Mathematical Ecology MCQs

\[ \textbf{Difficult MCQs on Mathematical Ecology with Answers} \] \[ \textbf{Q1: In the Lotka-Volterra predator-prey model, which of the following equations represents the prey population growth?} \] \[ \text{(A) } \frac{dN}{dt} = rN – \alpha NP \] \[ \text{(B) } \frac{dP}{dt} = \beta NP – \gamma P \] \[ \text{(C) } \frac{dN}{dt} = rN \] \[ \text{(D) } \frac{dP}{dt} = \alpha NP \] \[ \textbf{Answer: (A) } \frac{dN}{dt} = rN – \alpha NP \] \[ \textbf{Q2: In the context of population modeling, what does the term “carrying capacity” (K) represent?} \] \[ \text{(A) } \text{The maximum rate of growth of a population.} \] \[ \text{(B) } \text{The maximum population size that an environment can support.} \] \[ \text{(C) } \text{The minimum population size needed for survival.} \] \[ \text{(D) } \text{The number of individuals in a population at equilibrium.} \] \[ \textbf{Answer: (B) The maximum population size that an environment can support.} \] \[ \textbf{Q3: In the logistic growth model, the differential equation that describes population growth is:} \] \[ \text{(A) } \frac{dN}{dt} = rN(1 – \frac{N}{K}) \] \[ \text{(B) } \frac{dN}{dt} = rN \] \[ \text{(C) } \frac{dN}{dt} = r(N – K) \] \[ \text{(D) } \frac{dN}{dt} = r(K – N) \] \[ \textbf{Answer: (A) } \frac{dN}{dt} = rN(1 – \frac{N}{K}) \] \[ \textbf{Q4: The predator-prey interaction in the Lotka-Volterra equations is represented by:} \] \[ \text{(A) } \frac{dP}{dt} = \beta NP \] \[ \text{(B) } \frac{dN}{dt} = rN – \alpha NP \] \[ \text{(C) } \frac{dP}{dt} = \alpha NP – \gamma P \] \[ \text{(D) } \frac{dN}{dt} = rN – \beta NP \] \[ \textbf{Answer: (C) } \frac{dP}{dt} = \alpha NP – \gamma P \] \[ \textbf{Q5: Which of the following describes the concept of “competitive exclusion” in ecology?} \] \[ \text{(A) } \text{Two species with similar ecological niches can coexist indefinitely.} \] \[ \text{(B) } \text{One species outcompetes another for resources, leading to the exclusion of the weaker species.} \] \[ \text{(C) } \text{Species that compete for resources must share the resources equally.} \] \[ \text{(D) } \text{The presence of one species enhances the growth of the other species.} \] \[ \textbf{Answer: (B) One species outcompetes another for resources, leading to the exclusion of the weaker species.} \] \[ \textbf{Q6: In the context of predator-prey models, what does the term “functional response” refer to?} \] \[ \text{(A) } \text{The change in predator population due to changes in prey population density.} \] \[ \text{(B) } \text{The change in the availability of prey due to environmental changes.} \] \[ \text{(C) } \text{The relationship between predator and prey densities.} \] \[ \text{(D) } \text{The relationship between predator search rate and prey density.} \] \[ \textbf{Answer: (D) The relationship between predator search rate and prey density.} \] \[ \textbf{Q7: Which of the following is a key assumption of the classic Lotka-Volterra predator-prey model?} \] \[ \text{(A) } \text{The prey population is dependent on both its own density and the predator population.} \] \[ \text{(B) } \text{The predator population can survive without a prey population.} \] \[ \text{(C) } \text{Predators and prey have constant interactions with no time delay.} \] \[ \text{(D) } \text{The predator population decreases as prey population decreases.} \] \[ \textbf{Answer: (C) The predators and prey have constant interactions with no time delay.} \] \[ \textbf{Q8: Which of the following factors can lead to the stabilization of predator-prey oscillations in a system?} \] \[ \text{(A) } \text{Increased birth rate of predators.} \] \[ \text{(B) } \text{Immigration of prey into the system.} \] \[ \text{(C) } \text{Limited resources for prey and predators.} \] \[ \text{(D) } \text{Constant rate of predation with no feedback loops.} \] \[ \textbf{Answer: (C) Limited resources for prey and predators.} \] \[ \textbf{Q9: What is the main purpose of matrix population models in mathematical ecology?} \] \[ \text{(A) } \text{To predict the growth rate of a single species.} \] \[ \text{(B) } \text{To model the interactions between different species in an ecosystem.} \] \[ \text{(C) } \text{To predict the population size over time for multiple age classes.} \] \[ \text{(D) } \text{To represent the migration patterns of species.} \] \[ \textbf{Answer: (C) To predict the population size over time for multiple age classes.} \] \[ \textbf{Q10: In the theory of metapopulations, what is the key factor influencing the persistence of a species in a fragmented habitat?} \] \[ \text{(A) } \text{The size of the habitat fragments.} \] \[ \text{(B) } \text{The isolation of the habitat patches.} \] \[ \text{(C) } \text{The migration rate between patches.} \] \[ \text{(D) } \text{The stability of the environment.} \] \[ \textbf{Answer: (C) The migration rate between patches.} \]