Course overview

• Course information on AtL and at http://lalashan.mcmaster.ca/theobio/3SS/
• Lecture notes for each section will be available on AtL the evening before you need them
• Check AtL frequently for announcements and new information
• Contacts:
  • Marvin Gunderman, course coordinator:
    first contact for any administrative issues
    gundermn@mcmaster.ca; LSB 116; x23556
  • Ben Bolker, professor:
    http://www.math.mcmaster.ca/bolker;
    Hamilton Hall 314 or LSB 336

Expectations of professor

• Start and end on time
• Focus on conceptual understanding
• Make clear what terminology and facts must be learned
• Open to questions
  • in class (within reason)
  • office hours (Thurs 1:30-2:30, or by appointment)
  • AtL forums (for general questions)
  • e-mail, bbolker@mcmaster.ca:
    please include BIO 3SS3 and MacID in title of e-mail

Expectations of students

• Courtesy/rules
  • Don’t talk while other students are talking, or while I am responding to student questions
  • If you must talk at other times, be unobtrusive
  • Don’t connect to the internet in class
  • Give the professor his 50 min
  • Lectures are required
  • Tutorials are required, unless otherwise specified
  • Don’t cheat (see the official course outline; your first assignment is to read it thoroughly)
• Intellectual
  • Wrestle with the material
  • Please do ask questions

Texts

• The primary text for this course is the lecture notes
• Readings will be posted to AtL
• You are required to have an Ecology textbook
• Any 2F03 textbook is OK (Molles; Molles and Cahill; Cain, Bowman and Hacker)

Structure of presentation

• Required material will be clearly outlined in the notes
• Required terminology will be presented in bold
• Class material may also be required; take notes on these in your own words
• I will be using PollEverywhere for class responses
  • Polls will count for extra credit
  • You will need a cell phone with a texting plan; if don’t have one but want the extra credit, e-mail me with an interesting fact or idea related to the missed question(s)
    (e.g. from a scientific paper, from an ecology textbook, or from a reputable scientific web site or blog)
  • Why are you taking this class?
  • What is ecology good for?

Ecology vs. environmentalism, science vs. policy

tree huggers vs. Hummer drivers ecology $\ne$ environmental science $\ne$ environmentalism ecologists (in their professional capacity) should say what will happen, not what you should do … “I do think we should, in fact have a moral obligation, to be involved in public process by actively seeing to it that our scientific evidence is known to all contending parties, and to the public at large via the media. I think we can safely point out the value implications of our results, and point out alternative, potential courses of action. But these should be given impartially to all sides on an issue, and we should stop short of advocating any one course.” (Wagner 1999)

it takes all kinds …

Opinions about advocacy

“Scientists should …” (Lach et al. 2003)

Definitions

What is population ecology? What other kinds of ecology are there? Hierarchical scales: Behavioural, physiological Population Community Ecosystem Taxon-specific: plant, animal, microbial, insect, human, …

When I use a word … it means just what I choose it to mean—neither more nor less

Goals of ecology

Goals Understanding (basic science) Prediction Control/management What population are you interested in? Some practically interesting populations: humans, crops, trees, fish, game, pests, invasive species, endangered species, microbes, infected cells, …

things we care about

Population ecology: questions

• What processes affect organisms’ population sizes?
• How do population sizes respond to these effects?
  • Why are some populations large, and others small?
  • Why are some cyclical and others stable?
  • When can similar species coexist in the same area?

Math and models

Population ecology uses models, and math Math is a critical tool for linking processes to outcomes; it will play a central role in the course We will keep it simple (not necessarily easy) Logic is more important than math (Platt 1964), but math is still important

Hergé (1978)

Malaria

A nasty disease spread by mosquitoes In some places (e.g., the southeastern US), it has been eradicated almost by accident They still have mosquitoes there In other places it persists at high levels despite concerted efforts at elimination What are the risk factors for malaria spread, and what determines when it can be controlled?

