AP Environmental Science Quiz: Carrying Capacity

What this quiz covers

This quiz focuses on Carrying Capacity, giving you a quick way to practice the rules, question types, and explanations that matter most for AP Environmental Science.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. $K$ increases because reduced food spillage lowers disease transmission
2. $K$ decreases because fewer resources are available to support mice long term (correct answer)
3. $K$ stays the same because carrying capacity depends only on birth rate
4. $K$ becomes irrelevant because populations always grow exponentially in barns

Explanation: Carrying capacity (K) is determined by the availability of essential resources and limiting factors in an environment, representing the maximum population that can be sustainably supported. For the mouse population in the barn, food availability is a primary limiting factor. When the new grain storage system reduces food spillage, it directly decreases the amount of food resources available to the mice. With less food available, the environment can support fewer mice in the long term, causing K to decrease. This illustrates how K is not fixed but can change based on environmental conditions - it depends on multiple factors including food, water, shelter, and space, not just birth rate. The mouse population will adjust to this new, lower carrying capacity through reduced reproduction and/or increased mortality.

Question 2

1. The population growth rate increases because more individuals reproduce near $K$.
2. The population growth rate decreases as environmental resistance increases, causing the curve to level off near $K$. (correct answer)
3. $K$ represents the birth rate at which the population stops growing.
4. The population will continue to grow exponentially above $K$ as long as predators are absent.

Explanation: Carrying capacity, denoted as K, is the maximum population size that an environment can sustainably support given available resources like food, water, and space. In logistic growth, a population starts with exponential growth when small but slows as it approaches K due to increasing environmental resistance from density-dependent factors such as competition and disease. The correct answer B accurately describes this process, explaining that the growth rate decreases and the curve levels off near K because environmental resistance intensifies, limiting further increases. In contrast, choice A is incorrect because growth actually slows near K, not increases, as fewer resources per individual reduce reproduction. Choice C misrepresents K as a birth rate rather than a population limit, and D is wrong since populations do not grow exponentially above K in logistic models; instead, growth halts or reverses.

Question 3

1. Unlimited food supply and constant mild weather
2. Increased competition for food, spread of disease, and limited burrow space (correct answer)
3. Higher genetic diversity and increased mating opportunities
4. A decrease in predators as rabbit density increases

Explanation: Carrying capacity K limits population size by balancing resources and environmental pressures. Logistic growth incorporates environmental resistance, which includes density-dependent factors that intensify with population density, curbing growth near K. Choice B is correct as it lists factors like competition, disease, and space limitations that exemplify environmental resistance for rabbits, slowing growth as density rises. Choice A represents ideal conditions for exponential growth, not resistance, while C would enhance growth rather than limit it. Choice D might reduce predation but is not environmental resistance, which focuses on internal limits rather than external predators.

Question 4

1. A logistic curve leveling off near a carrying capacity determined by food and disease (correct answer)
2. A straight line increasing at a constant rate forever
3. An exponential curve that increases without limit regardless of resources
4. A curve that immediately jumps to $K$ at time 0

Explanation: Carrying capacity, denoted as K, is the maximum population size that an environment can sustainably support over time given available resources and limiting factors. Logistic growth describes how a population grows rapidly at first when resources are abundant, but slows and levels off as it approaches K due to density-dependent factors like competition, disease, and resource scarcity. The correct answer A represents this pattern accurately, as the rodent population would initially grow exponentially with plentiful food and no predators, but then level off near K when food becomes scarce and disease spreads, creating a classic S-shaped logistic curve. In contrast, option B suggests arithmetic growth, which is a straight line and does not account for environmental limits, making it unrealistic for natural populations. Option C describes unlimited exponential growth, ignoring the role of carrying capacity in imposing limits. This scenario illustrates how biotic factors like food and disease regulate population size toward equilibrium at K.

Question 5

1. About 800 individuals (correct answer)
2. The initial population size at time 0
3. The steepest slope of the curve
4. The time when growth first becomes rapid

Explanation: Carrying capacity K is the population size at which growth stabilizes because births equal deaths in a sustainable environment. Logistic growth curves show an S-shape: rapid increase followed by leveling off at K due to resource constraints. Choice A correctly identifies K as about 800 individuals, the level where the curve plateaus, indicating the environment's sustainable limit. Choice B is the starting point, not K, while C represents the maximum growth rate, not the capacity. Choice D marks the lag phase end, but K is the plateau value, not a time point.

Question 6

1. Exponential growth levels off at $K$, while logistic growth has no limit.
2. Logistic growth includes a carrying capacity $K$ that limits growth; exponential growth assumes no effective limit. (correct answer)
3. Both exponential and logistic growth ignore limiting factors.
4. Carrying capacity $K$ is the same as the intrinsic growth rate $r$.

Explanation: Carrying capacity K is central to logistic growth, imposing a limit where growth ceases. Exponential growth assumes unlimited resources, leading to unchecked increases, while logistic includes density-dependent limits. Choice B correctly distinguishes them: logistic has K as a cap, unlike exponential's no-limit assumption. Choice A reverses the models, and C ignores that logistic accounts for limits. Choice D confuses K with growth rate r, which is separate.

