2 questions, one for each idea where we can. Answer them, then see which ideas to fix.
Question 1 of 2
Which statement best describes the carrying capacity (K) of an ecosystem for a population of a particular species?
Answer and reasoning
AThe largest population size of the species that has ever been recorded in the ecosystem A student who reads the peak of a population record as K picks this. A population can rise above what its resources can sustain for a time and then decline; K is the size that can be sustained.
BThe population size that the ecosystem's available resources sustain over timeCorrect Carrying capacity is the sustainable abundance of a species that can be supported by the ecosystem's total available resources.
CA number set by the biology of the species that is the same in every ecosystem it lives in A student who thinks K is a fixed property of a species picks this. K depends on the resources of a particular ecosystem, so it differs between places and changes with conditions.
DThe population size at which births and deaths both stop, so that its size no longer changes A student who thinks a stable population has no births or deaths picks this. At K births and deaths continue but balance each other.
A population of a hypothetical beetle lives in a habitat with a carrying capacity (K) of 100 beetles. Its maximum per capita growth rate (rmax) is 0.50 per year. Using the logistic growth equation, what is the population growth rate (dN/dt) when the population size (N) is 60 beetles?
Answer and reasoning
A30 beetles per year A student who leaves out the effect of density picks this, using the exponential equation dN/dt = rmax N = 0.50 × 60 = 30. Near K, the term (K − N)/K reduces the growth rate.
B18 beetles per year A student who thinks growth speeds up as N approaches K picks this, using N/K in place of (K − N)/K: 0.50 × 60 × 0.60 = 18. In the logistic equation the factor shrinks as N approaches K.
C12 beetles per yearCorrect dN/dt = rmax N((K − N)/K) = 0.50 × 60 × (40/100) = 12 beetles per year. With N at 60% of K, growth is well below the exponential rate.
D60 beetles per year A student who confuses the population size with its growth rate picks this, giving N = 60 as the answer. dN/dt is the change in N per year, calculated from the logistic equation.
Working dN/dt = rmax N((K − N)/K) = 0.50 per year × 60 × ((100 − 60)/100) = 0.50 × 60 × 0.40 = 12 beetles per year.
In preparation: 0 of 2 sections compiled and reviewed. The rest show key terms and common mistakes from our question bank until they are.
8.4.A.1 Carrying capacity (K) Fix
Carrying capacity (K)
The sustainable abundance of a species that can be supported by the ecosystem's total available resources. It is a property of the population in a particular environment, so it changes when the amount of available resources changes.
Population density
The number of individuals of a population per unit area or volume, for example snails per square meter.
Limiting resource
A resource, such as food, water, nesting sites or shelter, whose supply restricts how large a population can become; competition for it increases as the population grows.
Students often think The carrying capacity is the largest population size that has ever been recorded in that place. In fact No. Carrying capacity is the population size that the available resources can sustain over time. A population can temporarily rise above it, for example after a run of good years, before falling back.
Students often think Carrying capacity is a fixed number set by the species' biology, the same in every ecosystem and in every year. In fact No. Carrying capacity depends on the total resources available in a particular ecosystem, so it differs between places and changes when resources change, for example in a drought.
8.4.A.2 Density-dependent factor Fix
Density-dependent factor
A factor whose effect on a population, measured per individual (for example, the proportion of individuals killed or the births per individual), becomes stronger as population density increases, such as competition for limited resources, disease spread by contact and predation that intensifies when prey are crowded.
Density-independent factor
A factor that affects a similar proportion of a population whatever its density, such as a severe frost, a flood or a fire.
Logistic growth
Population growth that slows as the population size approaches carrying capacity, giving an S-shaped curve of N against time; modeled by dN/dt = rmax N((K − N)/K).
Maximum per capita growth rate (rmax)
The highest rate at which a population can grow per individual, reached when resources are not limiting. In the logistic equation it is a constant; the realized growth rate is reduced by the term (K − N)/K.
