Harvesting of Population • Avoid overexploitation • Avoid underexploitation (economic, conservation) • How much? How often?
Jan 15, 2016
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