Question 7

1. An increase in available resources that raises $K$
2. A decrease in resource availability that lowers $K$ (correct answer)
3. A change that affects only intrinsic growth rate $r$ and not $K$
4. A density-independent factor that guarantees exponential growth

Explanation: Carrying capacity K decreases when resources are reduced, as seen with invasive species competing for food, lowering the sustainable population. Logistic growth curves would shift to a lower asymptote in response. Option B accurately describes this as a decrease in resource availability lowering K. Distractor A incorrectly suggests raising K, which would require more resources, not less. This example shows how biotic invasions alter ecosystem dynamics. It reinforces that K is not static but responsive to changes.

Question 8

1. The population will likely grow slowly because limiting factors increase as $N$ approaches $K$. (correct answer)
2. The population will grow at its maximum rate because $N$ is close to $K$.
3. The population will decline to zero because all resources are depleted at $N < K$.
4. $K$ will automatically increase as $N$ increases, so growth will remain exponential.

Explanation: Carrying capacity K represents the upper limit of population size that resources in an environment can support without degradation. Logistic growth models show rapid initial increases when the population N is much less than K, but growth slows as N approaches K due to limiting factors like resource scarcity. Choice A is correct because at N = 19,500 close to K = 20,000, limiting factors would cause slow growth, aligning with the logistic model's prediction of reduced net growth near K. Choice B is incorrect as maximum growth occurs around N = K/2, not near K, where growth nears zero. Choices C and D fail because resources are not depleted below K, and K does not automatically increase; instead, the population stabilizes near K without exponential continuation.

Question 9

1. Increase supplemental feeding to encourage faster growth
2. Reduce habitat quality so $K$ becomes smaller
3. Implement controlled harvesting to keep the population from exceeding $K$ (correct answer)
4. Eliminate all predators so the population can remain above $K$

Explanation: Carrying capacity K represents a balance point, but overshoots and crashes occur if populations exceed it, depleting resources. Logistic growth aims for stability near K, but management can help prevent extreme fluctuations. Choice C is correct as controlled harvesting reduces population before overshoot, stabilizing it near K by mimicking natural mortality. Choice A might cause larger overshoots by boosting growth, while B would lower K unnecessarily. Choice D risks unsustainable growth above K, leading to crashes.

Question 10

1. Carrying capacity is fixed and cannot change with environmental conditions.
2. The reduction in oxygen is a limiting factor that decreases $K$. (correct answer)
3. Lowering $K$ will always increase the population growth rate.
4. The algae biomass will increase above 1,000 g because stress increases reproduction.

Explanation: Carrying capacity K can change with environmental conditions, as it depends on resource availability and limiting factors. In logistic growth, alterations like reduced oxygen affect mortality and reproduction, adjusting K downward. Choice B is correct because the heat wave's oxygen reduction acts as a limiting factor, lowering sustainable biomass from 1,000 g to 600 g. Choice A is wrong as K is dynamic, not fixed, and C fails since lowering K typically slows growth. Choice D is incorrect; stress usually decreases, not increases, biomass above K.

Question 11

1. A density-dependent limiting factor contributing to environmental resistance (correct answer)
2. A density-independent factor that raises $K$
3. A factor that increases intrinsic growth rate $r$ indefinitely
4. A factor that makes $K$ irrelevant to population size

Explanation: Carrying capacity K is influenced by density-dependent factors that increase resistance as population grows. Limited nesting sites become scarcer with density, fitting environmental resistance in logistic models. Choice A is correct as this is a density-dependent limiting factor slowing growth near K. Choice B is density-independent, like weather, and C would not increase r indefinitely. Choice D is wrong; such factors enforce K, not make it irrelevant.

Question 12

1. Island 1 has greater habitat area and more consistent food resources (correct answer)
2. Island 1 has a higher intrinsic growth rate ($r$), which automatically increases $K$
3. Island 1 has more predators, which raises $K$ by removing weak individuals
4. Island 1 has a smaller population currently, so $K$ must be higher

Explanation: Carrying capacity (K) represents the maximum sustainable population size that an environment can support based on available resources and space. The difference in K between the two islands (1,000 vs 300 birds) reflects differences in environmental conditions rather than population dynamics. Island 1's higher K of 1,000 birds is best explained by having greater habitat area and more consistent food resources - these physical and biological factors directly determine how many individuals the environment can sustain. The intrinsic growth rate (r) affects how quickly a population grows but does not determine K itself. Similarly, current population size is independent of K, and while predators can influence population dynamics, they typically reduce rather than increase carrying capacity by adding mortality pressure.

Question 13

1. Increased sunlight and increased dissolved oxygen
2. Decreased nutrient availability and accumulation of metabolic waste (correct answer)
3. Increased immigration and increased genetic variation
4. Decreased competition and decreased disease transmission

Explanation: Carrying capacity (K) in a closed system is reached when environmental resistance from limiting factors prevents further population growth. For bacteria in a closed container, the most critical limiting factors are nutrient depletion and waste accumulation. As the bacterial population grows rapidly through cell division, it consumes the finite nutrients available in the closed system. Simultaneously, metabolic waste products (like acids and toxins) accumulate in the medium since there's no way to remove them in a closed container. These two factors create increasing environmental resistance as the population approaches K - eventually, insufficient nutrients and toxic waste concentrations cause death rates to equal birth rates, stabilizing the population. Unlike open systems, closed containers cannot have increased immigration or renewed resources, making nutrient limitation and waste buildup the primary drivers of carrying capacity.

