Lecture 14

Trophic Interactions

Overview

• Trophic interactions involve the relationships between producers, consumers, and decomposers in ecosystems.

• Key aspects include:

  • Types of trophic interactions

  • Resource/prey adaptations (defenses)

  • Consumer/predator adaptations

  • Population limitation and predator-prey cycles

  • Modeling predator-prey cycles (Lotka-Volterra models)

  • Functional and numeric responses

  • Applications of these concepts

Lynx and Hares

• The snowshoe hares are a significant part of the lynx diet, making up approximately 75-80% in certain regions.

• The relationship between lynx and snowshoe hares serves as a practical example for studying predator-prey dynamics.

Population Dynamics of Lynx and Hares

• Predator-prey populations often oscillate cyclically over time, indicative of interdependent population dynamics.

  • Example: The cycles of lynx and hare populations are synchronized and occur roughly every 10 years.

• The population sizes of both species vary significantly over time, with hare populations peaking and subsequently influencing lynx populations:

  • In 1850, lynx populations were around 3, increasing to an estimated 16 by 1925, while hare populations oscillated ranging significantly alongside.

Population Oscillations

• Population oscillations are evident in predator-prey interactions, wherein:

  • The prey population size influences the predator population size and vice versa.

  • The lengths of these cycles are variable, often reduced in smaller organisms.

• The concept originates from Gause's work in the 1930s, which demonstrated predictable oscillations in consumer-resource interactions.

Lotka-Volterra Ecosystem Models

Predator-Prey Dynamics

• Fundamental equations unpinning the model:

  • Prey population change: $\frac{dN}{dt} = rN - cNP$

  • Where:

    • $N$ = population size of prey

    • $r$ = intrinsic per capita growth rate of prey

    • $c$ = capture rate (predation rate) of prey by predators.

  • Predator population change: $\frac{dP}{dt} = acNP - dP$

  • Where:

    • $P$ = population size of predators

    • $a$ = conversion rate of prey to predator growth

    • $d$ = death rate of predators.

Assumptions of the Lotka-Volterra Model

• Assumptions include:

  • The prey population can increase exponentially in the absence of predators.

  • The predator population can only persist when prey is present.

  • Individual predators can consume an infinite number of prey.

  • There are random encounters between predators and prey.

  • No density-dependent factors or “real foraging behavior.”

Equilibrium Isoclines

• Isoclines represent all points for both populations where there is zero growth:

  • For prey: $\frac{r}{c} = P$

  • For predators: $N = \frac{m}{ac}$

• Stability analysis:

  • If $rN = cNP$, then the prey population has zero growth; when prey increases, predators tend to follow and vice versa.

• Phase-plane diagram shows the population trajectory of prey and predator jointly:

  • When both populations are at the equilibrium point, cycles are rare, leading to regular oscillations elsewhere.

Functional and Numeric Responses of Predators

Responses to Prey Abundance

• Numerical Response

  • Change in predator abundance in response to changes in prey abundance, influencing predator populations either through birth rates or immigration/emigration.

Functional Responses

• Relationship between prey density and predator feeding rate.

• Types include:

  • Type I: Linear increase in prey consumption with rising prey densities, often unrealistic due to ignoring handling time.

  • Type II: Consumption plateaus as prey density increases, factoring in handling time and predation limits.

  • Type III: S-shaped response seen in generalist predators where feeding rate increases but plateaus at higher densities due to prey switching and search image formation.

Practical Applications of Consumer-Resource Dynamics

Biocontrol Example: Prickly Pear Cactus in Australia

• Introduction of the prickly pear cactus led to ecological issues, spreading across 20 million hectares.

• Introduction of the Cactoblastis moth in 1925 effectively controlled the cactus but did not eliminate it completely.

  • The impact led to a monument in Queensland commemorating the success of the biological control agent.

Conservation Applications

• These models help predict consequences of population changes in ecological settings, aiding in:

  • Management strategies for wildlife and pest control.

  • Conservation efforts directed towards threatened and endangered species.

Assessment Questions and Applications

• Discussion points encourage consideration of ecological meanings behind model predictions, not just numerical solutions.

• Assignments encourage visual representation of population cycles, predicted responses, and the connection between phase-plane dynamics and real population trajectories.