[Solution]Population Growth

Population Growth Introductory Information:   A population is defined as individuals of the same species living in a defined area. Population growth depends on four…

Population Growth

Introductory Information:
 
A population is defined as individuals of the same species living in a defined area. Population growth depends on four factors: natality (birth rate), mortality (death rate), emigration (physical movement out of a population), and immigration (physical movement into a population).
There are two commonly used ways to model population growth: exponential and sigmoidal models. Exponential growth is just as it implies – a population grows at an exponential rate. Exponential growth is usually associated with populations growing under conditions where resources are not limiting. It’s worth mentioning, however, that exponential growth does not usually last for much time, and population growth eventually decreases, often dramatically.
In the natural environment, a group of organisms that often exhibit exponential growth are invasive species. In the Great Lakes, for example, the round goby (introduced in 1990) has quickly become the most abundant fish in the Great Lakes with lake-wide densities up to 7.76 individuals m-2, far exceeding registered densities in their native range in the Sea of Azov (0.28 ind. m-2; Johnson et al. 2005). This high rate of population growth can be attributed to release from parasites/predators (Gendron et al. 2012), use of under-exploited niches (i.e. round goby consume zebra mussels which most native species cannot; Ray and Corkum 1997), and produce high numbers of offspring (Corkum et al. 1998).
Sigmoidal population growth is also commonly applied to populations. Sigmoidal growth is characterized as initially occurring at a high rate, which slows as the population approaches carrying capacity. A carrying capacity is the maximum population density, beyond which the population cannot be sustained.
Within an ecosystem, populations of predators and prey interact with each other in complex webs. The growth of any individual species is dependent upon the health and population of the other organisms within its food web. This results in a cycle of predator-prey interactions, where one party declines as the other flourishes, carrying capacity for the flourishing party is reached, and the decline of that species leads to an increase in the other’s population. This coupled system is an important component of population growth. In Part 1 of the lab we will be examining an example of a population which follows the Lotka-Volterra model. In this model there are a few assumptions which we will make here: the prey population would increase exponentially in the absence of the predator, the predator population would starve in the absence of the prey, predators can consume an infinite number of prey individuals, and the environment is homogeneous. Form more information on this model and how it works, visit the website linked here: http://www.tiem.utk.edu/~gross/bioed/bealsmodules/predator-prey.html .
In part 1 of this lab we will model a coupled predator-prey system over several generations and graph the rise and fall of the predator and prey populations. In part 2 we will use population data to fill out a life table and create both mortality and survivorship curves for a population.
 
Objectives:
 
This lab provides an introduction to the basics of population biology and predator/prey relationships, while teaching students how to fill out a life table. From the life tables, students will learn how to create survivorship and mortality curves.
 
Materials: Pencil, paper, calculator, shark and fish cards
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Procedure:
 
Part 1: Working individually, obtain the set of small fish cards (prey) and larger shark cards (predators). Work in one of the 2×2 ft “environments” taped off on a table. Each packet should contain 35 shark cards and 150 fish cards. This is the carrying capacity of the sharks and fish respectively. Do not exceed this population limits while playing your game.
Begin by placing 3 prey cards evenly spaced at the top of your square. One card should be placed in each of the upper corners with the third card in the middle.
Add one predator card to the plot, attempting to capture as many prey as possible. A prey organism is considered captured when touched by a predator card. A predator can only survive a round by capturing 3 prey. In this initial round, it will be impossible for your predator to capture more than 1 prey, so it dies.
At the beginning of each round, or generation, the number of remaining predators and prey doubles unless that number is zero, in which case you will begin the next round with 1 individual. For example, in the first round your predator was able to capture a single fish, leaving 2 fish alive. In the second generation this doubles, and you begin with 4 prey cards. Prey cards should be dispersed evenly in rows of 3 throughout your 2×2 square, only adding more prey to each row after you have 5 rows of 3 prey cards each. Be sure to remove all captured prey cards and all predator cards at the end of each round.
At the beginning of each new generation the beginning number of prey and beginning number of predators should be recorded. At the end of each generation the surviving number or prey and surviving number of predators should be recorded.
After several generations the population density of the prey cards should eventually become sufficient to support the predator population. A predator survives when it is able to capture 3 prey in one round. If a predator does this, it survives to the next generation and the number of predators doubles.
Continue this process and fill out the table below for 20 generations. (2 pts)
 

