Chapter 17 Predation + Herbivory
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Transcript of Chapter 17 Predation + Herbivory
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This WEEK:Lab: last 1/2 of manuscript due Lab VII Life Table for Human Pop Bring calculator! Will complete Homework 8 in lab
Next WEEK: Homework 9 = Pop. Growth Problems Start early!
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Chapter 17 Predation + Herbivory
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Objectives• Review growth in unlimited environment• Geometric growth (seasonal reproduction)• Exponential growth (continuous reprod.)• Population Problems• Growth in limiting environment• Logistic model dN/dt = rN (K - N)/ K• Density-dependent birth and death rates• Assumptions of model• Reality of models
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Ch 14: Population Growth + Regulation dN/dt = rN dN/dt = rN(K-N)/K
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• Geometric growth:• Individuals added at one time of year (seasonal reproduction)
• Exponential growth: • individuals added to population continuously (overlapping generations)
• Both assume no age-specific birth /death rates
Two models of population growth with unlimited resources :
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Geometric growth:
N
N0
> 1 and g > 0
= 1 and g = 0
< 1 and g < 0
time Growth over 1 time unit:
Nt+1 = Nt
Growth over many time units:
Nt = t N0
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exponential growth:dN/dt = rN
rate of contribution numberchange of each of in = individual X
individualspopulation to population in thesize growth
population
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dN / dt = r N
• r = difference between per capita birth (b) and per capita death (d) rates
• r = (b - d) = # ind./ind./yr
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Exponential growth:
• Growth over many time units:
Nt = N0 ert
• Doubling time: t2 = ln2/r
r > 0
r < 0
r = 0
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The two models describe the same data
equally well: ln = r
TIME
Exponential
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How does population size change through time?How does age structure change through time?
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How to use a life table to project population size and age structure one time unit later.
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Through time• population size increases fluctuates, then becomes constant
• stable age distribution reached
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With a stable age distribution,
• Each age class grows (or declines) at same rate ().
• Population growth rate () stabilizes.
• Assumes survival and fecundity = constant.
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*** What is a stable age distribution for a population and under what conditions is it reached?
• SAD = pop in which the proportions of individuals in the age classes remain constant through time
• Population can achieve a SAD only if its age-specific schedule of survival and fecundity rates remains constant through time.
• Any change in these will alter the SAD and population growth rate
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Populations have the potential to increase rapidly…until balanced by extrinsic factors.
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Population growth rate =
Intrinsic Population Reduction in
growth X size X growth rate
rate at due to crowding
N close
to 0
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Population growth predicted by the logistic model.
K = carryingcapacity
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Assumptions of the exponential model
• 1. No resource limits• 2. Population changes as proportion of current
population size (∆ per capita)• ∆ x # individuals -->∆ in population;• 3. Constant rate of ∆; constant birth and death
rates• 4. All individuals are the same (no age or size structure)
1,2,3 are violated when resources become limited.
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Population growth rates become lower aspopulation size increases.• Assumption of constant birth and death rates is
violated.• Birth and/or death rates must change as pop. size changes.
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Population equilibrium is reached when birth rate= death rate. Those rates can change with density (= density-dependent).
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Density-dependent factors lower survival.
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Reproductive variables affected by habitat quality (K is lowered).
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Reproductive variables are density-dependent.
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r (intrinsic rate of increase) decreases as a linear function of N.• Population growth is density-dependent.
rm
r
r0
N K
slope = rm/K
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• Describes a population that experiences negative density-dependence.• Population size stabilizes at K, carrying capacity • dN/dt = rmN(K-N)/K,• dN/dt = rmN(1-N/K) • where rm = maximum rate of increase w/o resource limitation
= ‘intrinsic rate of increase’ K = carrying capacity • (K-N)/K = environmental break (resistance) = proportion of unused resources
Logistic equation
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Logistic (sigmoid) growth occurs when the population reaches a resource limit.• Inflection point at K/2 separates
accelerating and decelerating phases of population growth; point of most rapid growth
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Logistic curve incorporates influences of decreasing per capita growth rate and increasing population size.
Specific
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Assumptions of logistic model:
• Population growth is proportional to the remaining resources (linear response)
• All individuals can be represented by an average (no change in age structure)
• Continuous resource renewal (constant E)• Instantaneous responses to crowding No time lags.• K and r are specific to particular organisms
in a particular environment.
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Logistic equation assumes:• Instantaneous feedback of K onto N• If time lags in response --> fluctuation of N
around K• Longer lags---> more fluctuation; may crash.
N
K
time
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Models with density-dependence:• Built-in time delay ---> can’t continually adjust• Patterns of oscillations depend on value of r (=b-d)
>>2 = chaos
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Density-dependent factors drive populations toward equilibrium (stable population size),
• BUT
• they also fluctuate around equilibrium due to:
• changes in environmental conditions
• chance
• intrinsic dynamics of population
responses
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What controls population size?
time
time
time
N
density-dependent
chance
density-independent
K
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How well do populations fit the logistic growth model?
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Population dynamics reflect a complex interaction of biotic and abiotic influences, and are rarely stable.
Review Ch 15: Temporal and Spatial Dynamics of Populations
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What is K, the carrying capacity of the planet?
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Ecological footprints of some nations already exceed available ecological capacity.
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Objectives• Review growth in unlimited environment• Geometric growth (seasonal reproduction)• Exponential growth (continuous reprod.)• Population Problems• Growth in limiting environment• Logistic model dN/dt = rN (K - N)/ K• Density-dependent birth and death rates• Assumptions of model• Reality of models
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Vocabulary
Chapter 14 Population Growth and Regulation demography exponential growth* geometric growth per capita age structures* stable age distribution life tables fecundity survival survivorship cohort life table static life table* intrinsic rate of increase* net reproductive rate generation time doubling time carrying capacity (K) logistic equation* inflection point density-dependent factors density-independent factors self-thinning curve -3/2 power law r max* arithmetic* geometric* survivorship curves* doubling time model assumptions time lag size hierarchy Leslie matrix projection matrix transition probabilities life cycle figure life expectancy little r lambda (