Chapter 6: Population Ecology, mods 18-21

    Modules 18-21 F/R text
    See also chapter 5 in Withgott:
    Evolution, species interaction, communities and species interactions
    Lab: Predator prey phase delay (bunnies and lynxes)

    Module 18-abundance and distribution
    Start with this:
    Click for full-size image
    A crude example of this might be:
    population-HPA students
    biosphere-the world

    some rabbit individual
    some of the rabbit's friends, a population of rabbits
    rabbits and the things they eat and eat them-community
    ecosystem-the plants that support both ends of this process
    biosphere-the planet

    We covered ecosystem energy and matter a few weeks ago, this chapter is about population ecology.
    Population dynamics

    Notation: Population size is represented as N (note not "n"): population size within a defined area at a specific time (brings in migration).
    So, we could say the student population of HPA would be all students here this year, 2022-2023

    Check out the diagrams on population distribution: random, uniform and clumped. Important vis a vis biodiversity
    Structures: age and gender (sex)

    • Density dependent factor: e.g. food or reproductive rate in rats (more rats, lower "fecundity" or birthrate)
    • Something that influences reproduction or survival...
    • Density independent factors: storms, disasters, fires (note density independent: one bambi or 100 bambi all perish in the same fire)
    • Limiting resource: usually food, but could include space, nutrients, etc.
    • Carrying capacity: K (note not "k"): how many individuals an environment can support

    Module 19: growth models
    Imagine you are a happy bacteria, or rabbit, with lots of food, land and no predators. Your population growth curve might look like this:

    This is called exponential growth, or "J shaped growth"
    Note that it has no end, or limiting factor.

    Small r is the growth rate. If you have had physics (yay!) this is usually "k" in some examples, or related to RC decay/growth.
    Learning this equation is VERY useful.
    Note that it depends on two things:
    the starting amount in the population (No)
    and the growth rate (r)
    Here is an example:
    Click for full-size image

    You might also find this link useful:

    Many systems follow J shaped exponential growth until they run out of food or space, then there is overshoot and die-off:

    A more ideal version of this is the S shaped curve, called logistic growth:

    Here is a formula for logistic growth that we'll discuss:

    Click for full-size image
    Don't be intimidated by this formula...
    dN/dt is just delta N over delta t, or the ∆ in number over the ∆ in time, (∆ means change)
    or the rate of population growth (some of you may see this as the slope of the S curve)
    Note that when the ratio N/K is very small or close to zero, the stuff in the parentheses becomes 1, so the formula is rate = rN, or J curved exponential growth.
    Recall: J curved exponential growth only depends on starting population and reproductive rate.

    As N/K nears one (number of critters equals carrying capacity) the term in the parentheses becomes zero, so no growth.
    Note also that if N/K is GREATER than one, the growth rate (slope of the curve) become negative. This is overshoot and die off.


    Logistic growth worksheet

    First: exponential growth:

    Imagine 10 imaginary rabbits (No=10)

    Assume r = 0.5 (50 percent growth rate, or each rabbit makes 0.5 rabbits per year)

    Find the population 2 years later:

    Nt = Noe^rt

    Nt = 10e^0.5*2

    Nt = 27 rabbits

    After 4 years:

    After 10 years:


    Next, use the logistic growth formula, same data, with a carrying capacity (K) of 100:

    Small population: 10 rabbits

    ∆N/∆t = rN(1-N/K)

    = 0.5*10(1-10/100)

    = 5(1-0.1)

    = 5(0.9)

    = 4.5 rabbits per year

    Find the rabbits per year for these populations:

    Medium population: 27 rabbits

    Near K: 74 rabbits

    Above K: 1489 rabbits

    quiz (you may use your worksheet only)

    1. 30 rabbits live on an island with carrying capacity 200. They reproduce at a rate of 0.5 per year. How many rabbits will be on the island after 3 years? (hint: you would do the calculation three times-this is only an estimate though, the true formula would be a bit more complex)
    2. What will be the slope of the growth curve at this point?
    Next: predator/prey phase diagrams
    Check this out:

    Click for full-size image
    Note the phase (timing) relationship between the abundance of the food and the population of the prey, then the predator.
    Predator Prey Lab:
    Download file "predator-prey-simulation12.pdf"
    Worksheet: (uses Numbers application)
    Download file "Population Growth Model.numbers"
    Worksheet: excel version:
    Download file "Population Growth Model.xls"
    Download file "ESI-24-modeling_population_growth.pdf"

    Now we can discuss generalizations of r and K strategists:
    Note: r comes from small r (growth rate) in the growth formula, while K comes from large K in the same formula (carrying capacity):
    Where do you fit in? How about Nemo?

