Species interactions

What is a fundamental niche?

The set of conditions allowing species to survive when there are no other species around to interfere with gorwth

What is realised niche?

Only those conditions where species is actually recorded

What are the interactions types between species?

→Competition (--)

→Predation (+-/-+)

→Mutualism (++)

What is the Lokta model for autocatalytic chemical reactions

dx/dt=αx-βxy

What is the Volterra model for fisheries in the adriatic sea

dy/dt=δxy-γy

Competitive Lotka-Volterra model with density dependence

dN₁/dt=r₁N₁(K₁-N₁-α₁₂N₂/K₁)

dN₂/dt=r₂N₂(K₂-N₂-α₂₁N₁/K₂)

Competitive Lotka-Volterra Model Phase planes: N₁=K₁-α₁₂N₂

Competitive Lotka-Volterra Model Phase planes: N₂=K₂-α₂₁N₁

What is the outcome of this phase plot?

Species 1 wins

What is the outcome of this phase plot?

Species 2 wins

What is the outcome of this phase plot?

Unstable equilibrium

What is the outcome of this phase plot?

Stable quilibrium (Coexistence)

Describe the plot of predator-prey Lotka-Volterra model

What are the assumptions for the predator-prey Lotka-Volterra model?

1)Prey population finds ample food at all time

2)Food supply of the predator population depends entirely on the size of the prey population

3)Rate of change of population is proportional to its size

4)Predators have limitless appetite

Functional response equation:

f(R)=aR^h/1+aT_hR^h

a→attack/search rate

h→hill exponent

Th→Handling time

Lotka-Volterra model with functional response:

dN₁/dt=r₁N₁-α₁₂N₁N₂/1+α₁₂T_hN₁

dN₂/dt=α₂₁N₁N₂/1+α₁₂T_hN₁ -d₂N₂

What does each term in this model represent?

dN₁/dt=r₁N₁-α₁₂N₁N₂/1+α₁₂T_hN₁

dN₂/dt=α₂₁N₁N₂/1+α₁₂T_hN₁ -d₂N₂

r₁N₁→Prey growth

α₁₂N₁N₂/1+α₁₂T_hN₁→Prey loss from predation

α₂₁N₁N₂/1+α₁₂T_hN₁→Predatoe growth from consumption

d₂N₂→Predator mortality