Carrying Capacity and Logistic Growth (L7)

Question 1

Model

Answer 1

• small system that represents larger system
• used to predict response of larger system to perturbation

Question 2

System

Answer 2

• specified group of processes with clearly defined boundaries

Question 3

Population

Answer 3

• group of organisms of same species in a specific area

Question 4

Habitat

Answer 4

• physical, geographic place where organisms live
• organism specific

Question 5

Accumulation equation

Answer 5

dN/dt = Nin - Nout + (bN - dN)

Accumulation(dN/dt): numbers of organisms added/removed to syster over time (organisms/time)

Birth rate(bN): organisms produced per unit time (organisms/time)

Instantaneous specific birth rate (b): organisms produced per organism per unit time (organisms/organism/time OR time^(-1))

Death rate (dN): organisms that die per unit time (organisms/time)

Specific death rate (d): organisms that die per organism per unit time (organisms/organism/time OR time^(-1))

Net specific growth rate (r = b - d): orgnaisms produced or that died per organism per unit time (organisms/organism/time OR time^(-1))

Question 6

Exponential Growth Model

Answer 6

Assumptions:
1. migration in/out ignored
2. no predation (all death from old age)
3. unlimited resources
4. no toxic accumulation of wastes
5. ideal environmental charactersitics/ no inhibitors
6. no competition

EQUATION SIMPLIFIES TO:
Nt = No e^(rt)

Question 7

Resource-limited Growth

Answer 7

• death rate (dN) increases
• birth rate (bN) decreases
• net specific growth rate (r =b-d) goes to zero
• steady state eventually achieved (dN/dt = rN = 0)

Question 8

Carrying Capacity

Answer 8

• when growth is limited only by resource availability point ay which dN/dt = 0 is K (carrying capacity of habitat for given species)
• K is integer (like N) number of organisms (round up or down)

Question 9

Assumptions of Logistic Growth Model

Answer 9

1. no migration in/out
2. no predation
3. limited but replaceable resources
4. carrying capacity is constant

Question 10

Logistic Growth Model Equation

Answer 10

• b, d, r are functions of resource availability
• dN/dt is function of carrying capacity

Nt = (K No e^rt) / (K - No + No e^rt)