Population growth rate (dN/dt)
The change in population size per unit time. In logistic growth it is low when N is small, greatest at an intermediate population size (about K/2) and approaches zero as N approaches K.
Per capita birth and death rates
Births and deaths per individual per unit time. As density increases toward K, per capita births tend to fall and per capita deaths to rise; at K they are equal, so the population stops growing while births and deaths continue.
Exponential growth
Population growth in which dN/dt = rmax N, so the population increases faster and faster; it occurs only while resources are not limiting.
Students often think A population keeps growing exponentially until its resources are completely used up, and then it crashes. In fact No. As a population grows, density-dependent factors such as competition for resources reduce births or increase deaths, so growth slows before resources are exhausted; logistic growth typically ensues.
Students often think Individuals choose to have fewer offspring when the population is crowded, so that enough resources are left for the group. In fact No. Birth rates fall at high density because individuals have less food or other resources, not because they act for the good of the group or the habitat.
6 more questions. Every wrong answer here is a real mistake students make, and you see why it is wrong as soon as you answer.
Question 1 of 6
A grassland has supported a population of a hypothetical grazing mammal near its carrying capacity for many years. A change in climate then reduces the amount of grass the grassland produces each year for the foreseeable future. Which prediction is best supported?
Answer and reasoning
ACarrying capacity will stay the same, as it is a fixed property of the species of grazing mammal. A student who thinks K is a fixed property of a species picks this. K depends on the resources available, so a lasting fall in grass production lowers it.
BThe population will stay the same size, as births and deaths stop once it reaches carrying capacity. A student who thinks births and deaths stop at carrying capacity picks this. At K births and deaths continue but balance; with less grass, births fall or deaths rise, so the population declines toward a lower K.
CThe grazers will choose to have fewer young so that enough grass is left for the whole group. A student who explains population change by individuals acting for the group picks this. Births may fall, but because each individual gets less food, not because animals choose to save grass for others.
DThe population will decline, as the reduced grass supply lowers the carrying capacity.Correct Carrying capacity is set by the ecosystem's total available resources. Less grass means fewer grazers can be sustained, so K falls; with less food per individual, births fall or deaths rise until the population is near the new K.
The graph shows the growth of a population of a hypothetical protist in a laboratory culture given a fixed daily food supply. Based on the graph, at what time was the population growing fastest (greatest dN/dt)?
Answer and reasoning
AAround day 5, when the population was about half of its final sizeCorrect The curve is steepest between days 4 and 6 (about 95 protists added per day), when N was about 170 to 360, roughly half of the final size of about 500. dN/dt is greatest at intermediate N, as the logistic model predicts.
BAround day 12, when the population had reached its largest size A student who thinks a population grows fastest when it is largest picks this. Between days 11 and 12 the population grew by only about 2 protists; near K, growth slows almost to zero.
CAt day 0, when there were fewest protists and the most food per protist A student who confuses growth per individual with growth of the population picks this. Each protist reproduced fastest at the start, but with only 10 protists the population grew by only about 12 in the first day.
DEqually at all times, as the maximum per capita rate (rmax) stayed the same A student who thinks a constant rmax gives a constant growth rate picks this. The curve's slope changes greatly over time; dN/dt depends on N and on how close N is to K, not on rmax alone.
Researchers test the hypothesis that competition for food limits the number of offspring produced per beetle in a hypothetical species of flour beetle. They place 10, 20, 40 or 80 adult beetles in identical containers, each holding 20 g of flour as food, and count the offspring produced per adult beetle after 30 days. Which is the independent variable?
Answer and reasoning
AThe mass of flour supplied as food in every container A student who takes the factor named in the hypothesis as the independent variable picks this. Every container holds 20 g of flour, so the food supply is a controlled variable; competition is varied by changing the number of beetles sharing it.