Question 14

1. The growth rate approaches zero because births approximately equal deaths due to environmental resistance (correct answer)
2. The growth rate is at its maximum because resources are most abundant near $K$
3. The growth rate becomes negative only because genetic diversity decreases near $K$
4. The growth rate becomes exponential because density dependence no longer matters

Explanation: Carrying capacity (K) represents the maximum sustainable population size in an environment, where resource availability and environmental resistance balance population growth. In logistic growth, the population growth rate changes depending on how close the population (N) is to K. When N is very close to K (N ≈ K), the population experiences maximum environmental resistance through factors like competition for limited resources, increased disease transmission, and reduced reproductive success. At this point, the birth rate approximately equals the death rate, causing the net growth rate to approach zero. This differs from when N is much smaller than K, where growth is nearly exponential, or when N = K/2, where the absolute growth rate is actually at its maximum.

Question 15

1. Population size is approaching $K$, and the slope of the curve is decreasing. (correct answer)
2. Population size is near zero, and the slope is near zero.
3. Population size is far below $K$, and resources are abundant.
4. Population size is constant because reproduction has stopped permanently.

Explanation: Carrying capacity K causes deceleration in logistic growth as populations approach it, with the curve's slope decreasing due to rising environmental resistance. This phase follows initial acceleration and precedes equilibrium. Option A accurately indicates the decelerating phase when N nears K and slope decreases. Distractor B describes the lag phase near zero, not deceleration. This phase recognition helps track population progress toward K. It explains the transition from rapid to slow growth in resource-limited settings.

Question 16

1. Density-dependent limiting factor (correct answer)
2. Density-independent limiting factor
3. Abiotic factor that always increases $K$
4. Factor that eliminates environmental resistance

Explanation: Carrying capacity dynamics involve limiting factors, density-dependent ones intensifying with population size. Competition for nests increases with density, affecting K. Choice A is correct: it's density-dependent, contributing to resistance. Choice B is independent, like fires, and C would not increase K. Choice D eliminates resistance, opposite of competition.

Question 17

1. When $N \ll K$
2. When $N \approx \frac{K}{2}$
3. When $N \approx K$ (correct answer)
4. When $N$ is increasing rapidly but still far below $K$

Explanation: In logistic growth, the net population growth rate (dN/dt) approaches zero as the population size (N) approaches carrying capacity (K). This occurs because environmental resistance becomes maximal when the population is at K, causing birth rates to equal death rates. The logistic equation shows that growth rate equals rN(K-N)/K, which becomes zero when N = K. At this equilibrium point, the population has filled the environment to capacity and growth ceases. Option C correctly identifies this relationship. Option B describes the point of maximum growth rate (not near-zero growth), while options A and D describe situations where growth would still be substantial.

Question 18

1. Environmental resistance is relatively low, so growth can be near exponential. (correct answer)
2. Environmental resistance is highest, so the population cannot increase.
3. Environmental resistance forces the population to decline until it reaches $K$.
4. Environmental resistance eliminates all density-dependent factors.

Explanation: Carrying capacity K marks high environmental resistance, but below K, resistance is low. When N << K, growth approximates exponential due to minimal limits. Choice A is correct: low resistance allows near-exponential growth early on. Choice B is opposite; resistance peaks near K. Choices C and D are wrong as resistance does not force declines below K or eliminate factors.

Question 19

1. Availability of resources (food, water, space) and strength of limiting factors in the environment (correct answer)
2. The population's current age structure only
3. The number of births in a single year only
4. The latitude of the ecosystem only

Explanation: Carrying capacity K is primarily set by environmental factors like resource availability and biotic/abiotic limits, determining sustainable population size. In logistic growth, these factors cause the S-shaped curve, with growth slowing as resources per individual decrease near K. Answer A is correct, identifying resources and limiting factors as key determinants of K. Option B fails by focusing only on age structure, which influences growth rates but not K directly. This emphasizes that K is environmentally driven, not solely demographic. Understanding this aids in assessing ecosystem health and sustainability.

Question 20

1. A fixed constant that never changes in any ecosystem
2. The maximum sustainable population size given current environmental conditions and limiting factors (correct answer)
3. The maximum birth rate the population can achieve
4. The minimum population size needed to avoid extinction

Explanation: Carrying capacity K is the maximum population size sustainably supported by current environmental conditions and limiting factors, varying with ecosystem changes. In logistic growth, it's the asymptote where growth stabilizes. Option B provides the best definition, emphasizing sustainability under given conditions. Distractor A wrongly calls it fixed and unchanging, ignoring its dynamic nature. This conceptualization is core to ecology. It differentiates K from rates or minimums in population models.