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POPULATION PRACTICE PACKET
AP Environmental Science Population Growth, Curves & Reproductive Strategies Growth Curves The number of individuals in a population can change based on many variables. Density independent factors affect all individuals in a population the same and may include physical factors such as climate, weather or salinity or catastrophic events such as floods, fires or drought. Density dependent factors are more effective with a high-density population and include food supply, disease, parasitism, competition and predation.
- In cooler climates, aphids (plant lice) go through a huge population increase during the summer months. In the fall, their numbers decline sharply. Identify one density dependent and one density independent factor that regulates this seasonal fluctuation. Populations show two types of growth, exponential and logistic. With exponential growth, a population increases by a fixed percent and its resulting graph is the classic “J- shaped” curve. Exponential growth occurs in nature with a small population and ideal conditions; however, it cannot be sustained indefinitely. With logistic growth, due to of environmental resistance, population growth decreases as density reaches carrying capacity. Carrying capacity (K) is the maximum number of individuals a habitat can support over a given period of time due to environmental resistance. The graph of individuals vs. time yields a S-curved growth curve. The maximum rate at which a population can increase is its biotic potential. The biotic potential of a species is influenced by the age at which reproduction begins, the time the species remains reproductive, and the number of offspring produced during each period of reproduction. Complete the following table for the two types of growth curves: growth curve shows unlimited, unchecked growth growth limited by extrinsic or intrinsic factors shape of curve (S or J) shows carrying capacity for a population typical of short term or long term growth
- exponential
- logistic For each of the following scenarios circle whether the population growth would best be represented by a logistic or exponential growth curve.
- a strep bacterium invades your throat and reproduces for 4 hours exponential or logistic
- the flea population on a rat is monitored for 5 weeks with flea powder added exponential or logistic
- loggerhead turtle populations are tracked for 5 years in the Atlantic exponential or logistic
- a lucky yeast cell falls into your glass of grape juice and reproduces for 10 hours exponential or logistic
- bull frog population in a local pond is monitored for 3 seasons exponential or logistic
Exponential Model When a population of organism’s increases grows in a geometric or exponential manner, the increase in the number of organisms gets larger during each time interval. When a geometric set of data is graphed, the curve resembles the letter J and is thus sometimes referred to as a J-curve.
9. Explain what the characteristics are in this population that makes the graph take on this shape. The exponential graph (J curve) can be represented by an equation. Nt = N 0 ert - Nt = estimate of the populations future size after some time - N 0 = starting population size - r = growth rate - t = time - e = the base of the natural logarithms (ex^ on calculator or 2.72) Example: A population of rabbits that has an initial population size of 10 individuals (N 0 =10). The growth rate for a rabbit is r=0.5 (or 50%), which means that each rabbit produced a net increase of 0.5 rabbits each year. With this information, we can predict the size of the rabbit population 1 year from now: - Nt = N 0 ert - Nt = 10 x e0.5x - Nt = 10 x e0. - Nt = 10 x 1. - Nt = 16 rabbits 10. You have a new population of 10 rabbits. Their growth rate is 1.0. Calculate and predict the size of the population after 1, 5, and 10 years. Show all of your work, box in your answers. Logistic Model Environments cannot support an unending population increase. Eventually the population reaches or exceeds its maximum sustainable level; also know as its carrying capacity. Given enough time, the size of a population will maintain itself at a level equal to the carrying capacity. If you start with a small initial population there is typically and initial period of slow arithmetic growth, followed by a period of rapid geometric growth which then levels off when the population reaches the carrying capacity. When graphed, the shape of this curve is somewhat like the letter S, and is known as an S-curve. 11. Explain what the characteristics are in this population that makes the graph take on this shape. 12. What is the growth rate of the population in the graph above at time 90? 13. At what time on this graph did the population reach its carrying capacity? 14. Did the graph above experience overshoot or die-off?
Population Calculations
You will need to be familiar with these equations for this unit. POPULATION DENSITY
population
= Population Density area for example:
270,000,000 people
9,166,605 sq. km. )^ = 29 people per square kilometer
BIRTH OR DEATH RATES:
of births or deaths per year
= Birth or Death Rate Total population NOTE: to find Crude Birth/Death Rates(# per 1000 people), multiply the rate by 1, for example:
23,452 births
942,721 people^ )^ = 0.025 = 2.5% birth rate
25 = Crude Birth Rate (25 per 1000 people) FINDING POPULATION GROWTH RATE/NATURAL INCREASE RATE (r): (This does not include immigration or emigration)
crude births – crude deaths
= r % 10 for example:
40 - 30
10 )^ = 1.0%
FINDING THE DOUBLING TIME OF A POPULATION: THE RULE OF 70!!!