BThe offspring produced per adult beetle by day 30 A student who confuses the measured variable with the independent variable picks this. Offspring per beetle is what is measured, the dependent variable.
CThe length of time, 30 days, before offspring were counted A student who thinks time is always the independent variable picks this. Every container is counted after the same 30 days, so time is a controlled variable here.
DThe starting number of adults put in each containerCorrect The independent variable is the one the researchers deliberately change between groups: here, the number of adults (10, 20, 40 or 80), which changes the density and so the amount of food per beetle.
In a study of a hypothetical species of pond snail, the percentage of snails killed by a parasite and the percentage killed by a severe frost were measured in eight ponds with different snail densities. The graph shows the results. Which claim is supported by the data?
Answer and reasoning
AThe parasite acted in a density-dependent way and the frost did not, as only the parasite's percentage rose with density.Correct The percentage killed by the parasite rose from 3% to 40% as density increased, so its effect per individual grew with density: density-dependent. The frost killed about 20% at every density: density-independent.
BBoth acted in a density-dependent way, since more snails died from each cause in the denser ponds. A student who classifies factors by the number of deaths picks this. The frost killed about 20% at every density; more snails died in dense ponds only because there were more snails, so the frost was density-independent.
CThe frost acted in a density-dependent way and the parasite did not, as frost killed more snails in most ponds. A student who thinks the factor that kills most is the density-dependent one picks this. Whether a factor is density-dependent depends on how its percentage changes with density: frost stayed near 20%, while the parasite's share rose.
DThe parasite caused the snails to reach high densities, since it killed the most snails in the densest ponds. A student who reads a correlation as showing which variable caused the other picks this. A parasite that kills snails would be expected to lower snail density, not raise it; the data fit higher density increasing the parasite's effect.
A bacterial disease of a hypothetical rabbit species is spread by direct contact between rabbits. Which statement best explains why this disease acts as a density-dependent factor?
Answer and reasoning
AAt high density, there are more rabbits for the disease to infect, so a larger number die. A student who classifies factors by the number of deaths picks this. Any factor kills more individuals when there are more of them; the disease is density-dependent because the proportion infected rises with density.
BThe bacterium is a living factor, and living factors limit populations in a density-dependent way. A student who thinks all living factors are density-dependent picks this. The classification depends on whether the effect per individual changes with density, which here comes from more frequent contact.
CAt high density, rabbits meet more often, so a larger proportion of them become infected.Correct Contact between rabbits is more frequent when they are crowded, so the disease spreads to a larger fraction of the population. Its effect per individual increases with density, which makes it density-dependent.
DThe disease kills more rabbits than any other cause of death, which makes it density-dependent. A student who thinks the main cause of death must be density-dependent picks this. A factor is density-dependent because its effect per individual changes with density, not because it is the largest cause of death.
The model shows how the per capita birth rate and per capita death rate of a population of a hypothetical fish in a lake change with population size (N). Based on the model, what will happen to a population whose size is at point P?
Answer and reasoning
AIt will keep increasing, because populations grow until all of their resources are used up. A student who thinks populations grow until resources run out picks this. At P the death rate exceeds the birth rate, so the population falls toward K.
BIt will decrease, because the per capita death rate is higher than the per capita birth rate.Correct At P, to the right of K, the death-rate line lies above the birth-rate line, so more individuals die than are born per unit time and the population shrinks toward K, where the two rates are equal.
CIt will stay the same, because births and deaths stop once a population passes K. A student who thinks births and deaths stop at carrying capacity picks this. The model shows both rates above zero at P, with deaths exceeding births.
DIt will decrease, because the fish choose to breed less so that the lake does not become overcrowded. A student who explains population change by individuals acting for the group picks this. The decline results from each fish getting fewer resources at high density, which lowers births and raises deaths; fish do not limit breeding to protect the lake.
Compiled from the AP Biology Course and Exam Description (effective Fall 2025) and our question bank · Specialist review in progress. How these pages are made · Free, no account
