Effects of Harvest

Exponential Mortality Model

Z

total instantaneous mortality rate

Z=F+M

Z=-ln(S)

S

annual survival rate, proportion surviving in a year

S=e^-Z

A

Annual mortality rate, proportion dying in a year

A=1-e^-Z

A=u+v

F

Instantaneous fishing mortality rate

M

Instantaneous natural mortality rate

Baranov Catch Equation

Ct=F/Z(1-e^-Z)Nt

Allows you to calculate how many fish are caught in a year; multiplies the proportion of fish dying from fishing by both the annual death rate and abundance

u

Exploitation rate, or proportion of population dying from fishing in 1 year

u=FA/Z

v

Proportion of population dying from natural causes in a year

v=MA/Z

Type II Fishery

Fishing and natural mortality continuous throughout the year

Type I Fishery

Fishing occurs in short pulse, natural mortality elsewhere

Catch

Ct=utNt

Surplus Production

The excess biomass generated above what is needed to maintain the population at its current biomass

MSY

Largest catch that can be supported by the population over an indefinite period; maximizes long term yield

rK/4

Bmsy

Biomass where MSY is generated

K/2

Umsy

Rate of exploitation at MSY

r/2

Fmsy

Instantaneous fishing mortality rate that generates MSY