight of this course is a week-long canoe trip along the Rio Grande River through Big Bend National Park. Some of the lessons in this blog-

1) Rivers and the hydrologic cycle

2) Importance of the physical environment

3) Adaptations to desert environments

4) Riparian zones

5) Stream Ecology

6) Disturbance Ecology

7) Invasive species

Ecology: The Science Behind Environmental Issues http://sciencebehindenvironmentalissues.blogspot.com/

This is a upper division seminar course that I teach in the Honors College. The goal of this course is to provide the basic ecological information required to understand current environmental issues. Some of the topics covered in this blog include-

1) Global carbon cycle and climate change

2) Ecosystem services

3) Biodiversity

Perspectives in Nature and the Environment http://perspectivesinnature.blogspot.com/

This is a seminar course for incoming Freshmen in the Honors College. Some of the topics covered in this course include-
1) Community Ecology and the Portal Experiment
2) Ecosystem Ecology
3) Environmental Ethics
4) Religion and the Environment

UM Special Topics in E&B http://umspecialtopics.blogspot.com/

This is the course that I taught about Ecology and Biodiversity (E&B) at the University of Malaya (UM) in Kuala Lumpur, Malaysia last year while I was a Fulbright Scholar in Malaysia.

Human Population Growth

I have spent a lot of time telling you that exponential growth is an unrealistic model of population growth. Interestingly, human populations have experienced exponential-like growth. How can this be?

What makes humans different from other species?

In other species per capita birth rates and per capita deaths rates are density dependent. However, as human populations have increased there has been no corresponding decline in per capita birth rates or increase in per capita death rates. What makes humans different from other species?

Humans have the ability to alter their environment so that they can avoid the density dependent effects on birth and death rates. 1) Humans have increased food production by improvements in agriculture (e.g., irrigation, fertilization, mechanized farming, genetically improved crops). 2) Humans have been able to decrease death rates by improvements in medicine and public health (things as simple as not pooping in the water you drink helps a lot!). 3) Humans have elimnated most human predators (ocassionally, someone gets killed by a shark or a mountain lion).

Where is human population growth occuring?

The rates of human population growth are not the same in all regions. Today, human populations are increasing in size much faster in developing countries (e.g., Mexico, other countries in Central America, Africa, and Southeast Asia) than they are in developed countries (e.g, USA, Canda, Western Europe). The figure at the top of this post shows the patterns of population growth in developed and developing nations.

Thus we see that populations are increasing most rapidly in the countries that are least able to deal with a rapidly increasing population. See "Population Challenges-The Basics" that can be downloaded from the Population Institute's website.
http://www.populationinstitute.org/population-issues/index.php

Human Population Growth Problem?

There is a great deal of debate about whether increasing human populations are a problem or not, and if they are what should be done about it. Unfortunately, we don't have time to discuss this issue in very much detail in class. My personal opinion is that we have too many people consuming too many resources and the last thing that we need are billions more people living on the planet. This is an issue that I am always intersted in talking more about if you would like to chat.

Further Reading

Here is a link to the article "Human Population Explostion" from the EoE.
http://www.eoearth.org/article/Human_population_explosion

Really Cool Video

Here is a link to a YouTube video on "World Population" The first minute and a half or so is a little boring, so you can skip over it if you wish. However, I think the animation showing when and where human population growth has been occuring is really cool.

http://www.youtube.com/watch?v=4BbkQiQyaYc

Expected Learning Outcomes

By the end of this course a fully engaged student should be able to

- describe patterns of human population growth in developed and developing nations

- discuss some reasons why the pattern of population growth in humans is so different from that in other species

- describe the demographic transition

- discuss their own personal view of human population growth.

Population Growth. Final Thoughts

We have discussed how population ecologists have tried to develop a model (the logistic growth model) that helps them to understand the factors that affect population growth.

We talked a lot about the graph plotting how the population size would vary over time in a population that started much smaller than the carrying capacity (the s-curve). Why does logistic growth show this pattern?

Initially, the population is growing slowly. When populations are small the per capita growth rate is large but because there are only a few individuals in the population rN is small. Over time, the population growth rate increases becasue populations are still small enough that r is still relatively large and now a larger N allows rN to be a bigger number. Population growth rate starts to slow as populations reach their carrying capacity because in large populations the per capitat growth rate is small and even though N is large rN is small. When the population reaches its carrying capacity b = d, so population growth stops.

Density Dependent Population Regulation

We notice that populations don't keep increasing in size forever. That is because populations are naturally self regulating. As population size increases the per capita birth rate declines for the biological reasons that we discused earlier. (When a parameter decreases as population size increases that parameter is said to be negatively density dependent. As population size increases the per capitat death rates increase for the biological reasons that we discussed earlier. (when a parameter increases as the population size increases that parameter is said to be positively density dependent). Thus, the per capita birth and death rates are naturally density dependent in such a way that eventually causes the population size of species to stop growing.

