Unit 8 · Topic 8.3 end-of-topic test
Suggested time: about 47 minutes. Answer everything, then press Submit the test to see the feedback and scoring guides.
Ecologists survey the shore of an island and a second island 60 km away, which no bird flies between. Their counts are in the table below.
Which of the following groups of birds is one population?
A student counts 150 bumblebees of one species and 120 bumblebees of a second species in one meadow, and writes: “The meadow’s bumblebee population is 270.”
Which of the following is the error in the student’s statement?
Each of the following is a feature of an organism in its own place.
Which feature helps its organism get energy?
Gannets nest in a colony on a cliff. The table below gives the chicks hatched and the gannets that died in two years.
Compared with year 1, how does the colony grow in year 2?
Wallabies live in a national park. At the start of a year the park holds 480 wallabies. In that year 96 joeys are born and 51 wallabies die.
Which of the following is dN/dt for the wallabies?
Opossums live in a wood. The population holds 340 opossums now, and its rate of change of population size is −18 opossums per year.
Which of the following is the size of the population after 5 years, if the rate stays the same?
Two islands hold nutria of one species, both with food to spare. At the start of this year the larger island held 400 nutria, and over the year it gained 80 nutria. The smaller island held 100 nutria at the start of the year.
Which of the following is the smaller island’s gain this year?
A pond holds 800 mosquitofish and 200 killifish, both with food to spare. In one week the mosquitofish gain 160 fish and the killifish gain 80 fish.
Which species has the higher maximum per capita growth rate, r<sub>max</sub>?
A tank of zebrafish has been breeding for a year. The fish crowd the tank and their food is gone by the end of each day. A student moves ten of the zebrafish into a large tank of fresh water with food to spare.
Does the equation dN/dt = r<sub>max</sub> N apply to the fish in the new tank, and why?
Suppose a lake holds loach and bream, both with food to spare. The table below gives each population’s size and its maximum per capita growth rate.
Which population gains more fish in the next year?
Ecologists count the crossbills in a pine wood every two years. The table below shows the counts.
Which of the following describes the growth of the crossbill population?
A student counts the cells of one green alga in a bottle of water with light and nutrients to spare, once a day. The graph below plots the counts on a log-scale y-axis; its minor gridlines sit at 2, 3 and 5 times each labeled gridline.
Which of the following is the count at 3 days?
Nettles spread in two abandoned fields. Ecologists count the plants in each field every year and plot both counts on one log-scale y-axis, shown below. Both sets of points lie on straight lines.
Which population multiplies by the larger factor each year?
A student follows the fungus gnats in a greenhouse for four months, counting them once a month, and draws the graph below.
Which of the following is the one fault in the student’s graph?
Suppose a student counts the capybaras along a river once a year for six years. The counts climb from 12 capybaras to 1 900 capybaras.
Which row lists the right choices for showing these counts against time?
A student plots a count of 700 individuals on the log-scale y-axis drawn below. Its minor gridlines sit at 2, 3 and 5 times each labeled gridline.
Between which two gridlines does the point sit?
A population grows with nothing holding it back, so dN/dt = r<sub>max</sub> N applies.
Which of the following multiplies dN/dt by four?
The table below gives one year’s births and deaths in four populations of moorland birds.
Which population shrinks over the year?
(a) Calculate dN/dt for the gorse population in year 4. (1 point)
Write down the values in the question:
Write down the equation:
Substitute the values into the equation, and calculate:
A full-credit answer: dN/dt = B − D = 360 − 36 = 324 gorse plants per year.
(b) Determine whether the gorse population is growing exponentially, using the counts in the table. (1 point)
A full-credit answer: The population is growing exponentially.
Each count is three times the count the year before: 6, 18, 54, 162, 486.
Multiplying by the same factor in equal times is exponential growth.
Check the box for each point your answer earns
Common slip: Answering yes because the count rises. A count that rises by the same number every year also rises; exponential growth multiplies by the same factor.
(c) A student predicts the count in year 6 by adding two years of year 4’s rate of change to the year-4 count. Evaluate the student’s prediction. (1 point)
A full-credit answer: The prediction is too small.
The student’s method keeps the gain at 324 plants every year: 486 + 2 × 324 = 1 134 plants.
The plants have space to spare, so each plant keeps adding the same number of seedlings.
Each year there are more plants adding, so the yearly gain grows above 324.
The count in year 5 alone is 486 × 3 = 1 458, already more than 1 134.
Check the box for each point your answer earns
Common slip: Judging the prediction right because 324 is the latest rate. A rate that is right for year 4 is too small for year 5, when more plants are adding.
(d) Explain the shape of the ecologist’s graph. (1 point)
A full-credit answer: The points lie on a straight line.
Each year the count multiplies by the same factor, three.
On a log-scale y-axis, equal distances along the y-axis are equal factors.
So each year the point climbs the same distance.
Equal steps along the x-axis and equal rises along the y-axis give a straight line.
Check the box for each point your answer earns
Common slip: Saying the plants add the same number every year. The yearly gain grows; it is the factor that stays the same.
(a) Explain why dN/dt = r<sub>max</sub> N describes the ptarmigan population in the years after the release. (1 point)
A full-credit answer: Nothing holds the ptarmigan back: they have plants to spare, nothing eats them and no disease reaches them.
So each ptarmigan adds its most, r<sub>max</sub>, every year.
So the population adds r<sub>max</sub> N ptarmigan each year, and the equation describes it.
Check the box for each point your answer earns
Common slip: Listing the island’s features and stopping. The point needs the link: nothing holds the birds back, so each adds its most, so the population adds r<sub>max</sub> N.
(b) Calculate dN/dt for the 60 ptarmigan. (1 point)
Write down the values in the question:
Write down the equation:
Substitute the values into the equation, and calculate:
A full-credit answer: dN/dt = r<sub>max</sub> N = 0.35 × 60 = 21 ptarmigan per year.
(c) Predict how the population’s yearly gain changes over the following years while the island stays as described. (1 point)
A full-credit answer: The yearly gain grows: each year the island gains more ptarmigan than the year before.
Check the box for each point your answer earns
Common slip: Predicting the same gain every year because r<sub>max</sub> stays the same. r<sub>max</sub> is the gain per bird; the gain in all is r<sub>max</sub> times a growing N.
(d) Justify your prediction. (1 point)
A full-credit answer: Each ptarmigan keeps adding the same number of young per year, r<sub>max</sub>.
Each year the island holds more ptarmigan than the year before.
More birds, each adding the same number, add more young in all.
So the yearly gain, r<sub>max</sub> N, grows as N grows.
Check the box for each point your answer earns
Common slip: Saying each bird adds more young each year. Each bird adds the same number; more birds are adding.