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Lecture 5

Lecture 5 & 6

5 Pages
137 Views

Department
Biology
Course Code
BIO120H1
Professor
Ingrid L.Stefanovic

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Lecture 4 & 5 22:09
Models of Population Ecology
Population ecology was developed by zoologists
More ambiguity about plant individuals
Plants:
Aspen: one seed produces many identical, connected stems
Larkspur: many unique seeds; produce many unique plants
Dandelion: no sex; many identical seeds produce many identical, unconnected
plants.
Hemi-epiphyte: plants that start life as an epiphyte, seed grows but as it gets bigger
the roots descend to the ground.
Strangler Fig: multiple different seedlings fuse together to make on tree with
several genotypes
Mathematical Models:
Continuous versus discrete generations (= differential equations vs. difference
equations)
Density-dependent vs. density independent models
Models with or without age-structure
The goal of most population models:
Project the trajectory of population growth through time; i.e., N as a function of t
How many individuals are in the population now? N sub t
Time advances one step t t + 1
When using differential equations, time steps are infinitesimally small: use concept
of limits and calculus; growth is smooth; best suited for species with continuous
reproduction.
When using difference equations, time steps are discrete units (days, years, etc): use
iterated recursion equations; growth is stepwise.
Assume no immigration or emigration
Treat birth and death as per-capita rates that are fixed constants
Then, population changes by a constant factor each time step: N sub t+1=λN sub t
www.notesolution.com
λ= factor by which population changes over one time unit (net productive rate)
This is geometric growth
Alternative version with continuous line
Instantaneous per-capita rates of birth and death fixed (b and d)
Instantaneous, per-capita rate of population change = b-d=r
Solving the 2 simplest models of unlimited growth:
Discrete time: N sub t+1 = λN sub t
Solve for N vs. t:
N sub t = N sub 0 λ to the power t
Geometric growth (bumpy) if λ > 1
Continuous time: dN/dt = r N
Solve for N vs. t
N sub t = N sub 0
Exponential growth
No species has ever grown or shrunk exponentially for a long period of time.
Some factors must tend to keep populations from exploding or going extinct
Two kinds of factors may be acting:
Density-dependent (growth depends on N)
Density-independent
Allee effects: social benefits such as mate finding, group living, group defense
Populations may fluctuate between carrying capacity K and some lower limit
Dropping below the lower limit goes to extinction
Very important in conservation
Age Structured Population Growth: see lecture slides for terminology
Fecundity Schedules: age classes denoted by subscript x
B sub x = # daughters born to female of age x during the interval x to x + 1
Shape of b sub x curve characteristic of species
Reproductive period usually preceded by resource-accumulation phase
Fecundity-survivorship tradeoffs?
www.notesolution.com

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Description
Lecture 4 & 5 22:09 Models of Population Ecology Population ecology was developed by zoologists More ambiguity about plant individuals Plants: Aspen: one seed produces many identical, connected stems Larkspur: many unique seeds; produce many unique plants Dandelion: no sex; many identical seeds produce many identical, unconnected plants. Hemi-epiphyte: plants that start life as an epiphyte, seed grows but as it gets bigger the roots descend to the ground. Strangler Fig: multiple different seedlings fuse together to make on tree with several genotypes Mathematical Models: Continuous versus discrete generations (= differential equations vs. difference equations) Density-dependent vs. density independent models Models with or without age-structure The goal of most population models: Project the trajectory of population growth through time; i.e., N as a function of t How many individuals are in the population now? N sub t Time advances one step t t + 1 When using differential equations, time steps are infinitesimally small: use concept of limits and calculus; growth is smooth; best suited for species with continuous reproduction. When using difference equations, time steps are discrete units (days, years, etc): use iterated recursion equations; growth is stepwise. Assume no immigration or emigration Treat birth and death as per-capita rates that are fixed constants Then, population changes by a constant factor each time step: N sub t+1=N sub t www.notesolution.com
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