Here is the link to my Smart Board Notes for June 22nd.

http://www.slideshare.net/MarkMcGinley/smart-board-notes-622

Fun With Graphs. Quiz Yourself

Here are some questions that I have designed to let you know if you are understanding the graphs well enough to meet the course expected learning outcomes. I suggest that you do not try to answer these questions until you have thoroughly reviewed all of the information about the population ecology graphs. (I will put the answers for the multiple choice questions at the bottom of this post, for the others you need to find out whether your answers are correct or not).

1. What are the correct axes for a graph showing how population growth rate depends on population size in logistic growth?

a) x- N y- t
b) x- N y- dN/dt
c) x- dN/dt y- N
d) x- dN/dt y- t
e) x- N y- r

2. Which of the following best describes the graph that shows how the per capita growth rate varies over time in exponential growth?

a) the per capita growth rate decreases over time
b) the per capita growth rate increases over time
c) the per capita growth rate does not change over time
d) the per capita growth rate increases until it reaches a maximum and then decreases to zero when the population reaches the carrying capacity
e) the per capita death rate is initially very negative and gets less negative over time.

3. What would I ask to make you draw this graph?
a) show how the population size varies over time in logistic growth when the initial population size is much smaller than the carrying capacity
b) show how the population growth rate depends on the population size in logistic growth when the intitial population is much smaller than the carrying capacity
c) show how the population size depends on population size in logistic growth when the initial population size is much smaller than the carryuing capacity
d) show how the population size varies over time in logistic growth when the intitial population is much larger than the carrying capacity

4. What are the axes of a graph showing how the per capita growth rate depends on the population size in logistic growth?

a) x- logistic y- exponential
b) x- logistic y- r
c) x-N y-r
d) x-r y-N
e) x-N y-dN/dt

5. Which of the following is true when populations are at their carrying capacity?

a) N = 100 individuals
b) dN/dt = 0
c) b > d
d) b = d
e) b and d

6. Describe how the population growth rate varies over time in logistic growth when the intial population size is much larger than the carrying capacity.

7. Draw the graph that shows how the population size varies over time in logistic growth when the initial population size is much smaller than the carrying capacity.

Answers. 1.b, 2.c, 3.b, 4.c, 5.e

Population Biology. Logistic Growth

We are trying to develop a mathematical model that helps us to understand patterns of population growth. So far our first attempt, the exponential growth model, did not help us to understand population growth (for reasons that I hope that you understand by now).

The "Real" world

In our attemtp to think about population growth in the real world, we attempted to examine how per capitat birth rates and per capitat death rates should vary as population size varies. The model that describes this pattern of growth is known as the logistic growth model. It is important to realize that although this model is much more realistic, and therefore useful to us, than the exponential growth model, the logistic growth model still only exmaines what I call "the theoretical real world". That is, this model applies to our ideas about how populations should generally behave and do not thus relate directly to studying the population sizes of white tailed deer in central Texas or parrot fish on a coral reef in Fiji. These real world situations are much harder to understand than the simple "idealized" populations that I am talking about in BIOL 1404. You can take an Advanced Population Biology course if you want to learn more about how to apply these models to the "real real world".

Logistic Growth

We have discussed why, in the real world, r should decrease as population sizes increase. If this is the case then there is a population size at which the per capita birth rate equals the per capita death rate. We call this population size the carrying capacity.

1) When populations are smaller than the carrying capacity we expect them to increase in size until they reach the carrying capacity.

2) When populations are larger than carrying capacity we espect them to decrease in size untile they reach the carrying capacity.

3) When the population size equals the carrying capacity we expect no change in the size of the population.

The logistic growth equation is a mathematical equation developed by biologists to describe patterns of population growth consistent with the ideas above. Before focusing on the biological isights that we can gain from the logistic growth model (the real purpose of everything we have been doing) it is important to really understand patterns of logistic growth. Hopefully, this powerpoint presentation will help you understand these patterns better.

Powerpoint Presentation

Click here for a powerpoint presentation entitled "Fun With Graphs- Logistic Growth"

http://www.slideshare.net/secret/gyB3cjnSplLw41

Expected Learning Outcomes

By the end of this course a fully engaged students should be able to

- define the carrying capacity
- draw, and interpret the following graphs associated with logistic growth
-how population size changes over time in logistic growth when the initial population size is much smaller than the carrying capacity
-how the population size changes over time in logistic growth when the initial population size is much larger than the carrying capacity
-how population growth rate changes over time in logistic growth when the initial population size is much smaller than the carrying capacity
-how the population growth rate changes over time in logistic growth when the initial population size is much larger than the carrying capacity
-how the per capita growth rate varies over time in logistic growth
-how the population growth rate varies over time in logistic growth

- discuss the causes for the shape of the s-curve (this answer will need to include a discussion of both math and biology)

- discuss the factors that regulate population size, be able to distinguish between density dependent and density independent factors that regulate population growth and give examples

Link to Smart Board Notes- http://www.slideshare.net/MarkMcGinley/smart-board-notes-621

Fun With Graphs- Exponential Growth

How do I know which graph to draw?

