Sensitivity and elasticity

Question 1

Define Elasticity (equation define)

Answer 1

product of value of matrix element and sensitivity of that element, divided by asymptotic growth rate

Question 2

Elasticity analyses

Answer 2

scale sensitivity to units. Elasticities are proportional sensitivities scaled so that they are dimensionless and directly comparable

Question 3

Right eigenvector ( _ )

Answer 3

w

Question 4

Left eigenvector ( _ )

Answer 4

v

Question 5

define right eigenvector

Answer 5

age or stage class structure, when the stable state is reached. Stabilized proportion of each age class. column vector

Question 6

define left eigenvector

Answer 6

reproductive value or worth of each age/stage class row vector

Question 7

Sensitivity analyses

Answer 7

how small changes in fertility and Probability (transition and staying in same stage) will affect lambda when others are held constent the values indicate the factor by which lambda will change. Sensitivity is represented as a slope, the most sensitive matrix elements produce the largest slope

Question 8

What does sensitivity analysis tell us in terms of management perspective

Answer 8

identify the life history stage that will contribute the most to population growth of a species.

Question 9

how to determine left eigenvector

Answer 9

transpose the matrix, then multiply with matrix algebra the transposed matrix times the number in each age or stage class

Question 10

asymptotic population growth rate

Answer 10

when the growth rate (lambda) has stabilized when multiplying many iterations of the matrix

Question 11

eigenvalue

Answer 11

value of lambda when population has stabilized when the eigenvalue (numbers) is multiplied by a vector of abundences yields same result as matrix multiplied by vector of abundances.

Question 12

Sensitivity (equation)

Answer 12

Sij= (vw)/()

Question 13

Computing sensitivity

Answer 13

1. running the projection model until population reaches stable distribution 2. calculate w (stable stage structure) 3. calculate v (reproductive values) 4. calculate sensitivity equation

Question 14

scalar

Answer 14

single number product of the w and v - need to adjust so v*w will give a single number.

Question 15

Elasticity analysis estimates?

Answer 15

the effect of a proportional change in the vital rates on population growth

Question 16

elasticity equation

Answer 16

eij= (aij*sij)/lambda aij= matrix elements sij= sensitivity of a matrix element

Question 17

Parts of a maxtrix

Diagonal lines?

top row?

Answer 17