Department

Biology

Course Code

BIO120H1

Professor

Ingrid L.Stefanovic

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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