Happy Birthday 7 Billionth Person

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

7th Billion Person- http://www.thehindu.com/sci-tech/science/article2412108.ece

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

This link contains lots of interesting data- take a look

http://www.worldometers.info/

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 Biology 3. 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

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

Population Biology 2. Exponential Growth

From our earlier lessons 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/Exponential_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

Population Biology 1. Basic Parameters

Here is a brief introduction to some of the important parameters that we will need to understand to be able to study population ecology. For each of the parameters it is important that you know (1) the name of the parameter, (2) the algebraic symbol used to represent the parameter, (3) the units of measurement for the parameter, (4) how to calculate the parameter, and (5) how to describe (in words) what a particular value of that parameter means.

It is probably easiest for me to introduce these concepts using an example.
Imagine that in a population of 100 elephants that in one year 10 elephants are born and 5 elephants die.

1) Population Size (N) units- individuals. Measures the number of individuals in a population.

N = 100 individuals

In this population, there are 100 elephants.

2) Population Birth Rate (B) units- number of births per time. Measures the number of births per time that occur in a population.

B = 10 births/year

In this population, each year there are 10 births.

3) Population Death Rate (D) units- number of deaths per time. Measures the number of deaths per time that occur in a population.

D = 5 deaths/year

In this population, each year there are 5 deaths.

4) Population Growth Rate (dN/dt) units- number of idividuals per time. Measures the rate of change of the population size.

dN/dt = B - D

dN/dt = 10 births/year - 5 deaths/year = 5 individuals/year

In this population, the population size increases by 5 individuals each year.

5) Per Capita Birth Rate (b) units- births per time per individual. Measures the number of births per time averaged across all members of the population.

b = B/N

b = (10 births/year)/100 individuals = 0.10 births/year/individual

In this population, each year 0.10 babies are born for each individual in the population.

6) Per Capita Death Rate (d) units - deaths per time per individual. Measures the number of deaths per time averaged across all members of the population.

d = D/N

d = (5 deaths/year)/100 individuals = 0.05 deaths/year/individual

In this population, each year 0.005 individuals die for each individual in the population.

7) Per Capita Growth Rate (r) units = individuals/time/individual. Measure the rate of change in population size averaged across all individuals. The per capita growth rate can be calcuated two ways.

a) r = b - d

r = 0.10 births/year/individual - 0.05 deaths/year/individual = 0.05 ind/year/ind

b) r = (dN/dt)/N

r = (5 individuals/year)/100 individuals = 0.05 individuals/year/individual

In this population, each year 0.05 individuals are added for each individual in the population.

Practice Problem

In a population of 50 tigers, in one year 10 tigers are born and 20 tigers die. What is B, D, dN/dt, b, d, r?

Readings


Population- http://www.eoearth.org/article/Population

Population ecology- http://www.eoearth.org/article/Population_ecology

Population growth rate- http://www.eoearth.org/article/Population_growth_rate

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


Expected Learning Outomes

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

- define and calculate the value of basic population ecology parameters

- draw and interpret the following graphs

a) how population size changes over time in exponential growth

b) how population size changes over time in logistic growth

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

- define and explain the carrying capacity

- 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

Midterm Exam!

Here is your midterm exam. The exam is due in class on Monday. You may use your notes or any other written sources of information. Please do not discuss the exam questions with any classmate or other people (i.e., you can't call Dr. Tilman to ask him about ZNGIs). Good luck.

1. (20 points)

We used Tilman's model to try to understand the conditions under which it is possible for two competing species to coexist. Define- ZNGI, consumption vector, supply vector, and resource supply point and discuss why a knowledge of all 4 of these components is necessary if we are to understand when coexistence is possible.

2. (30 points)

Many plants and animals are involved in mutualistic relationships with microorganisms. Why are mutualisms between animals/plants and microorganisms likely to be more common than mutualisms between two species of animals, two species of plants, or an animal and a plant?
Be sure to think about both the origin and the maintenance of the mutualism in your answer.

3. (30 Points)

Discuss at least two environmental problems that arise as a result of humans altering nutrient cycles.

4. (20 points)

Discuss why niche partitioning might be easier for animals than for plants.

