End-of-topic test: Effect of Density on Populations

Unit 8 · Topic 8.4 end-of-topic test

Suggested time: about 47 minutes. Answer everything, then press Submit the test to see the feedback and scoring guides.

Answer every question. For each multiple-choice question, pick one option. When you have answered every question, press Submit the test; the feedback then gives the reasoning for each. For the free-response questions, write one short sentence for each step of your reasoning, each on its own line, and make every link clear (so, because, therefore). That is what the exam’s ‘paragraph form’ means for you: linked sentences, not bullet points. Then open the scoring guide and mark your own work against it. The formula sheet gives the growth equations, dN/dt = B − D, dN/dt = rmax N and dN/dt = rmax N ((K − N)/K), and percent change = (final − initial) / initial × 100.

Question 1

The four woods’ muntjac counts and areas.

Ecologists count the muntjac, a small deer, in four woods. The table below gives each wood’s count and its area.

In which wood do the muntjac have the highest population density?

A. Wood J B. Wood M C. Wood R D. Wood W

Question 2

The pool’s bullhead counts, months 0 to 16.

Bullheads, small bottom-living fish, are released into a new stream pool and counted every month. The graph below shows the counts.

Which of the following is the pool’s carrying capacity, K, for bullheads?

A. 30 bullheads B. 420 bullheads C. 690 bullheads D. 840 bullheads

Question 3

The tank’s prawn counts, weeks 0 to 24.

Prawns are bred in a tank that gets the same amount of food every day. The graph below shows the count of prawns every two weeks.

Which of the following explains why the curve flattens after week 16?

A. The tank holds as many prawns as can fit, so no more prawns can be born B. Each prawn’s share of the food shrinks as the count rises, so fewer prawns are born and more die, until births equal deaths C. Each prawn keeps adding the same number of young, but a hazard from outside the tank kills a fixed fraction every day D. The prawns have used up all the food in the tank, so every prawn stops breeding and the count stays where it is

Question 4

What each tank gets, and the count its sandhoppers settle at.

Sandhoppers, small jumping crustaceans of the shore, are kept in four tanks of the same size at the same temperature. Each tank gets dead seaweed to eat and an area of damp sand to hide in. The table below gives what each tank gets and the count the sandhoppers settle at.

Which of the following is the limiting factor for the sandhoppers?

A. The seaweed B. The damp sand C. The seaweed and the damp sand together D. Neither: the sandhoppers’ own nature sets the count

Question 5

The two plantations’ saplings, and how many the fungus killed.

Two plantations of the same size hold young larch trees, one planted thinly and one planted densely. A fungal disease reaches both plantations in the same spring. The table below shows the saplings in each plantation and how many the fungus killed.

Which kind of limiting factor is the fungus, and why?

A. Density-dependent, because the fungus killed more saplings in the dense plantation B. Density-dependent, because the fungus killed a larger fraction of the dense plantation’s saplings C. Density-independent, because the fungus killed a fraction of the saplings in both plantations D. Density-independent, because a fungus spreads through a plantation whatever the spacing of its trees

Question 6

Each of the following limits a population’s growth.

Which of the following is a density-independent factor?

A. A disease that passes from one animal to another when the two touch B. A shortage of nest holes shared by all the birds of a wood C. A hawk that hunts where its prey are easiest to find D. A late frost that kills a fraction of a field’s seedlings

Question 7

The two meadows’ water voles, and how many the buzzards took.

Buzzards hunt water voles on two meadows of the same size. The table below shows the voles on each meadow and how many the buzzards took in a week.

Which meadow lost the larger fraction of its voles, and why?

A. Meadow P, because a buzzard finds a vole after a shorter search where voles are dense, and other buzzards gather there B. Meadow P, because it holds five times as many voles, so far more voles are there to be taken C. Meadow J, because each vole there stands alone in the grass and is easier for a buzzard to see D. Neither: a buzzard takes the same fraction of the voles on any meadow it hunts over

Question 8

Suppose a reef’s food and hiding places can support no more than 2 450 wrasse, a reef fish: K is 2 450 wrasse. The reef holds 490 wrasse.

Which of the following is the braking term for the wrasse?

A. 0.2 B. 0.8 C. 5 D. 1 960

Question 9

Suppose the braking term for a flock of capercaillie, large grouse of pinewoods, is 0.25.

Which of the following is true of the flock?

A. The flock is at 25 % of its K B. The flock has room for 25 % more birds than it holds now C. The flock is at 75 % of its K D. The flock is above its K

Question 10

An ecologist uses the logistic equation for the turnstones, a shore bird, on one estuary.

Which of the following does K stand for in the logistic equation?

A. The number of turnstones on the estuary now B. The most turnstones each turnstone adds per year, with nothing holding the flock back C. The room left on the estuary as a fraction of the whole D. The most turnstones the estuary’s resources can support

Question 11

Which of the following is the logistic equation, as the formula sheet writes it?