Generation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

Beginning # prey
3
4
6
10
18
32
58
104
150
150
150
150
150
150
150
140
104
64
50
64

Beginning # predator
1
1
1
1
1
1
2
3
4
5
6
7
8
9
10
11
12
13
15
15

Surviving #
prey
2
3
5
9
16
29
52
80
118
110
102
94
86
78
70
52
8
25
8
19

Surviving # predator
0
0
0
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

 
 
 
 
 
Assignment:
 
Graph the data recorded in the table above. Generations should be on the x-axis, with population numbers on the y-axis. Use two different colored lines to graph predator and prey data on the same graph. Label the curves with either shark or fish.
 
Graphs (3 pts)
 
Answer the following questions:
 
1. Describe any trends you see in the graph. (3 pts)
 
 
 
 
 
 
 
 
2. What do you predict would happen in generation 21 if another predator was added? (2 pts)
 
 
 
 
 
 
 
 
 
3. Explain how this simulation models a real ecosystem. (2 pts)
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Part 2: The following data was collected from a marked cohort of recently metamorphosed spotted salamanders living in Michigan (see table below). The females breed in the spring, after a brief embryonic period the eggs hatch and undergo a larval period that lasts 4 months. The larvae metamorphose and leave the pond as juveniles. The female juveniles mature at one-, two-, or three-years of age and then continue to live for one or two more years.
In the spring of 2000, 72345 eggs (males and females) were laid in the pond. Of these, 68800 successfully hatched (embryos) began their larval period. Four months later 3020 juvenile salamanders (metamorphs) were marked as they left the pond. For the next 5 years, adult females breeding for the first time and adults breeding for a second or third time were recaptured. The following table summarizes the recapture data. Letters in parentheses indicate females breeding for the first time as one-year olds (a), two-year olds (b), and three-year olds (c). It is important to note that life tables follow the females in a population but do not include males. Pay attention to this as you are entering your data into the table below.
 

 
New Adult Females
Recaptured Adult Females

 
 
(a)
(b)
(c)

Year 1
24 (a)
0
0
0

Year 2
75 (b)
3
0
0

Year 3
6 (c)
0
15
0

Year 4
0
0
4
2

Year 5
0
0
1
0

 
 
1. Construct a life table with the following entries: (6 pts)
 

x (age in months)
nx (# alive)
lx (proportion surviving)
dx (Proportion dying)
qx (mortality rate)

0 (eggs)
36172.5
1
0.0490013135
0.049001313

0.5 (embryos)
34400
0.95099
0.90925
0.9565

4 (juveniles)
1510
0.04174
0.01785
0.42781457

12 (1 year)
864
0.023885548
0.020899855
0.875

24 (2 year)
108
0.002985694
0.002405142
0.805555556

36 (3 year)
21
0.000580557
0.00041468
0.714285714

48 (4 year)
6
0.000165872
0.000138227
0.833333327

60 (5 year)
1
2.76453E-05
2.76453E-05
1

 
 
2. Make plots of the survivorship and mortality curves.
 
 
Plots:
For more help with Life Tables visit this website:
https://www.measureevaluation.org/resources/training/online-courses-and-resources/non-certificate-courses-and-mini-tutorials/multiple-decrement-life-tables/lesson-3
 
Remember to multiply your y-values by 1000 before plotting.
 
To calculate proportion surviving (lx), divide the number of individuals observed at a given stage by the original number of individuals.
 
To calculate proportion dying (dx) subtract the values of the proportion surviving ((lx.)-(lx+1))
e
To calculate the mortality rate (qx), divide the proportion dying by proportion surviving (dx/lx).
 
 
 
Assignment:
 
Create a mortality curve by plotting age on the x-axis and mortality rate (qx) on the y-axis. Remember to multiply y-values by 1000. (3 pts)
 
Create a survivorship curve. Plot age on the x-axis and proportion of individuals surviving (lx) on the y-axis. Remember to multiply y-values by 1000. Use a log-scale for the y-axis. (3 pts)
 
 
Answer the following questions:
 
1. What type of survivorship curve does this population best represent? (2 pts)
 
 
 
 
 
2. What are some key characteristics of this type of curve? (4 pts)

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