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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 continuouslyreproducing 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 jshaped points,
 exponential results in jshaped curve
 Geometric and exponential growth overlap b/c equations are similar in form, ʎ is replaced by er

Geometric/Exponential
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
growth
 Pop is closed (no migration)
 Constant birth and death rates (constant ʎ or r). Implies unlimited resources for growth

Limits to pop growth
Densityindependent factors – effects on birth&death rates are independent of pop density. same effects on small and large pops such as variation in weather, catastrophes
 Densitydependent 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
growth
 Closed population
 Constant carrying capacity
 Linear density dependence (growth rate decreases steadily as pop size approaches K)

Nt+1 = ʎNt
Nt = ʎN0
geometric

dN/dt = rN
Nt= N0ert
Exponential


/0
 amensalism
 elephants trample vegetation. Grass/shrubs are harmed, elephants are not. Penicillin and bacteria.




Interspecific competition
 interaction b/w 2 species in which each is harmed by their shared use of a limiting
 resource.

Types
of competition
 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
 V
 resource

Dominancediscovery tradeoff
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.

competitive coexistence
both species harmed, but neither die

Resource partitioning
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 flyant)

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.
 Counteradaptations – 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)

Producer
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

Consumer
 (heterotroph) – orgs that obtain energy by
 eating other organisms’ remains
Detritivores – eat dead organic matter

Trophic levels
 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
Bottomup control
 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.

Topdown control
energy flow is governed by rates of consumption at highest trophic levels

