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
Friday, January 23, 2009
Population Ecology II. Exponential 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/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
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 Ecology I. 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 (r) 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?
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?
Wednesday, January 21, 2009
Sexual Selection- Powerpoint
Let's see if I am smart enough to put the Powerpoint presentation on the blog. If you click here you should be able to view the Sexual Selection Powerpoint.
http://www.slideshare.net/secret/CG2HHvtrLA1KwL
http://www.slideshare.net/secret/CG2HHvtrLA1KwL
Tuesday, January 20, 2009
Genetics of Behavior
During the first portion of BIOL 1404 I have chosen to examine social behaviors as an example of a genetically controlled trait that can be influence by natural selection. In reality, we don't understand the mechanisms by which genes influence behavior, but we know that it must be quite complicated.
However, we are learning more about this topic all of the time. A recent issue of Science (the most prestigious science publication in the United States) published on November 7, 2008 contained a Special Section entitled "From Genes to Social Behavior". This section reviews some of the recent work on this field and includes articles such as "Parsing the Genetics of Behavior", "Genes and Social Behavior", Oxytocin, Vasopressin, and the Neurogenetics of Sociality, and "Wired for Sex: The Neurobiology of Drosophila Mating Decisions". If you are interested in learning more about this topic, then these articles would be a great place to start.
However, we are learning more about this topic all of the time. A recent issue of Science (the most prestigious science publication in the United States) published on November 7, 2008 contained a Special Section entitled "From Genes to Social Behavior". This section reviews some of the recent work on this field and includes articles such as "Parsing the Genetics of Behavior", "Genes and Social Behavior", Oxytocin, Vasopressin, and the Neurogenetics of Sociality, and "Wired for Sex: The Neurobiology of Drosophila Mating Decisions". If you are interested in learning more about this topic, then these articles would be a great place to start.
Monday, January 19, 2009
Sexual Selection
I think that sexual selection is one of the most interesting topics in all of biology. First, studyign this topic helps to illustrate that natural selection is much more than "survival of the fittest". Second, many of the traits produced by sexual selection are particularly bizzare. Finally, I think that it is fun to use what we have learned about mate choice in animals to helping us to understand human behavior.
Expected Learning Outcomes
By the end of this course a fully engaged student should be able to
- discuss the critical difference between males and females and discuss how this difference influences differences in behavior and morphology between species.
- discuss why sexual selection is just a subset of natural selection
- discus why females should be choosier about who they mate with than males
- discuss why males often compete with other males to fertilize eggs of females
- compare and contrast male-male competition in species with internal fertilization and species with external fertilization
- describe the studies used by scientists to see if females are capable of choosing the best males
- discuss how females can determine which is the best male
- discuss why the variation in female reproductive success is much less than the variation in male reproductive success
- discuss how you would use sexual selection to help you understand human behavior
Past Exam Questions (answers at the bottom of the post)
1. Why are females choosier than males about who they mate with?
(a) female gametes are much more expensive than male gametes
(b) male gametes are much more expensive than female gametes
(c) in some species, males are larger than females
(d) in some species, males compete to mate with the female
(e) c and d
(a) female gametes are much more expensive than male gametes
(b) male gametes are much more expensive than female gametes
(c) in some species, males are larger than females
(d) in some species, males compete to mate with the female
(e) c and d
2. Why should females prefer to mate with the oldest males?
(a) because they can pass on good mating genes to their daughters
(b) because they can pass on good survival genes to their sons
(c) because the can pass on good survival genes to their daughters
(d) a and c
(e) b and c
(a) because they can pass on good mating genes to their daughters
(b) because they can pass on good survival genes to their sons
(c) because the can pass on good survival genes to their daughters
(d) a and c
(e) b and c
3. Why might females sometimes cause male-male competition to occur?
(a) to assure that she mates with the oldest male
(b) to assure that she mates with the most symmetric male
(c) the male who wins the fight is likely to have “good genes”
(d) a and c
(e) a, b, and c
(a) to assure that she mates with the oldest male
(b) to assure that she mates with the most symmetric male
(c) the male who wins the fight is likely to have “good genes”
(d) a and c
(e) a, b, and c
Further Reading
Here is a link to a website that a student sent to me last year called "The 30 Strangest Animal Mating Habits" http://www.neatorama.com/2007/04/30/30-strangest-animal-mating-habits/
Take a look at this and see if you can relate what the animals are doing to some of the theories that we have talked about in class.
Here is a link to a youtube video showing the mating display of lyrebirds. I was lucky enough to see a lyrebird doing its mating display when I was a kid living in Australia. There was a professional nature photographer who had been hiking around the bush for a couple of weeks waiting to see the display and he was pissed that my Dad and I were able to see the display after spending only about an hour in the woods. What do you think is going on with the lyrebirds?
Answers. 1. a, 2. e, 3. c
Sunday, January 18, 2009
Antibiotic Resistance
Expected Learning Outcomes
By the end of this course the fully engaged students should be able to
- discuss the evolution of antiobitic resistant microbes as an example of natural selection
- discuss mistakes by both medical practioners and patients that led to this problem
- discuss how a broad exposure to diverse fields of biology may help future health science professionals.
Further Reading
Here is a link to an in-depth discussion of antibiotic resistance published by the World Health Organization http://www.who.int/infectious-disease-report/2000/other_versions/index-rpt2000_text.html
Past Exam Questions (answers at the bottom of the post)
In the 1950s, Japanese physicians began to notice that some hospital patients suffering from bacterial dysentery, which produces severe diarrhea, did not respond to antibiotics that had generally been effective in the past.
1. In order for the result described above to have occurred, which of the following must have been true in the population of dysentery-causing bacteria?
(a) there was variation in the susceptibility of the bacteria to antibiotics
(b) antibiotic resistance was heritable
(c) bacteria that were more resistant to antibiotics had higher survival rates than less resistant bacteria
(d) a, b, and c
(e) neither a, b, or c was true
2. What can be done in future to limit the problem of antibiotic resistance in disease-causing microorganisms?
(a) Doctors should only describe antibiotics when appropriate
(b) Doctors should prescribe larger doses of antibiotics
(c) patients should make sure to take all of the pills when antibiotics are prescribed
(d) a and c
(d) a, b, and c
Answers 1. d 2. d
By the end of this course the fully engaged students should be able to
- discuss the evolution of antiobitic resistant microbes as an example of natural selection
- discuss mistakes by both medical practioners and patients that led to this problem
- discuss how a broad exposure to diverse fields of biology may help future health science professionals.
Further Reading
Here is a link to an in-depth discussion of antibiotic resistance published by the World Health Organization http://www.who.int/infectious-disease-report/2000/other_versions/index-rpt2000_text.html
Past Exam Questions (answers at the bottom of the post)
In the 1950s, Japanese physicians began to notice that some hospital patients suffering from bacterial dysentery, which produces severe diarrhea, did not respond to antibiotics that had generally been effective in the past.
1. In order for the result described above to have occurred, which of the following must have been true in the population of dysentery-causing bacteria?
(a) there was variation in the susceptibility of the bacteria to antibiotics
(b) antibiotic resistance was heritable
(c) bacteria that were more resistant to antibiotics had higher survival rates than less resistant bacteria
(d) a, b, and c
(e) neither a, b, or c was true
2. What can be done in future to limit the problem of antibiotic resistance in disease-causing microorganisms?
(a) Doctors should only describe antibiotics when appropriate
(b) Doctors should prescribe larger doses of antibiotics
(c) patients should make sure to take all of the pills when antibiotics are prescribed
(d) a and c
(d) a, b, and c
Answers 1. d 2. d
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