Harvesting of Populations

• Avoid overexploitation• Avoid underexploitation (economic, conservation)

• How much? How often?

Harvesting of Populations

0

500

1000

1500

2000

2500

3000

0 20 40 60 80 100

% harvest

Ad

Po

p, P

up

ae

pro

d,

Na

t M

ort

0

1

2

3

4

5

6

7

8

Lif

es

pa

n (

da

ys

)

0

2000

4000

6000

8000

10000

0 50 100 150 200 250 300 350

AJ Nicholson(1895-1969)

High intraspecificcompetition

Low intraspecificcompetition

Nicholson’s Blowflies

BHT, table 16.6

• harvest reduce competition…

• … thereby increasing fecundity, survivorship and lifespan

• harvest reduce population size

Carrying Capacity

• high yields if populations are below carrying capacity!

Harvesting of Populations

Maximum Sustainable Yield (MSY): fixed quota

BHT, fig 16.11

Low recruitment rate(few individuals)

Low recruitment rate (high competition)

Fixed-quota harvesting

High quota

Low quota

Medium quota

MSY: the highest harvesting rate that the population can match with its own recruitment

Stable

Unstable MSY(risky business!)

Harvesting of Populations

KNK

rNdtdN

Maximum Sustainable Yield (MSY): fixed quota modelThe logistic equation

Pop

ula

tion s

ize (

N)

Intrinsic rate of increase

Carrying capacityK = 1000r = 0.6

Harvesting of Populations

KNK

rNdtdN

Maximum Sustainable Yield (MSY): fixed quota modelThe logistic equation with harvest

Pop

ula

tion s

ize (

N) K = 1000

r = 0.6

– h Harvest quota

Sustainable yield: dN/dt = 0

KNK

rNhKN

rrN2

Harvesting of Populations

Maximum Sustainable Yield (MSY): fixed quota modelThe logistic equation with harvest

Pop

ula

tion s

ize (

N) K = 1000

r = 0.6

– h Harvest quota

Sustainable yield: dN/dt = 0

KNK

rNh

h

N K

KNK

rNdtdN

Max sustainable yield: dh/dN = 0

KN

rrN2

KN

21rKN

2rrdNdh

= 0 Nm =

2K

Nm

• MSY harvested from a population size of K/2 …• … to yield (rK/4) animals per year

hm=150

=500

Harvesting of Populations

Maximum harvesting frequency: at what N?

BHT, fig 16.12

harvest ...

Highest frequency

The logistic equation:

N = K/2

Harvesting of Populations

Maximum Sustainable Yield (MSY): fixed quota

BHT, fig 6.12

extinction!

– h(…)

KNK

rNdtdN

Nm

Fixed-quota: not a very safe management strategy

Population size

Effort (/days)

Efficiency (catch/vessel)

Harvesting of Populations

h(…) = q E N

Maximum Sustainable Yield (MSY): fixed effort

Population size

Effort

Efficiency

Stable MSY

Stable SY

Fixed-effort: a much safer management strategy(requires monitoring of N which can be expensive)

cost

Large net yield

Economy is important!

BHT, fig 16.14a

BHT, fig 16.14b

Harvesting of Populations

h(…) = q E N

Maximum Sustainable Yield (MSY): fixed effort model

Population size

Effort

Efficiency

KNK

rNh(...)KN

rrN2

Finding Em: The logistic equation

KN

rrNqEN2

qKN

rqr

E

2qr

qKN

rqr

E mm

Pop

ula

tion s

ize (

N) K = 1000

r = 0.6

h

N K

Nm

hm=150

=500

Em = 0.3

Harvesting of Populations

Instability of harvested populations: climate

BHT, fig 16.17