Ecology Exam 2

finite rate of increase equation

λ = N(t+1)/Nt

geometric population growth

• assumes unlimited environment

• deaths included

• discrete generations

exponential population growth

• dN/dt = rN or Nt =N0e^rt

• use when need to know instantaneous pop sizes (for overlapping generations)

relationship between λ and r

r = ln(λ)

r max

per-capita rate of increase for a species under perfect (unlimited) conditions

• determined by life history/biology of an organism

K

equilibrium density of individuals = carrying capacity

logistic growth equation

shows effects of intraspecific competition (within)

density dependent limiting factors

size of effect is proportional to pop density

• competition, disease, predation, parasitism

• more important in favorable environments

• impact larger animals more

density independent limiting factors

size of effect is not related to pop density

• climate/weather, disasters

• impact small organisms more

components of metapopulations

• populations are spatially structured

• group of locally breeding pops

• migration occurs between pops

• pops re-establish after extinctions

• defines dP/dt (fraction of patches occupied)

metapopulation dynamics can increase stability of local populations

patch occupancy dynamics equation

P = fraction of occupied patches

c = colonization rate

e = extinction rate

metapopulation model assumptions

• habitat patches equal in size/isolation

• pops have same behaviors

• all pops contribute equal migrants

• all pops equally likely to be colonized

• migration doesn’t affect local pop dynamics

• local dynamics faster than metapopulation dynamics

demographic stochasticity

allee effect

reaction time lag

• duration of lag or cycle depends on generation time

net reproductive rate R0 and time lag

Ro ≈ 1 and small time lag: results in logistic curve

Ro ≈ 1.5 and small time lag: results in damped oscillations

Ro ≈ 2 and small time lag: results in stable cycle

consequences of fluxuations

overshoot K, damage resource base of population; recovery time (resilience) of biotic resources important

interspecific interactions

reduction of fundamental to realized niche caused by

competition, predation, parasitism

indirect competition

competition for resources

ex. self-thinning in plants

interference competition

allelopathy, territoriality, preemption

allelopathy

chemical interference

affects seed germination and growth of same and different species

preemption

interference

get there first and take up preferred space

competition between equivalent competitors

competition between non equivalent competitors

α12 = effect of species 2 on species 1 = competition coefficient

when multiplied by N2 = total effect of species 2 on species 1

4 possible outcomes of competition

stable equilibrium

• negative feedback

• starting pop size doesn’t matter

• interspecific competition is less than intraspecific competition

• K1/α12 > K2

• K2 / α21 > K1

unstable equilibrium

• positive feedback

• coexistence only when starting pops are the same

• interspecific competition more than intraspecfic

• K1/ α12 < K2

• K2 / α21 < K1

coexistence and α

the less similar the two species are in terms of resource use (lower α) the more likely is coexistence)

lotka-volterra model assumptions

• homogeneous, stable environment

• no immigration or emigration

• instantaneous effects of competition

• competition is only major interaction

3 types of exploitation

parasitism, herbivory, predation

endoparasites advantages/disadvantages

• may be hard to get in

• host system may attack

• once in, may be hard for host to physically remove (advantage)

ectoparasites advantages/disadvantages

• easy access

• avoid host immune system

• easier for host to remove

transmission pathways

active (direct movement towards a host) vs passive

parasitoid

parasite (usually insect) that sterilizes or kills host

effects of parasites on hosts

• death or major fitness reduction

• behavioral manipulation

• minor inconvenience

plant nutrition

• relatively low nutrition (low Kcal/gram, low N)

• lots of tough tissue

• low water content

herbivory in insects

• low conversion rates of food to body mass

• slower rates of development (smaller size as adults, less reproduction)

nutritional defense against herbivory

complex molecules in plants

cellulose, lignin

toxins

• type of plant chemical defense

• often induced by herbivory

• rapid synthesis, mobile

• small molecules, high cost (lots of N)