    Birds also fall into type II (no pun intended), as they randomly crash into stuff...
    There is a fourth type: deer. How would you imagine this curve?
    Another reason why genocides are so damaging to cultures: If an oral tradition (e.g. Hawaiians) are decimated by smallpox for example, it is the very old (the holders of the legends and history) and the very young (those who have time to listen, not work, and will then grow up and tell their kids) that are gone. This is a sort of cultural bottleneck...

    Module 20: Community ecology
    Competitive exclusion principle: two species competing for the same resources cannot co-exist, leads to...
    Resource partitioning: time, space, type of food (one species picks one, the other survives)
    Predation: predator and prey, one lives, the other dies
    Mutualism: both benefit
    Commensalism: one benefits, no harm to the other
    Parasitism: one benefits, harm to other
    quizlet review

    keystone species vs. indicator species

    Keystone species-many others depend on it, removal has an impact much greater than their relative population

    e.g. beavers: create habitat for others (dams), so they are also "keystone engineers", only they don't wear funny hats.

    Here's what a keystone looks like:

    In architecture, if you remove the keystone, the arch collapses. Cool term, right?

    This is different from a capstone (seniors might like this): a capstone is what you put on top of a finished structure

    Another example: "keystone predators" e.g. sea stars, which eat mussels, clearing space on rocks for other species

    Indicator species-signal health of a system, like some fish or worms signify water quality, also known as "bioindicators"

    Succession: one species takes over another in time

    Module 21: Community Succession

    Primary succession: From bare rock, no soil: (e.g. lichen)

    These hold moisture and some sort of matrix (e.g. soil) so that others can then grow

    Click for full-size image
    You might imagine driving from the Kohala coast up to Waimea, seeing bare lava along the coast, then fountain grass, then small bushes, then trees along the stream, then larger trees away from the stream.
    Water is the key to life, so anything that can trap and hold water (e.g. soil) can support life.

    Secondary succession: from disturbed area with soil (e.g. after a fire)-there is soil, but no plants, growth here might be quicker than primary sucession.

    Pioneer species: arrives first, sets up reliable system of water and matrix

    Climax community: stable, well evolved ecosystem, e.g. old growth forest, able to survive disasters (e.g. fire)

    Aquatic succession: from stream (flowing water) to pond (less flow) to shallow pond (even less flow) to marsh (mostly mud)

    Island biogeography (like here in Waimea): habitat size AND distance from others influences diversity (e.g. birds)

    This was Darwin's whole gig, also some folks off the coast of Chile, often with birds involved.

    Check out an alternate presentation of these in the Withgott text, with a special section about our island:


    Frog book chapter 5:

    Click for full-size image

    1. What three things in order are necessary for evolution to succeed?
    2. What are the characteristics of an r specific species. Give an example.
    3. What are the characteristics of a K specific species. Give an example as well.
    4. The population of wolves may rise and fall along with rabbits, but not at the same time. Explain why.
    Download file "withgott 7e ch.3 evolution.pdf"
    Download file "withgott 7e ch.4 species interactions.pdf"