How many years will it take for a location’s population to double??
or
= Doubling Time (dt) in years r (in percent form) r (in decimal form) for example:
70%
) or^ (
) = 10^ years
…meaning that it will take 10 years for this population to double in size! 7% 0.
Instructions: Complete the following problems NEATLY. Calculators are NOT allowed on
the AP Exam. All problems are to be solved WITHOUT using a calculator.
If a problem involves an equation – you must write out the equation for every problem. (Yes I understand that you will be writing the same equation over and over, but equations earn you points on the exam!) You must show ALL work. (This also earns you points on the exam!)
- List all variables.
- Show how numbers are plugged into the equation. If the problem involves units, you must include them. Numbers without units are meaningless. (Units earn you points on the exam! – seeing a pattern here?) Box your final answer.
Given the following information, answer questions 20- 23.
Schuhlsville is an island of 5,000 square miles off the coast of Jabooty. There are currently 250,000 inhabitants of the island. Last year, there were 12,000 new children born and 10, people were recorded as deceased.
- What is the current population density?
- What are the birth and death rates?
- What is the population growth rate (r)?
- In how many years will the population of Schuhlsville double?
Rate of Change The change in size of a population over a period of time is the rate of change of the population. To calculate the rate of change of a population, divide the change in the size of population by the period of time during which the change took place. To calculate the rate of change of the density of a population, divide the change of density by the time period in which the density change occurred. Reindeer Population/Rates of Change Procedure: In 1911, 75 reindeer- 15 males and 60 females – were introduced onto St. Paul Island, one of the Pribilof Islands in the Bering Sea near Alaska. St. Paul Island is approximately 106 km^2 in size (41 square miles), and is more than 323 km (200 miles) from the mainland. On St. Paul Island there were no predators of the reindeer, and no hunting of the reindeer was allowed.
- What was the size of the population at the beginning of the study?
- In 1920?
- What was the difference in the number of reindeer between 1910 and 1920? Use the following equation and examples for average annual increase or decrease. (the amount of an organism during the most recent date - the amount of an organism during the later date) (the amount of time between those two dates/times) Example 1 In 1960, there were 400 maple trees in a forest in Wisconsin. Thirty-five years later, in 1995, there were 925 maple trees in the same forest. The population of maple trees increased by 525 over a 35 - year period. The average rate of increase of maple trees in the forest was 15 trees per year. (925 maple trees in 1995 – 400 maple trees in 1960) = 15 trees per year (35 years) Average rate of increase Example 2 On the first day of fall in 1972, a group of biologist counted 475 deer in a nature preserve. Eight years later, in 1980, the biologists counted 379 deer in the persevere on the first day of fall. The population of deer decreased by 96 deer. The average rate of decrease of deer in the nature preserve was 12 deer per year. (375 deer in 1980 – 475 deer in 1972) = - 12 deer per year (12 fewer deer per year) (8 years) Average rate of decrease
- What was the average annual increase in the number of reindeer between 1910 and 1920?
- What was the difference in population size between the years 1920 and 1930?
- What was the average annual increase in the number of reindeer between 1920 and 1930?
- What was the average annual increase in the number of reindeer between 1930 and 1938? REINDEER POPULATION 0 100 200 300 400 500 600 700 800 900 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1900 1910 1920 1930 1940 1950 1960 YEAR Number of Reindeer
- During which of three periods- 1910 - 1920, 1920-1930, or 1930- 1938 - was the increase in the population of reindeer greatest?
- What was the greatest number of reindeer found on St. Paul Island between 1910 and 1950? In what year did this occur?
- In 1950, only eight reindeer were still alive. What is the average annual decrease in the number of reindeer between 1938 and 1950? Discussion
- Could emigration or immigration have played a major role in determining the size of the reindeer population? Explain your answer.
- What might account for the tremendous increase in the population of reindeer between 1930 and 1938, as compared with the rate of growth during the first years the reindeer were on the island?
- What effect might 2,000 reindeer have on the island and its vegetation?
- Consider all the factors an organism requires to live. What might have happened on the island to cause the change in population size between 1938 and 1950?
- Beginning in 1911, in which time spans did the population double? How many years did it take each of those doublings to occur? What happened to the doubling time between 1911 and 1938?
- If some of the eight reindeer that were still alive in 1950 were males and some females, what do you predict would happen to the population in the next few years? Why?
- What evidence is there that the carrying capacity for reindeer on this island was exceeded?
- What does this study tell you about unchecked population growth? What difference might hunters or predators have made?