\frac{d N}{d t} = r_{m a x} N

\frac{d N}{d t} = r_{m a x} N (\frac{N - K}{K})

\frac{d N}{d t} = r_{m a x} N (\frac{K - N}{K})

\frac{d N}{d t} = r_{m a x} (\frac{K - N}{K})

Question 12

Suppose a lagoon’s food can support no more than 2 720 smelt, a small fish: K is 2 720 smelt. The lagoon holds 680 smelt, and their r_max is 0.9 per year.

Which of the following is dN/dt for the smelt?

A. 153 smelt per year B. 459 smelt per year C. 612 smelt per year D. 1 836 smelt per year

Question 13

The four lakes’ carrying capacities and char populations.

Arctic char, a cold-water fish, live in four lakes. The table below gives each lake’s carrying capacity for char and its population size now. Every lake’s char have the same r_max, 0.1 per year.

Which lake’s char population adds the most fish this year?

A. Lake J B. Lake M C. Lake R D. Lake W

Question 14

The beach’s sanderling counts, years 1 to 10.

Sanderlings, small shore birds, are counted on one beach every winter for ten years. The beach’s food and roosting places stay as they were throughout. The table below gives the counts.

Which of the following is the best estimate of the beach’s carrying capacity, K, for sanderlings?

A. 140 sanderlings B. 432 sanderlings C. 520 sanderlings D. 560 sanderlings

Question 15

The number of blennies stocked in each tank, and the count a year later.

Blennies, small rock-pool fish, are stocked into four tanks of the same size with the same food each day. The table below gives the number stocked in each tank and the count a year later. A fifth tank of the same kind is then stocked with 345 blennies.

Predict what the fifth tank’s count does over the following year.

A. Falls toward 138 blennies B. Stays near 345 blennies C. Rises above 345 blennies D. Falls to 46 blennies

Question 16

Suppose whelks, sea snails, are counted on one shore: 1 300 whelks one spring and 1 040 whelks the next spring.

Which of the following is the percent change in the whelks’ count?

A. −25 % B. −20 % C. −0.2 % D. +20 %

Question 17

Suppose the insects along a stream feed no more than 330 wagtails: K is 330 wagtails. A flood scours away much of the streambed, and the insects left feed no more than 220 wagtails. The wagtails stand at 135.

Predict what the wagtails’ count does over the following years.

A. Falls below 135 wagtails B. Stays at 135 wagtails C. Rises toward the old K, 330 wagtails D. Rises toward the new K, 220 wagtails

Question 18

Vendace, small lake fish, are eaten by one kind of large predatory fish in their lake, and their count has stayed near the lake’s K for years. Anglers then remove every one of the predatory fish. A student says: “With the predators gone, nothing limits the vendace, so their count will climb for as long as the lake exists.”

Which of the following is the best evaluation of the student’s claim?

A. The claim is correct: with the predators gone, nothing holds the vendace back B. The claim is wrong: the vendace will stay at their old count, because K belongs to the vendace C. The claim is wrong: the count climbs, then levels off at a new, higher K set by the lake’s food and space D. The claim is correct: the count climbs for ever, because a lake’s food is never used up

How to tackle the free-response questions. Read the verb first: describe asks what you see or know; explain asks why or how, so name the mechanism; predict asks what will happen and why; justify asks for the evidence that supports a claim. Each point is earned by one idea, stated in a sentence that names the thing and the mechanism. Extra words earn nothing; a wrong extra can lose the point. If there is a figure or table, use what it shows. When you finish, check the box for each point your answer earns and compare your sentences with the full-credit answer.

Free response 1 · Analyze Model or Visual Representation · 4 points

A fast-spreading floating weed covers the surface of a shallow lake each spring. Three kinds of native water plant grow in the lake too: water crowfoot, bur-reed and marsh marigold. The upper table below gives the months in which each kind of plant puts up new shoots. Botanists net off two plots of the lake shore of the same size. They leave Plot J untouched. In Plot M they skim the weed off the water every week from March to September. At the end of the summer they count every plant in each plot; the counts are in the lower table. The botanists skim Plot M again the next summer, and at the end of that summer Plot M holds more native plants than it did at the end of the first.

The months in which each kind of plant puts up shoots, and the plants counted in the two plots at the end of the first summer.

(a) Describe what limits the native water plants in Plot J. (1 point)

A full-credit answer: The weed covers the surface first, so the natives’ shoots get too little light and too little surface space.
Light and surface space are resources the plants compete for, so the more plants share the plot, the smaller each plant’s share: a density-dependent factor limits the natives.

Check the box for each point your answer earns

the weed takes the light and surface space (or nutrients) before the natives, and the natives are held back by that shortage of a shared resource (accept: competition for light / space; a density-dependent factor).

Common slip: Saying the weed ‘kills’ the natives. The weed takes a resource; the natives are short of light and space.

