Download Populations III: Harvest Models

A history of whaling
10th Century – records of
whaling
1400-1700 Atlantic Arctic
fishery – targeting the
right whale
1600-1900 the Pacific
fishery
– more right whales
1800-1970s Sperm whale
fishery
Quantity of oil in a sperm whale
made it an attractive target
Innovation: Possible to make
margarine of almost 100 percent
whale oil.
Sperm Whale (Physeter macrocephalus)
1712 – Americans hunt sperm whale
1860 – Norwegians introduce steampowered boats and explosive harpoons
Factory ships and newer technologies
more species, more oceans, more countries
Blue whale
Minke whale
Sei whale
Fin whale
1946
17 nations signed a
license where the
International Whaling
Commission (IWC) set
a maximum catch in the
Antarctic.
1949-1960 – IWC sets annual “fixed” quotas for all whaling
1972 - the United Nations called for a cessation of whaling and
the United States Congress passed an Endangered Species Act
1987 - whale sanctuaries were declared in the 1970s and ’80s,
and a general moratorium on commercial whaling, adopted by
the IWC in 1982, took effect in 1987
Odocoileus virginianus
Clupea harengus
Populations III: Harvest Models
Oncorhynchus tshawytscha
Pinus sylvestris
Review
r – intrinsic or per capita growth rate
dN/dt = r*N – exponential growth
Nt=N0*ert
(We’re keeping it discrete)
1600
N
1200
800
400
Bye bye fuzzy duckling!!
0
0
20
Time
40
Rabbits in Australia – invasive species can grow exponentially at first
Review
N
Logistic growth – S-shaped or sigmoid curve
K – carrying capacity
Modify with “unused” component of K
(K-N)/K = (1-N/K) – used interchangeably
dN/dt = r*N*(1-N/K)
120
100
80
60
40
20
0
Logistic growth
r=0.25
K=100
0
20
40
Time
60
Review
Ceratotherium simum
200
Exponential
N
150
K=100
100
Logistic
50
0
0
20
40
Time
60
Review
Environmental resistance
Exponential
K=100
Logistic
How do we use this information to create harvesting quotas?
Two types of mortality:
Additive – added mortality causes a reduction in survival
any hunting is added mortality
if we want to control a population of invasives
Compensatory – added mortality does not affect survival,
up to a threshold
harvesting/ hunting is mortality “that would have happened
anyway” e.g. starvation, predation, disease
We assume that a “compensatory” decrease in non-harvest
mortality occurs – perhaps due to extra food availability
N
110
100
90
80
70
60
50
40
30
20
10
0
K
Inflection point
K/2
Logistic growth
r=0.25
K=100
0
10
20
30
Time
40
50
60
MSY = Maximum Sustainable Yield
K/2
7
MSY
6
Recuitment
K
5
4
3
2
1
0
0
Logistic growth
r=0.25
K=100
10 20 30 40 50 60 70 80 90 100
Population size N
?
7
K/2
?
K
MSY
h
Recuitment
6
5
4
3
2
1
0
0
Logistic growth
r=0.25
K=100
10 20 30 40 50 60 70 80 90 100
Population size N
OSY – Optimal Sustainable Yield
Problems with setting quotas
Estimating numbers is not easy
hard to obtain reliable MSY
You can’t just stop people that easily
noncompliance is a huge issue
Recruitment
K varies with environment = MSY changes
MSY?
N
K
K
K
Factors that affect K
• Density-independent factors
– Weather (storms, cold, drought)
– Density-independent diseases (DDT poisoning)
• Density-dependent factors
– Food
– Space (territories, denning sites, nest cavities)
– Density-dependent epizootics (rabies, SARS)
Trophic effects on K – remove large fish, remove fish
waste, removes fertilizer, removes smaller fish, up the
food chain, less fish to catch
H=q*E*N
Fixed Effort harvest
Yield = efficiency*Effort*Population
Recuitment or
Harvesting rate, h
E2
7
6
5
E1
EMSY
4
3
E2 > E1 > EMSY
2
1
0
0
10 20 30 40 50 60 70 80 90 100
Population size N
Hindsight always helps – the Allee effect
Low population density is prone to sudden extinction
Fewer mating opportunities; simply too few to be fit enough
Logistic
Allee model
dN/dt
N
Peruvian anchoveta (Engraulis ringens)
•
•
•
•
•
1960-1972 – world’s largest fishery
MSY estimated at 10 million tonnes/year
Expanded fishing fleet plus El Niño events meant collapse
20,000 people relied on it, so politically harmful to close
Repeated collapses – 1973, 1986 – still not recovered.
Peruvian Anchoveta Global capture estimate (tonnes)
source: FAO
14000000
12000000
10000000
8000000
6000000
4000000
2000000
0
1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001
Making a better model
Fish, deer, trees are not all one size or age
– We prefer adult or mature organisms
– Life-history events – reproduction, growth occur at
different times
– Next Lecture: life-tables and age-structure