Species Interactions

POP AND COM lecture 5

What is a niche (Hutchinson 1957)?

he set of environmental conditions and resources under which a species can survive and reproduce; a multi-dimensional hypervolume.

What is the difference between a fundamental and realised niche?

Fundamental niche = potential range without interactions; Realised niche = actual range occupied due to interactions like competition.

What does niche overlap imply?

Two species use similar resources, increasing potential for competition.

What is niche partitioning?

Behavioral or evolutionary changes that reduce competition between species (e.g., feeding at different heights or times).

What are the five types of species interactions?

• Competition (– –)

• Predation (+ –)

• Mutualism (++ )

• Amensalism (– 0) tall tree shades out ground plant

• Commensalism (+ 0)

What is the Lotka–Volterra competition model used for?

Modeling interspecific competition and predicting outcomes like exclusion or coexistence.

What are isoclines in phase plane analysis?

A: Lines where the growth rate of a species = 0; used to analyze stability and outcomes of species interactions.

predator-prey model

• dX/dt = aX-bXY

• dY/dt = gXY-rY

• X=pey

• Y=predator

• a=prey growth rate

• b=capture rate

• g=predator birth from consuming prey

• r=predator death

predator-prey model assumptions

1. Prey has infinite resources.
   
   

2. Predator depends entirely on prey.
   
   

3. Constant encounter rates.
   
   

• No satiation.
  

Lotka–Volterra Competition Model

Incorporates density dependence and interspecific competition.

• dN1/dt=r1N1(k1-n1-a12N2/k1)

• dN2/dt=r2N2(k2-n2-a21N1/k2)

• a12: effect of species 2 on 1

• a21:effect of 1 on 2

 Equilibrium Solutions:

• N1=K1-a12N2

• N2=K2-a21N1

What is the condition for stable coexistence in Lotka–Volterra?

α_12 * α_21 < 1

What are Holling’s types of functional responses?

• Type I: Linear (filter feeders)

• Type II: Hyperbolic (slows with handling time)

• Type III: Sigmoid (slow at low density, then accelerates)

Functional Responses (Holling, 1959)

Describes how a predator's consumption rate changes with prey density.

What do the parameters and state variables represent in models?

• Parameters: Constants like r, K, α

• State variables: Time-dependent quantities like N1, N2

What are Zero Net Growth Isoclines (ZNGIs)?

Lines representing population states where growth is zero; used in phase plane analysis.

What is Gause’s Competitive Exclusion Principle?

Two species competing for the same resource cannot coexist if ecological factors are constant.

What do Chapters 5 & 6 in Gotelli's Primer of Ecology cover?

• Ch. 5: Competition models, simulations, Gause's principle

• Ch. 6: Predator-prey models, limit cycles, functional responses

what insights does Clarence Lehman add to interaction models?

• Use of interaction matrices

• Phase space and dynamic systems

• Stability via Jacobian analysis

• Community modularity

What are the key ideas from niche and competition theory?

• Niche = conditions for survival

• Competition = resource overlap

• Isoclines & phase planes = model outcomes

• Functional responses = predator behavior

• Stability = depends on intra vs. inter competition