Outline

1. Density dependent population dynamics: logistic equation

2. Cyclic and chaotic populations3. Life history strategies4. K vs r selection (MacArthur)5. C-S-R models (Grime)6. Examples of adaptive life history traits and

strategies

Life table and population ecology resources

1. USGS interactive population model for spectacled eiders http://www.absc.usgs.gov/research/speimod/

2. Sample life table calculations from University of Cincinnati Clermont College: http://biology.clc.uc.edu/courses/bio303/life%20tables.htm/

3. Interactive models for human population http://simon.cs.vt.edu/geosim/IntlPop/

Density dependent growth• As intrinsic rate of increase goes up,

behaviour of model changes:– Carrying capacity: one equilibrium value for N– Stable limit cycles: N oscillates among several

values– As R increases, number of values in cycle

doubles (for 2.1<R<2.57)– Eventually (R>2.57) dynamics are CHAOTIC.

Not random, highly density dependent, but unpredictable.

• Time lags can also create cycles:– Resource availability changes with time and

population size (eg herbivores and food source)dN/dt=rN((K-N(t-T))/K)

– Classic example: lynx and hares…

Alee effect• Can get density dependent effects that

work in the opposite direction, especially for small populations

• For example: reduced reproduction if population is too small can accelerate decline to extinction. This “inverse density dependence” is called an Alee effect.

MetapopulationA “population of populations”. Dynamics driven by dispersal between

patches (colonization) and extinction of sub-populations.

Metapopulation• Usually more dispersal between close

patches, less extinction in large or good-quality patches.

• “Island Biogeography”• Small, poor patches may be “population

sinks” (cannot sustain population on own; are maintained by dispersal from “source” populations.

SummaryDemography affects current distributions,

historical range shifts/spread, gene frequencies, and population structures.

Population dynamics important for commercial species: yield, growth, survival, etc.

Use population models to create management plans for both endangered and invasive species

Herbivory (eg stock production) can affect population parameters of range species: Riginos and Hoffman (2003). Journal of Applied Ecology 40:615-625.

Life History StrategiesPrinciple of allocation: individuals have limited

resources to spend on growth, maintenance and reproduction

Life History Strategy: Pattern of resource allocation

(developed via natural selection) Successful strategy maximizes reproduction,

survival and/or growth in given environment

Assumption: there is a tradeoff between fecundity and survival. “Cost-benefit analysis”

Examples of tradeoffsCurrent and future reproduction. Poa pratensis

number of inflorescences in year one negatively related to number in year two

Colonization and competition. Large numbers of small seeds VS few large seeds.

Examples of tradeoffsCurrent and future reproduction. Poa pratensis

number of inflorescences in year one negatively related to number in year two

Examples of tradeoffsCurrent and future reproduction. Poa pratensis

number of inflorescences in year one negatively related to number in year two

Colonization and competition. Large numbers of small seeds VS few large seeds.

Root and shoot growth.

Examples of tradeoffsCurrent and future reproduction. Poa pratensis

number of inflorescences in year one negatively related to number in year two

Colonization and competition. Large numbers of small seeds VS few large seeds.

Root and shoot growth.Herbivore defense and competitive ability.

Defensive chemicals or structures are costly to make and may reduce growth/reproductive output.

Examples of tradeoffsCurrent and future reproduction. Poa pratensis

number of inflorescences in year one negatively related to number in year two

Colonization and competition. Large numbers of small seeds VS few large seeds.

Root and shoot growth.Herbivore defense and competitive ability.

Defensive chemicals or structures are costly to make and may reduce growth/reproductive output.

Growth and reproduction. Smaller growth increment or foliage production after large seed crop for trees

Allocation to resource acquisition

• Limiting resource model: there is a minimum level of a resource that is necessary for positive net growth

• Can see tradeoff between resource capture mechanisms (eg root vs shoot)

• Resource ratio hypothesis: mechanism for competition and succession.

– Coexistence if two species limited by different resources

– Shift in composition through succession because shift from limited soil resources to limited light

Allocation to survival• Longer lived species delay reproduction• Longer life span means investment in

maintenance and structure• Disturbed, ephemeral, and variable

environments favour short life span• Less disturbed, moderate environments

favour longer life span• Ephemeral- life span less than 6 months• Annual

Life histories

• Ephemeral – life span less than 6 months• Annual – complete life cycle in one year• Biennial – vegetative one year,

reproductive in following year• Perennial – lives for more than two years

Allocation to reproduction• Monocarpy or semelparity: Single period of

reproductive activity followed by death.

• Polycarpy or iteroparity: Multiple episodes of reproduction in lifetime.

• These two strategies have advantages and disadvantages...

Allocation to reproduction• Monocarpy or semelparity: mobilize large

reserves, synchronize across region and swamp predators, minimal investment in structure (annuals).

• Polycarpy or iteroparity: Multiple episodes of reproduction in lifetime, greater overall potential fitness, don’t have “all eggs in one basket”

Classifying life history strategies

• K and r selected species– A continuum between allocation to

reproduction and to survival. – At one end: selection maximizes intrinsic rate

of increase for population. This means seed output, dispersal, etc. This is r-selection. Occurs where mortality is DENSITY INDEPENDENT

– At other end: selection maximizes competitive ability or survival to maintain population near carrying capacity. This is K-selection. Occurs where mortality is DENSITY DEPENDENT

Characteristics of r vs Kr selected species: variable climate, low

competition, short life span, seed bank, seed dispersal, semelparous strategy. Type I survivorship. e.g. Cheatgrass.

K selected species: predictable climate, high competition, constant high population size, strong competition, no seed bank, delayed reproduction, iteroparous strategy. Type III survivorship. e.g. Sugar maple.

R, C, and S strategistsAnother classification for life histories (Grime 1977)

R=Ruderal; colonizing species. Good dispersers, high reproduction. Temporary habitats with high resources. Allocation to reproduction. EG ‘weeds’

C=Competitive species. Good at obtaining resources. Predictable habitats with high resources. Allocation to growth. EG rhizomatous grasses.

S=Stress-tolerant species. Can persist in harsh, low resource environments. Allocation to maintenance. EG lichens.

R, C, and S strategistsSpecies tend to have combinations of these traits.

S

C

R

CS

SR

CSR CR

Lab: life cycle diagrams, matrix models, life tables, and their applications for management

Next lecture: metapopulations, life history strategies, allocation.