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 Number of N t = λ N t − 1 individuals Time
Density and Growth Density with independent discrete growth N t = λ N t − 1 Independent continuous growth dN dt = rN
Density and Growth Density with independent discrete growth N t = λ N t − 1 Independent continuous growth dN dt = rN Density-dependent continuous growth 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 Carrying capacity K 100 80 60 Population size 40 20 20 40 60 80 100 Time
Exploitation
Species Comments Bison hunted almost to extinction Passenger pigeon hunted to extinction dye-hardwood tree Pau-Brazil vigorously harvested 1500-1850 (coastal Brazilian forests) ongoing harvest driven by Mahagony 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) 100 Tree diameter Juveniles 75 50 25 0 No harvest Light moderate persistent
Non-target species (Bycatch) “Species” Threat Death 10000/year Albatross long line fisheries (blackfooted albatross) In Mediterreanean sea Sea turtles long line fisheries 20000/year Sea snakes prawn trawlers 120000/y (Australia) skate prawn trawlers 1000/y
Biological theory of exploitation Reproductive rate Mortality rate rate equilibrium Population density
Biological theory of exploitation dN dt = rN (1 − N K ) − Y change of N per time t Yield (Surplus of population) population growth rate N=population size K=Carrying capacity
• 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.
Solving the equation yields this yield curve Yield maximum sustainable yield 0 K 50% Population size
Stability of yield in a constant quota system • Red: yield is higher than maximum sustainable yield: population goes extinct Yield • 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. 0 K 50% Population size
Comparison of different yields N 0 N 0 = 700 = 700 N 0 = 700 r = 0 . 4 r = 0 . 4 r = 0 . 4 K = 1000 K = 1000 = 1000 K Y Y = 100 = 50 Y = 105 Stable at K/ 2 Stable at K/ 2 UNSTABLE = 500 = 853 maximal sustainable yield dN dt = rN (1 − N for this example is 100 K ) − Y (per generation)
Constant effort Yield Effort Y = EN EN = rN (1 − N K ) N = K (1 − E r )
Stability of yield in a constant effort system Yield • 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. 0 K 50% Population size
Effort and Cost Yield • Yield (Ym) is maximized at Em, but gain (the distance between the black and the red curve is not maximal. Ym • Gain is maximized with effort Yb Eb, much less effort but almost Cost same yield as with Em . Yc • Yield (Yc) and cost are the same there is no gain. Gain = Yield-Cost Ec Eb Em Low High Effort
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 Costs of exploitation are shared by many, but benefits of exploitation are accrued by those who exploit (Hardin 1968) • 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. 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
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