Example titles from last semester Coral reef resilience and - - PowerPoint PPT Presentation

Example titles from last semester

Coral reef resilience and susceptibility due to human interference The ripple effect: the consequences of biological control Overfishing: without immediate reform the problems of yesterday will be here to stay Grizzly bear population management and Grizzly bear-human conflict Conservation efforts towards proper medical waste disposal Endangered species protection and HIV research Each essay needs at least 5 citations from the peer-reviewed literature (no websites!). The essay will use these citations to show facts, etc.

Population models revisited

Density and growth rate

Nt = λNt−1

Time Number of individuals

Density and Growth

Density with independent discrete growth Independent continuous growth

Nt = λNt−1 dN dt = rN

Density and Growth

Density with independent discrete growth Independent continuous growth Density-dependent continuous growth

Nt = λNt−1 dN dt = rN dN dt = rN(1 − N K )

Carrying capacity K

Carrying capacity K is the maximum stable population size

dN dt = rN(1 − N K )

Density and carrying capacity

20 40 60 80 100 20 40 60 80 100

Time Population size Carrying capacity K

Exploitation

Species Comments

Bison

hunted almost to extinction

Passenger pigeon

hunted to extinction

Pau-Brazil

dye-hardwood tree

vigorously harvested 1500-1850 (coastal Brazilian forests)

Mahagony

• ngoing harvest driven by

economical and not conservation

biology thinking

Non-timber-forest products

It is commonly thought that forest products other than timber can be harvested in a sustainable manner. But even such moderate harvest that tries to leave the forests intact is disturbing the forests. Y-axis is in percent (tree diameter in percent of the largest class)

25 50 75 100 No harvest Light moderate persistent

Tree diameter Juveniles

Non-target species (Bycatch)

“Species” Threat Death

Albatross long line fisheries 10000/year (blackfooted albatross) Sea turtles long line fisheries In Mediterreanean sea 20000/year Sea snakes prawn trawlers 120000/y (Australia) skate prawn trawlers 1000/y

Biological theory of exploitation

Reproductive rate Mortality rate

Population density rate equilibrium

Biological theory of exploitation

dN dt = rN(1 − N K ) − Y

change of N per time t population growth rate N=population size K=Carrying capacity Yield (Surplus of population)

• Yield is the population surplus that can be

removed sustainably.

• The logistic growth function can be solved

for Y and so we can get the surplus for known K and r.

K 50% Population size Yield

maximum sustainable yield

Solving the equation yields this yield curve

Stability of yield in a constant quota system

• Red: yield is higher than maximum

sustainable yield: population goes extinct

• Yellow: maximum sustainable yield:

unstable equilibrium, when actual population is smaller than the 50% population will go extinct, if population is bigger than the 50% then it will approach 50%.

• Green: two equilibria, only the upper (to

the right) is stable and desirable. Harvest close to the carrying capacity can be sustainable.

K 50% Population size Yield

dN dt = rN(1 − N K ) − Y

N0 = 700 r = 0.4 K = 1000 Y = 100 Stable at K/2 = 500 N0 = 700 r = 0.4 K = 1000 Y = 50 Stable at K/2 = 853 N0 = 700 r = 0.4 K = 1000 Y = 105 UNSTABLE

maximal sustainable yield for this example is 100 (per generation)

Comparison of different yields

Constant effort

Y = EN EN = rN(1 − N K ) N = K(1 − E r )

Effort Yield

Stability of yield in a constant effort system

• Red: very high effort, unstable
• Yellow: maximum sustainable yield with

medium effort, stable

• Green: low effort [right], high effort [left].

both are stable but low effort is preferrable with same yield, but population needs to be near carrying capacity.

K 50% Population size Yield

Effort and Cost

• Yield (Ym) is maximized at

Em, but gain (the distance between the black and the red curve is not maximal.

• Gain is maximized with effort

Eb, much less effort but almost same yield as with Em .

• Yield (Yc) and cost are the

same there is no gain.

High Low Effort Yield Cost Ec Eb Em Yc Yb Ym Gain = Yield-Cost

Tragedy of the commons

• When many share a resource, the resource is at strong risk

to get depleted (= species goes extinct) because the economical strategy is to get more than the others (=maximize gain). Of course this strategy does not work for conservation strategies. With protected or partition resources typically they are not depleted in the same manner.

• We see this problem in hunting/fishing but also on grazing on

public land.

Tragedy of the commons

• When many share a resource, the resource is at strong risk

to get depleted (= species goes extinct) because the economical strategy is to get more than the others (=maximize gain). Of course this strategy does not work for conservation strategies. With protected or partition resources typically they are not depleted in the same manner.

• We see this problem in hunting/fishing but also on grazing on

public land. Costs of exploitation are shared by many, but benefits of exploitation are accrued by those who exploit (Hardin 1968)

commons = rights or property owned by a group (NOT private property)

Community owned grazing lands

• 20 farmers, each with 5 cows
• Available grass supports 1000 kg milk/day
• Each cow = 10 kg milk/day, each farmer gets 50 kg milk/day

• One farmer adds a cow, increasing herd to 101
• Average milk production = 9.9 kg/day (1000 kg/day

distributed among 101 cows)

• But, this farmer now has six cows, so his production has

increased! 6 cows * 9.9 kg/day = 59.4 kg/ day

The tragedy of the commons

Costs of exploitation are shared by many, but benefits of exploitation are accrued by those who exploit (Hardin 1968) commons = rights or property owned by a group (NOT private property) a common precious resource (fish in a lake, ...) an individual can increase profit by increasing harvest all carry the same cost, as a results all try to harvest as much as possible (”at least one will be greedy”) the resource will decline