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You should be able to do the following after logging in with your account: To create a new page, click the ...Falseadmin2020-08-19T15:43:59+00:00adminadmin2013-02-05 02:24:03+00:002013-02-05 02:24:03updated4Added tag - hotadminadmin2013-02-05 02:24:02+00:002013-02-05 02:24:02addTag3adminadmin2013-02-05 02:05:35+00:002013-02-05 02:05:35updated2First createdadminadmin2013-02-05 02:03:35+00:002013-02-05 02:03:35created1wiki2013-02-05T02:24:03+00:00groups/apenvironmentalscience/wiki/394a8FalseEnergy notes/groups/apenvironmentalscience/wiki/394a8/Energy_notes.htmladmin4 updatesEnergy notes Week of 2.4.13: energy wrap-up e2 video: coal vs. nuclear in class AP exams: FRQ 2002.1 2004.2 2006.1 2007.2 2008.1 ...Falseadmin2013-02-05T02:24:03+00:00adminadmin2013-02-05 02:23:20+00:002013-02-05 02:23:20updated6Added tag - hotadminadmin2013-02-05 02:23:18+00:002013-02-05 02:23:18addTag5adminadmin2013-02-05 02:23:12+00:002013-02-05 02:23:12updated4adminadmin2013-02-05 02:21:48+00:002013-02-05 02:21:48updated3adminadmin2013-02-05 02:20:26+00:002013-02-05 02:20:26updated2First createdadminadmin2013-02-05 02:06:00+00:002013-02-05 02:06:00created1wiki2013-02-05T02:23:20+00:00groups/apenvironmentalscience/wiki/c360bFalseFeb-May plan/groups/apenvironmentalscience/wiki/c360b/FebMay_plan.htmladmin6 updatesFeb-May plan 1. conclusion of energy chapters (see previous wiki) 2. GCC AP questions FRQ: 2006.2 2005.3 2005.4 2007.3 ...Falseadmin2013-02-05T02:23:20+00:00adminadmin2012-03-07 05:53:55+00:002012-03-07 05:53:55updated14adminadmin2012-03-07 05:43:38+00:002012-03-07 05:43:38updated13adminadmin2012-03-07 05:41:35+00:002012-03-07 05:41:35updated12adminadmin2012-03-07 05:38:57+00:002012-03-07 05:38:57updated11Added tag - hotadminadmin2012-03-07 05:38:55+00:002012-03-07 05:38:55addTag10adminadmin2012-03-07 05:36:47+00:002012-03-07 05:36:47updated9adminadmin2012-03-07 05:22:26+00:002012-03-07 05:22:26updated8adminadmin2012-03-07 05:20:01+00:002012-03-07 05:20:01updated7adminadmin2012-03-07 05:18:58+00:002012-03-07 05:18:58updated6adminadmin2012-03-07 04:58:55+00:002012-03-07 04:58:55updated5adminadmin2012-03-07 04:57:33+00:002012-03-07 04:57:33updated4adminadmin2012-03-07 04:56:53+00:002012-03-07 04:56:53updated3adminadmin2012-03-07 04:54:20+00:002012-03-07 04:54:20updated2First createdadminadmin2012-03-07 04:53:33+00:002012-03-07 04:53:33created1weblog2012-03-07T05:53:55+00:00groups/apenvironmentalscience/weblog/de030FalseGreen Apple/groups/apenvironmentalscience/weblog/de030/Green_Apple.htmladmin14 updatesGreen Apple Team, Please watch this video about NYC: Trailer: http://www.pbs.org/e2/episodes/101_the_green_apple_trailer.html On the server: http://physics.hpa...Falseadmin2012-03-07T05:53:55+00:00adminadmin2011-09-13 19:08:24+00:002011-09-13 19:08:24updated4Added tag - hotadminadmin2011-09-13 19:08:22+00:002011-09-13 19:08:22addTag3adminadmin2011-09-13 19:08:10+00:002011-09-13 19:08:10updated2First createdadminadmin2011-09-13 19:04:30+00:002011-09-13 19:04:30created1weblog2011-09-13T19:08:24+00:00groups/apenvironmentalscience/weblog/4ecddFalseQuestions for Wednesday, wiki adds/groups/apenvironmentalscience/weblog/4ecdd/Questions_for_Wednesday_wiki_adds.htmladmin4 updatesQuestions for Wednesday, wiki adds Team, I'd like to try something for class tomorrow: each of you to create a question from chapter 3, and email it to me by this evening (Tuesday). 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