Upcoming Seminars:• EECB seminars – 4:00 Thurs in OSN 102

– Thurs Feb 12: Mark Lindberg (U. A. Fairbanks) “Patterns and rates of dispersal in avian populations: Is scale important?”

Outline1. Introduction to population ecology2. Spatial structure3. Plant interactions and density

dependence4. Age and size structure5. Plant demography6. Population growth models and

parameters7. Life tables8. Survivorship curves

Reading Assignments1. Textbook chapter 4 and 52. Radford et al. 2002. Austral Ecology

27:258-358.3. Supplemental (not required)

• Allcock and Hik 2004. Oecologia 138:231-241.

• Silvertown and Lovett-Doust 1993. Introduction to plant population biology. Blackwell Scientific Publications, London.

Population BiologyPopulation: collection of individuals of

the same species living in the same area

Population structure: spatial, age, size

Population biology tries to explain origin of structure types, how they interact, and how they change with time.

Spatial StructurePatterns of distribution: random,

dispersed, clumped.

Patterns affected by biological and abiotic interactions. Test for randomness mean:variance ratio, Poisson analysis

Spatial StructureWhy does pattern matter?

Spatial StructureWhy does pattern matter?

• Interpret causes of patterns• Stratification• Appropriate sampling regimes

(density, frequency, non-quadrat)• Affects interactions

Plant interactions• Space affects population biology in

two ways:– “neighborhood” – area of genetic or

ecological influence– Density – number of plants per unit area.

Affects resource competition.

• Density influences growth, survival, fitness.

Law of Constant YieldBiomass/unit area increases with density,

then levels off and becomes independent of density.

Y=wmN(1 + aN)-1

Y= Yieldwm=max potential biomass/plant

N=densityA=area necessary to achieve wm

Law of Constant Yield• At high density Y is constant and

proportional to wma-1 and w=Y/N.

• Plant size is inversely proportional to density : w=wm(1+aN)-1

• Generalization: to allow for changing curves at high density (some species DECLINE in yield) replace –1 exponent with “-b”

Competition-Density Effect

• w=wm(1+aN)-b describes variation in weight with density at a given moment in time.

• Parameters vary during growth and with environmental conditions.

• Competition also leads to reduction in N over time (self-thinning)

“-3/2 power law”• Self-thinning: smaller individuals die,

reducing density as plant size and competition increases. Density dependent mortality.w=cN-k and log w = log c – k log N-k = slope of “self thinning line”

(boundary)log c = constant between 3.5 and 5

-k is usually –3/2

• Dense populations reach boundary line before sparse ones

• Slope of w:N constant across very different plant groups

• Controversy about “law” but there is a geometrical explanation (Yoda 1963)

– Plant weight proportional to volume (L3), plant sits on area (L2).

– When plant occupies all available space, ratio of weight to area CANNOT exceed 3:2

Age and Size StructureSize distribution of a given age rarely

normal.Plants usually display highly skewed

frequency distribution ( L shaped curve)

Skewed size distribution• Two causes:

– Growth rate is normally distributed, and faster growing plants change normal size distribution to skewed.

– Larger plants suppress smaller ones (asymmetric competition).

– Self-thinning in even aged stand can return normal size/age distribution in time.

Age and Size Structure• Maturity affected by size• Size affected by environmental

conditions and intraspecific competition

• Age-based models of populations often not appropriate for plants…use stage (or size) based

Modular growth

• Plants have indeterminate growth• Plants grow by adding modules

(roots, stems, leaves, clones)• Genet = one genetic individual (e.g.

aspen grove)• Ramet = clonally produced part of a

plant (may be essentially independent)

DemographyStudy of changes in population size and

structure over time.

Nt+1=Nt + B – D + I – E

Nt+1/Nt = Finite rate of increase = λ

when λ = 1 population is stableWhen λ < 1 population is shrinkingWhen λ> 1 population is growing

Modeling populations: unrestricted growth

• Compare population at time t to population at time t+1 (difference equation)

Nt+1=RNt+Nt or Nt+1=λNt

λ=R+1 and R=geometric rate of increase

• For arbitrary time step: NT=N0λT

• For instantaneous growth (continuous time; differential equation)

dN/dt=rN(t) and N(T)/N(0)=erT

So N(T)=N(0)erT

Modeling populations: unrestricted growth

N

Time

Unrestricted growthWhat sorts of populations exhibit exponential

or geometric growth?1. Unrestricted resources2. No competition or other limitations

Unrestricted growthWhat sorts of populations exhibit exponential

or geometric growth?1. Unrestricted resources2. No competition or other limitations

Invasive species, expanding populationsExponential decline: constant mortality rate > birth

rate

Density dependent growth• Biological factors interact to produce a

negative feedback between N and R.• Examples:

– Resources decrease (are used up)– Available space is filled– Interference (agression etc) may increase– More efficient predation as prey density

increases– Emmigration or dispersal increases– Immigration decreases

Density dependent growth• Can model density dependent growth with

logistic equation:dN/dt=rN((K-N)/N)

K= population at equilibrium carrying capacity

• At K population growth rate is zero

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…

Characteristics of populations

• Ecologists use life tables and fecundity schedules to organize demographic data:

– Age or stage-specific survivorship, birth rates, death rates, reproductive value etc.

– Can be based on cohorts (cohort life table) or age/stage classes (static life table)

– May contain the following parameters:Age/stage, number surviving (Nx), survivorship

(lx=Nx/N1),

mortality (dx=(lx-1-lx)), mortality rate (qx=dx/lx), fecundity (bx= offspring per individual),

reproductive value (Vx = bx+ Σ(lx+I/lx)bx+I)

Survivorship Curves• Plots of number of survivors (log scale)

versus age/stage.• Three basic shapes: different life histories.

Type I

Type II

Type III

SurvivorshipWhat do the shapes of the survivorship curves

mean? Examples?

Type I

Type II

Type III

Importance

ImportanceDemography 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.

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

Next lecture: metapopulations, life history strategies, allocation.