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 steam-powered boats and explosive harpoons Factory ships and newer technologies

more species, more oceans, more countries

Blue whale Sei whale

Minke whale Fin whale

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

1946 17 nations signed a license where the International Whaling Commission (IWC) set a maximum catch in the Antarctic.

Populations III: Harvest ModelsOdocoileus virginianus

Oncorhynchus tshawytscha

Pinus sylvestris

Clupea harengus

Reviewr – intrinsic or per capita growth rate

dN/dt = r*N – exponential growth

Nt=N0*ert

(We’re keeping it discrete)

Bye bye fuzzy duckling!!

Rabbits in Australia – invasive species can grow exponentially at first

ReviewLogistic 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)

Logistic growth r=0.25K=100

Exponential

Logistic

K=100

Review

Ceratotherium simum

Exponential

Logistic

K=100

Review

Environmental resistance

Two types of mortality:

Additive – added mortality causes a reduction in survival any hunting is added mortalityif 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

How do we use this information to create harvesting quotas?

K

K/2

Inflection point

Logistic growth r=0.25K=100

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90 100

Population size N

Rec

uitm

ent

KK/2

MSY

MSY = Maximum Sustainable Yield

Logistic growth r=0.25K=100

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90 100

Population size N

Rec

uitm

ent

KK/2

MSY

Logistic growth r=0.25K=100 OSY – Optimal Sustainable Yield

? ?

h

Problems with setting quotasEstimating numbers is not easy

hard to obtain reliable MSY

You can’t just stop people that easily noncompliance is a huge issue

K varies with environment = MSY changes

N

Rec

ruit

men

t

K K K

MSY?

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

Fixed Effort harvest

0

1

2

3

4

5

6

7

0 10 20 30 40 50 60 70 80 90 100

Population size N

Rec

uit

men

t o

r H

arve

stin

g r

ate,

h

EMSY

E1E2

E2 > E1 > EMSY

H=q*E*NYield = efficiency*Effort*Population

Hindsight always helps – the Allee effectLow population density is prone to sudden extinction Fewer mating opportunities; simply too few to be fit enough

Allee model

N

Logistic

dN/dt

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

0

2000000

4000000

6000000

8000000

10000000

12000000

14000000

1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001

Making a better modelFish, 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