upcoming seminars: eecb seminars – 4:00 thurs in osn 102
DESCRIPTION
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? ”. Outline. Introduction to population ecology Spatial structure Plant interactions and density dependence - PowerPoint PPT PresentationTRANSCRIPT
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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?”
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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
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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.
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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.
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Spatial StructurePatterns of distribution: random,
dispersed, clumped.
Patterns affected by biological and abiotic interactions. Test for randomness mean:variance ratio, Poisson analysis
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Spatial StructureWhy does pattern matter?
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Spatial StructureWhy does pattern matter?
• Interpret causes of patterns• Stratification• Appropriate sampling regimes
(density, frequency, non-quadrat)• Affects interactions
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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.
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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
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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”
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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)
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“-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
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• 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
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Age and Size StructureSize distribution of a given age rarely
normal.Plants usually display highly skewed
frequency distribution ( L shaped curve)
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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.
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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
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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)
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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
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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
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Modeling populations: unrestricted growth
N
Time
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Unrestricted growthWhat sorts of populations exhibit exponential
or geometric growth?1. Unrestricted resources2. No competition or other limitations
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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
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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
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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
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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.
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• 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…
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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)
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Survivorship Curves• Plots of number of survivors (log scale)
versus age/stage.• Three basic shapes: different life histories.
Type I
Type II
Type III
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SurvivorshipWhat do the shapes of the survivorship curves
mean? Examples?
Type I
Type II
Type III
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Importance
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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.
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Lab: life cycle diagrams, matrix models, life tables, and their applications for management
Next lecture: metapopulations, life history strategies, allocation.