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Geometric pop growth
applies to species that reproduce in synchrony during discrete time periods (seasonally). Occurs when pop changes in size by constant proportion from one time period to another.
- Nt+1 = ʎNt (Nt is pop size after t
- discrete time periods)
- Nt = ʎt N0
- Ex: ʎ=2
- N0=100 individs
- What is predicted pop size at time t=20?
- N20 = 2.020(100) = 104,857,600 individs
Exponential pop growth
- occurs when a continuously-reproducing pop
- changes size by a constant proportion at each instant in time.
- dN/dt = rN
- r = exponential pop growth rate (intrinsic rate of increase)
- → the rate of change in pop size at each instant in time.
- (used to predict a pop size in the future, that
- grows continuously)
- Nt = N0ert
- Nt = pop size at time t.
- N0 = initial pop size (t=0)
- e is constant, base of ln(x)
- Geometric results in j-shaped points,
- exponential results in j-shaped curve
- Geometric and exponential growth overlap b/c equations are similar in form, ʎ is replaced by er
How do ʎ and r affect pop size?
- ʎ = 1 or r = 0
- Nt+1= (1)Nt →Nt+1 = Nt
- dN/dt = 0 pop stays the same
- ʎ < 1 or r<0 pop decreases
- ʎ > 1 or r>0 pop increases
Assumptions of geometric/exponential
- Pop is closed (no migration)
- Constant birth and death rates (constant ʎ or r). Implies unlimited resources for growth
Limits to pop growth
Density-independent factors – effects on birth&death rates are independent of pop density. same effects on small and large pops such as variation in weather, catastrophes
- Density-dependent factors - effects of birth, death, and dispersal (emigration) rates change with pop density. Intraspecific competition, predation.
- ↑pop density = ↓birth rates. ↑death rates, ↑
- dispersal ↓pop growth (ʎ or r)
Logistic population growth
- population increasing rapidly, then stabilizes
- at the carrying capacity.
- Carrying capacity (K) – max pop size that can be supported by the env.
- dN/dt = rate of change r = intrinsic
- rate of ↑ K= carrying capacity
- Suppose k = 1,000 When N is small (10), pop is growing at 99% of exponential growth
- When N is close to k? (990). rN(0.01) When N exceeds k. dn/dt < 0. Pop=regulated.
Assumptions of Logistic population
- Closed population
- Constant carrying capacity
- Linear density dependence (growth rate decreases steadily as pop size approaches K)
Nt+1 = ʎNt
Nt = ʎN0
dN/dt = rN
- elephants trample vegetation. Grass/shrubs are harmed, elephants are not. Penicillin and bacteria.
- interaction b/w 2 species in which each is harmed by their shared use of a limiting
- Exploitation competition – individs compete indirectly through their mutual effects on
- availability of shared, limited resources, ex plants depleting water.
- Sp. A (-)↔(-) Sp B
- (-) V (-)
- Limiting resource
- Interference competition – individs compete directly or access to a shared limiting resource.
- Ex hyena and vultures competing over a water buffalo, vine
- growing on tree.
- Sp. A (-)↔(-) Sp B
another species goes in and takes over the resource.
Competitive exclusion principle
2 species that use a limiting resource in the same way cannot coexist indefinitely.
both species harmed, but neither die
using resources in dif ways. Ex MacArthur (1958) warbler birds feed on insects in dif parts of the tree.
types of exploitation
- Predation – kill and consume prey
- Herbivory – consume living plant tissues/fluids
- Parasitism – live in/on host, consume fluid
- Pathogens – cause diseases ex, malaria
- Parasitoids – kill host to complete life cycle (ex phorid fly-ant)
Adaptations to exploitative interactions
- Defensive adaptations – when
- predators/herbivores exert strong selection pressure on prey and plants to evolve.
- Animals – large size, speed, body armor.
- Aposematism (warning coloration). Crypsis (camouflage), mimicry, behaviors.
- Plants – thorns, tough leaves, spines, toxic chemicals, chemicals that attract predators/parasitoids (tobacco and wasps killing caterpillars). Removal of plant tissues stimulates growth.
- Counter-adaptations – when prey and plants evolve to exert selection pressure back on predators and herbivores to evolve.
- Visual/chemical camouflage to sneak up on prey Tolerance or detoxification of chemical defenses (honey badger)
types of mutualsim
- Facultative mutualism – each species
- can live w/o one another (ants and honeydew aphids)
- Obligate mutualism – neither species
- can exist without each other. (leafcutter ants and fungus)
autotroph, primary producers measured in C or biomass
Net primary production: gross primary production – respiration
Factors affecting npp
- Climate/avg temp
- Avg precipitation
- Nitrogen, phosphorous
- (heterotroph) – orgs that obtain energy by
- eating other organisms’ remains
Detritivores – eat dead organic matter
- 1st (primary producers, autotroph),
- 2nd (primary consumers, herbivores),
- 3rd (secondary consumers primary carnivore),
- 4th (tertiary consumers, secondary carnivores)
Why pyramid shaped in terrestrial envs?
- Proportion of biomass at each trophic level not consumed
- Proportion of energy is lost in transfer
Control of NPP
- resources that limlit NPP determine energy flow through an ecosys. Aquatic sys are limited by nutrients.
- Silliman and Bertness(2002) manipulated snail density & found that grazing snails limit production of cordgrass. Removing the top predators (crabs ect) causes growth in snail pop, and decline in plant pop.
Ex of Trophic cascade – changes in abundance or species composition at one trophic level cause series of changes at other trophic level.
energy flow is governed by rates of consumption at highest trophic levels