1) In the population ecology portion of this course we will be discussing two models of population growth- exponential growth and logistic growth. Thus, you need to know which growth model you are describing before you know which graph to draw.

2) You can't draw a graph until you know what the axes are.

Hopefully, this is a review, but it is probably worth talking about. The x-axis (the horizontal axis) is known as the independent variable. The y-axis (the vertical axis) is the dependent variable. Changing the value of the independent variable results in a change in the dependent variable. Id DOES matter which variable goes on which axis so try to get it right.

In population ecology there will be two main independent variables that we are interested in studying. Because we are interested in patterns of population growth, we will often want to observe how variables change over time. Time is always the independent variable, so it always goes on the x-axis. Sometimes we are interested in how parameters depend on population size. In this case, population size is always the independent variable.

Powerpoint Presentation

This powerpoint presentation "Fun With Graphs: Exponential Growth" reviews the graphs you are expected to be able to draw, understand, and interpret.

http://www.slideshare.net/secret/mavlOD8flFs67G

Exponential Population Growth

From the first lesson on Population Ecology we learned that the population growth rate (dN/dt) can be calculated as the product of the per capita growth rate (r) and the population size (N).

dN/dt = rN

This is the fundamental equation describing population growth and this equation is always true.

If we want to use this equation to analyze how population sizes change over time, then it makes sense to start by examining the simplest formulation of this equation which occurs when the per capita growth rate is constant. The equation dN/dt = rN when r is constant is known as the exponential growth equation and this equation describes a patter on growth known as exponential growth.

The graph plotting how population size changes over time is shown in the Exponential Growth article. This graph shows an exponential growth curve (sometimes known as the "j-curve"). If you have questions about why the graph has this shape let me know and I will try to explain it more thoroughly.

It is important that you are able to look at this graph and determine all of the information held in the graph. The exponential growth curve allows us to discuss how two parameters change over time- 1) the population size (shown by the x-axis) and 2) the population growth rate (shown by the slope of the line). I find that it is easier to discuss only one parameter at a time so let's start with the population size.

1) Over time, the population size increases (we know this because the line has a positive slope).

Now let's think about the population growth rate.

2) Over time, the population growth rate increases (we know this becasue the line gets steeper over time.

3) Over time, the rate at which the population growth rate increases over time, increases over time (we know this because the slope increases faster and faster over time).

Thus, if populations are growing exponentially then they keep increasing in size at an ever faster rate forever and ever.

Now try this-

Can you draw the following graphs?

1) plot how the population growth rate varies over time.
(hint- we have alredy described what this pattern will look like using words- just turn these words into pictures).

2) plot how the population growth rate depends on population size.
(hint- this graph is a little trickier, but we do have an equation that relates the two variables)

3) plot how the per capita growth rate varies over time.
(hint- think about what the basic assumption we made aboiut exponential growth)

4) plot how the per capita growth rate
(see the hint from number 3)

Exponential Growth is Unrealistic
Because population sizes keep increasing at ever faster rates for ever, exponential growth does not seem to be an accurate description of population growth in most animals, plants, and microbes. If this is an unrealistic model then why did I teach it to you? I started with exponential growth becasue it is the simplest model of population growth and scientists always like to describe the world using the simplest models that they can.

Obviously, in this case we have started with a model that is too simple to realistically describe the world. What is wrong with the exponential growth model? The fundamental assumption we made about exponential growth is that the per capita growth rate is constant. This must not be a realistic assumtpion.

It is important that you understand, and are able to explain, both the mathematical reasons and biological reasons that exponential growth is an unreasonable model of population growth. I tried to explain biologically why exponential growth is unrealistic in the "Exponential Growth" article and the attached Powerpoint presentation so take a look at those.

Suggested Readings

Here are some articles you should look at from the Encyclopedia of the Earth. I wrote these so they are brilliant!!!

Population Ecology http://www.eoearth.org/article/Population_ecology

Exponential Growth http://www.eoearth.org/article/Exponential_growth

Logistic Growth http://www.eoearth.org/article/Logistic_growth

Carrying Capacity http://www.eoearth.org/article/Carrying_capacity

Intraspecific Competition http://www.eoearth.org/article/Intraspecific_competition

Powerpoint Presentation

Click here for the Powerpoint presentation "Why is Exponential Growth Unrealistic?"
http://www.slideshare.net/secret/IDPugQtl2wvONv

Expected Learning Outcomes

By the end of this course a fully engaged student should be able to

- draw and interpret the following graphs associate with exponential growth

a) how population size change over time in exponential growth

b) how population growth rate varies over time in exponential growth

c) how the population growth rate depends on the population size

d) how per capita growth rate changes over time in exponential growth

e) how per capita growth rate depends on population size

- explain why exponential growth is an unrealistic pattern of growth for most species

- define and explain the carrying capacity