Exponential and Logistic Population Growth Equations and Graphs

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What does the carrying capacity (KK) represent in the logistic growth equation?

The environment's resources limit the population growth.

The maximum population size that can be sustained indefinitely. (correct)

The rate of population growth increases over time.

The intrinsic growth rate of the population.

Which characteristic is unique to exponential growth and not logistic growth?

Growth rate decreases as the population approaches the carrying capacity.

The population growth initially resembles exponential growth.

The rate of population growth increases over time.

Population grows without bound if resources are unlimited. (correct)

In the logistic growth equation, what happens as the population approaches the carrying capacity?

The environment provides unlimited resources.

Growth rate decreases. (correct)

Population growth becomes exponential.

The growth rate increases rapidly.

How is the population curve represented on a graph for exponential growth?

Steep upward curve with indefinite increase. Signup and view all the answers

Which equation represents the rate of change of population over time in both exponential and logistic growth?

$dN=rNdtdt$ Signup and view all the answers

What does the parameter $\alpha$ represent in the Lotka-Volterra competition model?

The per capita effect of Species 2 on Species 1 Signup and view all the answers

According to the Lotka-Volterra competition model, how does a higher value of $\alpha$ affect the growth rate of Species 1?

It leads to a greater reduction in the growth rate of Species 1. Signup and view all the answers

How does the term $(1 - N_1 + \alpha N_2 / K_1)$ in the equation for Species 1 affect its growth rate?

It adjusts the growth rate of Species 1 based on its own population size (N_1) and the population size of Species 2 (N_2) multiplied by $\alpha$. Signup and view all the answers

What does the parameter $\beta$ represent in the Lotka-Volterra competition model?

The per capita effect of Species 1 on Species 2 Signup and view all the answers

According to the Lotka-Volterra competition model, how does a higher value of $\beta$ affect the growth rate of Species 2?

It leads to a greater reduction in the growth rate of Species 2. Signup and view all the answers

What do the parameters α and β in the Lotka-Volterra competition equations represent?

The intensity of interspecific competition Signup and view all the answers

How do higher values of α or β impact population growth rates?

They indicate stronger competition and affect growth rates more significantly Signup and view all the answers

What do the Lotka-Volterra equations allow researchers to predict?

Outcomes of competitive interactions between species Signup and view all the answers

How do the Lotka-Volterra equations describe species interactions?

By incorporating parameters like α and β to model interspecific competition Signup and view all the answers

What aspect of population dynamics do α and β help researchers understand in ecological communities?

How interspecific competition influences population growth rates Signup and view all the answers

What do the 'ghosts of competition past' refer to in the context of the text?

The enduring legacy of historical competitive interactions between species Signup and view all the answers

Why is understanding 'ghosts of competition past' important in ecology?

To unravel the complexities of species interactions and ecosystem functioning Signup and view all the answers

How do ecologists use shifts in traits and behaviors to understand species coexistence?

To determine the resource partitioning within ecosystems Signup and view all the answers

What aspect of species distributions and community structure is influenced by past competition?

Species richness in ecosystems Signup and view all the answers

In the context of the text, what do shifts in traits represent?

The influence of historical competitive interactions on present-day dynamics Signup and view all the answers

What do the parameters α and β represent in the Lotka-Volterra competition equations?

Effects of interspecific competition on growth rates Signup and view all the answers

How are the Lotka-Volterra competition equations different from the logistic equations in terms of species growth?

Species growth in Lotka-Volterra is affected by the presence of other species Signup and view all the answers

In the Lotka-Volterra competition equations, what does αN2 represent?

Competitive effects of Species 2 on Species 1 Signup and view all the answers

How does βN1 affect Species 2 in the Lotka-Volterra competition equations?

Competitive effects of Species 1 on Species 2 Signup and view all the answers

What happens to the growth of each species in Lotka-Volterra equations as opposed to logistic equations?

Affected by presence and abundance of other species Signup and view all the answers

In the Lotka-Volterra competition model, what do the parameters $\alpha$ and $\beta$ represent?

$\alpha$ represents the intraspecific competition coefficient for species 1, and $\beta$ represents the interspecific competition coefficient between species 1 and species 2. Signup and view all the answers

In the absence of competition (i.e., $\alpha = \beta = 0$), what does the Lotka-Volterra competition model reduce to?

The logistic growth model for each species. Signup and view all the answers

Suppose species 1 has a higher intrinsic growth rate than species 2 ($r_1 > r_2$), but species 2 has a higher carrying capacity ($K_2 > K_1$). What can be inferred about the long-term coexistence of the two species?

It is impossible to determine the long-term coexistence without additional information about the competition coefficients. Signup and view all the answers

In the Lotka-Volterra competition model, what is the condition for the existence of a stable coexistence equilibrium?

$\alpha \beta < 1$ Signup and view all the answers

In the Lotka-Volterra competition equations, what does the term $\alpha N_1^2$ represent?

The intraspecific competition effect of species 1 on itself. Signup and view all the answers

In the context of the realized niche, which of the following statements is true?

The realized niche is often narrower than the fundamental niche due to competitive interactions and other ecological constraints. Signup and view all the answers

What is the primary reason for the difference between the fundamental and realized niches of species?

Competition with other species for similar resources. Signup and view all the answers

According to the example of Galápagos finch species, what factor contributes to the shift in the realized niche of G. fortis on Santa Cruz Island?

The presence of a different finch species, G. scandens, competing for similar food resources. Signup and view all the answers

In the Lotka-Volterra competition model, what does the parameter $\alpha$ represent?

The effect of Species 2 on the growth rate of Species 1. Signup and view all the answers

In the Lotka-Volterra competition model, what does the term $(1 - N_1 + \alpha N_2 / K_1)$ represent for Species 1?

The effect of interspecific competition on the growth rate of Species 1. Signup and view all the answers

If the value of $\beta$ in the Lotka-Volterra competition model is higher, what can be inferred about the effect of Species 1 on Species 2?

The effect of Species 1 on the growth rate of Species 2 is stronger. Signup and view all the answers

In the context of species population dynamics, what does the term 'historical competitive interactions' refer to?

The past competition between species that has shaped their traits and behaviors. Signup and view all the answers

According to the example of Galápagos finch species, what adaptation did G. fortis exhibit on Santa Cruz Island to enhance its competitive advantage?

Developing larger beak sizes to exploit larger seeds. Signup and view all the answers

In the Lotka-Volterra competition model, what happens to the growth rate of Species 1 if the value of $\alpha$ is negative?

The growth rate of Species 1 increases as the population of Species 2 increases. Signup and view all the answers

In the context of the realized niche, what can be inferred about the range of beak sizes observed in G. fortis on Daphne Major?

The range of beak sizes reflects the fundamental niche of G. fortis. Signup and view all the answers