(b) Predict how the count of native water plants in Plot M changes over the summers after that, if the skimming continues. (1 point)

A full-credit answer: The count keeps rising for a few summers, then stays steady at a new, higher level.

Check the box for each point your answer earns

the count rises and then levels off (accept: climbs to a new, higher carrying capacity; an S-shaped curve).

Common slip: Predicting a rise with no levelling off. Once the natives crowd the plot, light and space limit them again.

(c) In a third netted plot, Plot R, the botanists remove every plant that comes up before the end of May, and then leave the plot alone. Determine which of the four kinds of plant are present in Plot R by the end of the summer. (1 point)

A full-credit answer: All four kinds are present in Plot R: the floating weed, water crowfoot, bur-reed and marsh marigold.
Every kind puts up shoots after the end of May, so every kind comes up once the removal stops.

Check the box for each point your answer earns

all four kinds, including the floating weed (accept the list alone; accept with the reason that every kind keeps putting up shoots after May).

Common slip: Leaving the weed out. The weed’s shoots come up until the end of September, so it comes back after the removal stops.

(d) In one April a late frost kills 30 % of the native plants in Plot M. A student says: “The frost has left Plot M’s carrying capacity for the native plants where it was.” Evaluate the student’s claim. (1 point)

A full-credit answer: The claim is right.
The frost killed plants, but it took no light and no surface space from the plot.
K is set by the plot’s light and space, so K is unchanged.
The count is now below K, so births outnumber deaths and the count climbs back toward it.

Check the box for each point your answer earns

the judgement (the claim is right) AND the ground (the frost took no resource from the plot — the light and surface space that set K are as they were — so K stays; the count falls for a season and climbs back).

Common slip: Judging the claim wrong because 30 % of the plants died. A hazard that leaves the plot’s resources moves the count, not K.

Free-response score: 0 of 4

Free response 2 · Analyze Data · 4 points

Cockles, small shellfish, live buried in the sand of an estuary. Every spring for twelve years an ecologist counts the cockles in one marked square of sand. The estuary’s food and sand stay as they were throughout. The counts are in the table below, and the graph plots them.

The square’s cockle counts, years 0 to 11, as a table and as a graph.

(a) Make a claim about the carrying capacity, K, of the square for cockles. Give K to the nearest 50 cockles. (1 point)

A full-credit answer: The square’s carrying capacity for cockles is about 1 750 cockles.

Check the box for each point your answer earns

K is about 1 750 cockles (accept any value from 1 700 to 1 800 cockles, given to the nearest 50).

Common slip: Claiming the highest count, 1 890, as K. The count fell back from it, so the square could not support 1 890 for long.

(b) Support your claim with evidence from the data. (1 point)

A full-credit answer: From year 7 the count wanders close to 1 750 and ends near it, on 1 760, in year 11.
When the count was above 1 750, in years 6 and 10, it fell back; when it was below, in years 8 and 9, it rose again.
The count keeps returning to about 1 750, so that level is K.

Check the box for each point your answer earns

the count returns to about 1 750 in the later years (years 7 to 11 lie within 100 of it), falling back when above it and rising when below it (accept: quoted counts from the later years).

Common slip: Quoting only the rise of the first years. The evidence for K is where the count settles or returns to, not how fast it climbed.

(c) Explain why the count fell between year 6 and year 7. (1 point)

A full-credit answer: In year 6 the count, 1 890 cockles, was above K.
So each cockle’s share of the square’s food was too small.
Cockles short of food produced fewer young and more of them died, so deaths outnumbered births and the count fell.

Check the box for each point your answer earns

the count was above K, so each cockle’s share of food was too small and deaths outnumbered births (accept: the braking term was negative above K, so the count fell back toward K).

Common slip: Saying a hazard struck in year 6. The stimulus says the estuary stayed as it was; the count fell because it had climbed past K.

(d) The cockles’ maximum per capita growth rate, r_max, is 0.7 per year. Using your value of K from part (a), calculate dN/dt for the cockles in year 0. (1 point)

cockles per year

Write down the values, with your K from part (a):

r_{m a x} = 0.7 per year

N = 440 cockles

K = 1 750 cockles

Write down the equation:

\frac{d N}{d t} = r_{m a x} N (\frac{K - N}{K})

Work the braking term first:

\frac{K - N}{K} = \frac{1 750 - 440}{1 750} = 0.749

Substitute the values into the equation, and calculate:

\frac{d N}{d t} = 0.7 \times 440 \times 0.749

\frac{d N}{d t} = 231 cockles per year

A full-credit answer: dN/dt = r_max N ((K − N)/K) = 0.7 × 440 × ((1 750 − 440)/1 750) = 0.7 × 440 × 0.749 = 231 cockles per year.

Free-response score: 0 of 4

Feedback and scoring guides appear after you submit.

Multiple choice checked: 0 of 18 correct.

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