Population-Dynamics

Population dynamics = study of births, deaths, and the movement of organisms

• Critical to:
  • Characterization of populations
  • Prediction (spatial and temporal)
  • Management

Size of a population at any given time is determined by

• Natality (births = B)
• Mortality (Deaths = D)
• Immigration (I)
• Emigration (E)

$Population Change = B - D + I - E$

$N_{t+1} = N_t + (\Delta N)$

Rate of change: Change = rate (deaths per number of individuals, births per female) growth rate (r) = birth rate (b) - death rate (d) + immigration rate (i) - emmigration rate (e) $r = (b-d+i-e)$

$\dfrac{dN}{dt} = rN$

Logistic growth: Pop'ns cannot grow at an exponential rate indefinitely due to food/space limitations, or the action of natural enemies

$\dfrac{dN}{dt}=rN \dfrac{K-N}{K}$

• K is carrying capacity; the threshold at which population growth rate (r) is zero, negative above (i.e., the maximum sustainable population)
• As the number of individuals (N) in the pop'n increases, b, d, i, and e changes due to resource limitation, predation, etc.

Factors affecting forest insect population size

Mortality factors

• climate and weather
• Food quantity/quality'Host susceptibility, habitat suitability
• Predation, parasitism, disease
• Intraspecific competition
• Interspecific competition
• Genetic defects

Density-independent factors Definition: the proportionate effect on population processes (b, d, i ,e) is not related to population density.

common density-independent factors:

• Site characteristics
  • Elevation, slope, aspect
• Weather
  • Wind, temperature, precipitation
• Biotic factos
  • Browsing, root trampling/compaction, harvesting, etc.

Because the impact of d-i factors on populations is unrelated to population size, the net effect is often dramatic population fluctuations

Density-independent effects: example 1

• Early frosts in 2002, 2005, and 2007 caused high mortality to a spruce budworm population

Density-dependent factors

Definition: the proportionate effect on population processes (b,d,i,e) is related to population density

common density-dependent factors:

• Competition
  • Interference vs. exploitation
    • Interference = direct competitive interactions
    • Exploitation = indrect interactions, e.g. preemptive use of a resource
  • Effects sometimes non-lethal (i.e. delayed development, reduced fecundity)
• Predation and parasitism
  • Numerical response
    • Predator/parasite population increases when prey/host abundant

Density-deendent effects: role in pop'n dynamics

• Only poissible through

The curse of small populations

Normally birth rate (b) increases as population decreases; in very small populations, however, the birth rate may decline due primarily to difficulties in mate location (or inbreeding): the Allee effect

• implications to endangered species, invasives
  • A threshold population density is required for a species to persist

Population eruptions

eruptive species are characterized by distinct population phases -- endemic (sub outbreak) where negative feedbacks predominate and epidemic (outbreak) where positive feedbacks facilitate rapid population growth/spread until negative feedbacks reassert themselves

• Mountain pine beetle as an example