Disturbance Ecology

The approach that community ecologists use to understand patterns of biodiversity depends on whether they think that communities are full (i.e., member of communities is limited by biotic interactions such as competition and predation) or whether communities are not full. The "equilibrial approach" to understanding community structure assumes that community membership is limited by competition. Thus, to understand the number of species in a community it will be necessary to understand the number of potential distinct niches. The "non-equilibrial approach" assumes that some procese or processes (such as predation or disturbance) have limited competitive exclusion.

Disturbance Ecology

Ecological disturbances are one example of a process that can limit competitive exclusion. If a disturbance disrupts population growth of a superior competitor, then the population size of the superior competitor may not get large enough to competitively exclude other species.

Powerpoint Presentation

http://www.slideshare.net/secret/GH30nvAxRaF4P


Further Reading

1) Here is a link to a chapter entitled - The response of animals to disturbance and their roles in patch generation. that Mike Willig and I wrote for a book Ecosystems of Disturbed Ground. The first portion of this chapter talks about our view of disturbance the second discusses some of my research in Texas.

http://hydrodictyon.eeb.uconn.edu/people/willig/Willig_pdf/094.Willig&McGinley.1999.pdf

2) The Fire Ecology Factsheet- http://www.eoearth.org/article/Fire_ecology_fact_sheet


Expected Learning Outcomes

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

- define disturbance
- list examples of disturbances
- distinguish between a disturbance and a disaster
- discuss the characteristics of a disturbance regime
- discuss some adaptations of organisms to disturbances
- discuss why disturbances are natural parts of many ecosystems
- discuss the intermediate disturbance hypothesis

Tilman's Model

Slideshow

http://www.slideshare.net/MarkMcGinley/tilmans-model-of-competition-for-two-resources

Expected Learning Outcomes

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

1)define ZNGI, consumption vector, supply vector, resource supply point

2)determine the outcome of competition when provided with information about ZNGIs, consumption vectors, and resource supply point.

3) distinguish between a stable and unstable equilibrium and be able to discuss why stable equilibria are particularly important outcomes from these models.

Competition in Animals and Plants

Readings

Competitive Exclusion Principle http://www.eoearth.org/article/Competitive_exclusion_principle

Resource Partitioning and Why It Matters
http://www.nature.com/scitable/knowledge/library/resource-partitioning-and-why-it-matters-17362658

Slideshow

http://www.slideshare.net/MarkMcGinley/competition-in-animals-and-plants

Expected Learning Outcomes

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

1) discuss the relationship between the fundamental and realized niche

2) discuss some ways animals can partition niches

3) define and describe character displacement

4) discuss why plants and animals may not be able to partition niches in the same way

5) explain Tilman's R* model

Is this the coolest wildlife video ever? From Kruger Park in South Africa

One of my former students sent me a link to this video. It seems like almost everything that we have talked about so far is going on in this video. The highlight of my biology life was visiting Kruger Park when I was about 13 (how sad to peak so young). I saw lots of amazing animals, but I didn't see anything like this. Enjoy! Make sure you watch all the way through- it just keeps getting better.

http://www.youtube.com/watch?v=LU8DDYz68kM

Writing Assignment #2: Ecosystem Services

Readings

Classic Paper

The value of the world’s ecosystem services and natural capital by Costanza et al.
NATURE |VOL 387 | 15 MAY 1997

http://www.uvm.edu/giee/publications/Nature_Paper.pdf

Value of the world’s ecosystem services: the influence of a single paper
http://www.eoearth.org/article/Value_of_the_world%C3%83%C2%A2%C3%82%C2%80%C3%82%C2%99s_ecosystem_services%3A_the_influence_of_a_single_paper

Other Readings

Biodiversity and ecosystem services- http://www.eoearth.org/article/Biodiversity_and_ecosystem_services

Marine ecosystem services- http://www.eoearth.org/article/Marine_ecosystem_services

Ecosystem services and human well-being synthesis: summary for decision-makers.
http://www.eoearth.org/article/Ecosystems_and_Human_Well-being_Synthesis:_Summary_for_Decision-makers

Expected Learning Outcomes

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

- define ecosystem services

- discuss the variety of services provided by the environment

- discuss how scientists have attempted to determine the monetary value of ecosystem services

Writing Assignment #2

After reading the materials on ecosystem services, write an article (3 page max, double spaced) discussing ecosystem services that could be published in the Lubbock Avalanche Journal.

Dates (note changes): First Draft due Friday October 7th. We will workshop the papers on Wednesday October 12th and the final papers will be due on Monday October 17th.