Lecture 2 DD growth

Question 1

Assuptions of the D-D B-D balance Model

Answer 1

• Population is geographically closed
• Birth and death rates are constant

→Across individuals (age, sex, etc)

→Across space

Question 2

What does “density-Dependence” mean?

Answer 2

• Primery population parmeters change as pupulation size changes
• Results in a change in pupulation grwth rate

→”Realized rate” < biotic potential (r_max)

• Recognize that resource limiataion should alter rates sch that numbers are related to resource (ie K)
• Note that density-dependeace is a result of an unspecified machanis (ie and abservatino) it is not the mechanism that reults in requlation near K

Question 3

Logistic Growth

Answer 3

• Incorporates the concept of carrying capacity
• The Verhelst- pearl equaion

→dN/dt =Nr_m (1-N/K)

-Establishes realized rate o growth as reduced by “environmental resistance”

→r_realized= r_m (1-N/K)

Question 4

The Ricker Modle

Answer 4

• A discrete-time form of the logistic mo
• Used in many fisheries and wildlife applications
• Verhult-Pearl N_t = K/1 +(K-N₀/N₀) e^rt
• N_t= N₀ e^rm (1-N/K)t

Question 5

Linear Density - Dependence

Answer 5

• Rearranging r_realized= -r_m(1-N/K)
• Gives us r_realized= r_m/KN+r_max
• The equation of a line the “standard” logistic modle assumes linear density-dependence

Question 6

Non-linear Density-Dependence

Answer 6

• Can be incorperated by the Theats Logistic model r=r_m(1-(N/K)^θ
• What is does θ>1 indicate?

→Density has little influence on rate until pupilation nears K

→Weak density-dependence

Question 7

Time-lagged Density-Dependence

Answer 7

-Simplu change the N in the realized rate of growth to a value at an earlier time step

r= r_m (1-(N_t-τ/K)θ)

Question 8

The Allee Effect

Answer 8

• Deals with positive density-dependence in overal per capita rate of growth at low population size
• Population size below which rate of growth is 0 is the minimum MVP

Question 9

Key Points For population assessment and management with density-dependence

Answer 9

• Logistic growth modles recognize that growth rate changes with population size
• Density-dependence has multiple forms created by a variety of ecological mechanisms that create the dependence

Question 10

Verhulst-Pearl

Answer 10

dN/dt=N_m(1-N/K)

Question 11

Ricker

Answer 11

N_t=N₀e^rm(1-N/K)t

Question 12

Theta Logistic

Answer 12

r=r_m(1-(N/K)^θ