Lecture 13 - Population Dynamics, Part 2 10/28
• Population age structure.
o Age structure is important to many ecological presses.
Including vital rates that determine population change.
• Ix : Survivorship function (probability of survival to age x).
• Mx (bx) : Maternity (birth) function (no. of female offspring born to a female of age x).
• Sx : Survivability function (proportion of individuals, age x, surviving to age x+1).
o Mean Generation Time (females age when she has her median daughter)
Approximately 25yrs for humans.
• Managing populations for stable age structures
o When age structure is stable, the proportions of individuals in each age class will remain constant regardless of population change.
Stability develops when environmental conditions are constant.
• Don’t count on this.
Constant environmental conditions are inferred if age specific fecundities and mortalities are constant.
These may be manipulated to produce a stable population.
• Hunting & fishing
o Stable age distribution
λ will be constant
Age distribution will be constant
o Leslie Matrix: Matrix algebra
Used to make prediction of future populations
• Population Viability Analysis
o Identifying threats faced by a species and evaluating the likelihood of future survival.
Oriented towards conservation and management of rare or threatened species.
• To improve their chance of survival.
o Risk of rarity.
Rare species have a measurable probability of extinction due to outside influences.
• Deterministic Extinction: λ < 1, population declines.
o Birth rate < death rate
Poaching rate > birth rate, as an example.
- Spatial dynamics allow systems where birthrates or death rates are out of balance to continue to thrive. Smaller island systems are good testing examples of limitations in species number, biodiversity, and population.
• Stochastic Extinction: rare population with λ ≥ 1
Chance variation processes.
• Demographic – sex ratio of offspring.
• Environmental – weather and food supply.
• Genetic drift / inbreeding
o Extinction Vortex: with each generation, the population cycles downward towards eventual extinction.
• PVA Approach
o Probabilistic approach assessing p(E) extinction.
• PVA Uses
o Planning research and data collection.
o Assessing vulnerability.
o Ranking management options.
• Distribution and spatial structures of populations.
o Population – individuals of a species within an area.
o Due to the “mosaic of environment”, populations are typically made of sub populations.
o The distribution or range of a species is the geographic range occupied.
o Population size is the number of individuals in the total population.
o Populations exhibit spatial structure in the number and spacing of sub populations
o The size and distribution of sub populations vary over time.
• “Fundamental” niche – range of environmental conditions in which an organism persists and therefore equated with resource limitation and competition.
• “Realized” niche – subset of a fundamental niche where an organism is actually found
o Determined by: competitors, predators….
o Often equated with a HABITAT.
o Models of spatial structure.
Metapopulations: patches are similar in quality but vary in size and are separated by unsuitable habitat
Source-sink dynamics: patches vary in quality so that b>d in some and b<d in others.
o Conservation implications of spatial structure
Patch connectivity ensures habitat matrix is suitable for individual dispersal.
Lost connectivity – increases “risk of rarity” and extinction.
Dispersal underlies the “rescue effect” or “lifeboat effect”.