Logistic Growth

open populations grow when

b + i > d + e (inputs > outputs)

_______ assumes that density dependent factors limit exponential rates of growth (r is not constant)

logistic equation

________ factors include any factors whose effects become stronger as crowding within a population increases

density dependent

population size is limited at the _______ of the envr

carrying capacity

carrying capacity ____ a stable equilibrium around which pop size will stabilize

is

true or false: carrying capacity changes with varying environmental conditions and is rarely constant

true

all natural populations exhibit pop regulation. The relative importance of DD and DI regulations will depend on the _______ of the species and the _____ and _____ of environmental variation

life history strategy, frequency, intensity

what factors reduce inputs relative to outputs

• biotic interactions among organisms (competition, predation)

• abiotic fluctuations in environmental conditions (temp)

density dependent

intensity of reduction is related to the density of individuals

density independent

intensity of reduction is unrelated to the density of individuals

• biased - reduced fitness

• unbiased - random mortality

what factors limit population growth (b, d, r) as population size increases (at higher N)

• intraspecific competition increases (limited food/habitat)

• predator density increases (higher risk of predator)

• parasite density (higher risk of parasitism)

• disease (higher rate of disease transmission)

density dependence may

reduce growth, survival and reproduction of inds in a pop, thereby affecting pop growth through b and d (r ) with increased crowding

logistic model of population growth-primary underlying assumption

factors limiting population growth exert stronger effects on b and d as a population grows (population growth is density dependent)

due to density dependence, we should expect ____ to vary with ___

r (=b-d), N

explain the top arrow to the bottom

• r is highest at low N (no/low competition: b is high, d is low)

• r decreases as N increases (competition increases: b decrease, d increase)

• r is lowest at high N (competition increases: b ~ d)

• when N=K, r=0 (b=d)

carrying capacity

(K), population size that the envr can carry or support

exponential equation

dN/dt=rN

logistic equation

dN/dt = rN (1- N/K)

the logistic model doesn’t represent the ______ dynamics of natural pops, it represents the ______ dynamics of natural pops

quantitative, qualitative

population sizes below K _____ towards K

increase

population size above K ____ towards K

decrease

density dependent factors …

tend to bring populations under control and maintain their size close to K

• caused by biotic factors (competition, predators, parasites, disease)

density independent factors…

tend to reduce populations far below K and initiate periods of population recovery

• caused by abiotic factors (temp, water)

• density independent ex: thrips

explain thrips during the spring, summer and winter

density independence

• spring: ideal for flowering - high resource abundance and mild climate so increased b, decrease d - large N increase

• summer: hot and dry - high d due to extreme heat and low water - large N decrease

• winter: cool and rainy - low b due to cooler temps - stable N

*thrips - population size mirrors what

seasonal changes in weather

the relative importance of D-D and D-I factors will depend on:

intensity and frequency of environmental (abiotic) fluctuations (life history characteristics of the population/species)

explain the graph

• frequent and extreme environmental fluctuations

• r selected

• mechanism of regulation: density independent

explain the graph

• infrequent and mild environmental fluctuations

• k selected

• mechanisms of regulation: density dependent