US Malaria, 1870

Red squirrels

Red squirrels are rapidly disappearing from England Loss of suitable habitat? Competition (for food) from gray squirrels introduced from North America? Diseases carried by gray squirrels? More than one of the above? Synergy?

squirrels

Gypsy moths

• Introduced to North America from Eurasia
• Dramatic population cycles: can devastate forests at peak population sizes
  • What causes gypsy moth population cycles, and how can these cycles be better controlled?
• FIXME: spruce budworms instead? Animation?

Population dynamics

• Why are there no fish in my favourite mountain lake? S * Not suitable S * Fish never arrived S * Fish thrived for a while and then something happened S * Disease, new predator, environmental catastrophe
• What factors will determine what will happen if I introduce some fish? S * Suitable environment (temperature, oxygen, …) S * Resources (mostly food) S * Competitors S * ``Enemies" – diseases and predators

Example: dandelions

Start with one dandelion; it produces 500 seeds, of which only 1% survive to reproduce. How many dandelions will there be after 3 years? Spreadsheet

Taraxacum officinale

Example: dandelions

Taraxacum officinale

Rabbits

• Imagine we have a population of rabbits
• Baby rabbits become adults after one month
• Each pair of adult rabbits produces one pair of baby rabbits each month
• Rabbits never die
• What happens to this population?
• Spreadsheet
• These are the Fibonacci numbers

Exponential growth

What is a model?

• A model is a set of assumptions that can be used to make predictions
• For example, we make assumptions about rabbit lifespan and reproduction, and then evaluate the consequences of these assumptions

QUESTION HERE??

Models are useful

Models link individual-level actions and population-level effects what is happening at a given instant, and the result over a longer time period

Results of SORTIE model

Models are approximations

The real world is much more complicated than any of our models: The map is not the territory (Korzybski, Bateson (1980), Borges, Carroll) “All models are wrong, but some are useful” (G. Box) … … for making precise quantitative predictions … for combining information from different (physical or temporal) scales When simple models fail, they can help us figure out where to look for what assumptions are wrong, or what additional assumptions are needed

La trahison des images (1929)

Ways to be wrong

• incorrect model: math mistake, or a bug in the program
  (e.g. “the rabbit model leads to linear population growth”)
• in ecology, model assumptions are (almost) never exactly right,
  but they may be close enough (“OK”);
  figuring out if they are OK is hard
• ditto for predictions

A classic example: Hardy-Weinberg equilibrium

In the early 1900s some geneticists thought that dominant alleles would take over a population Hardy (1908) used simple arithmetic (i.e., a mathematical model) to show that (in the absence of everything interesting) they would not - in fact the allele frequencies remain equal Hardy-Weinberg equilibrium

G. H. Hardy: “Nothing I have ever done is of the slightest practical use”

Our examples

• The rabbit and dandelion examples are models
• We didn’t assume exponential growth, we concluded it from our simple assumptions
• If individuals survive and reproduce at a constant rate, we expect populations to grow exponentially
• What can we conclude if the population doesn’t grow exponentially?

Growth and decline

• What is exponential growth?
  • When something grows proportionally to its own size
  • Grows faster and faster as it gets bigger and bigger
• What is exponential decline?
  • When something declines proportionally to its own size
  • Declines slower and slower as it gets smaller and smaller
• Geometric growth is a synonym for exponential growth
• What can we conclude if a population grows slowly?

The zeroth law of population dynamics

• change in population size =
  immigration - emigration + birth - death
• this is really the only immutable rule

The first law of population dynamics

• if per capita birth and death (and immigration/emigration) rates are constant
  • the population-level rate of growth (or decline) is proportional to the population size
  • the population grows (or declines) exponentially
• density-independent growth or decline

Scales of comparison

1 is to 10 as 10 is to …?

• If you said 100, you are thinking multiplicatively
• If you said 19, you are thinking additively

Arithmetic and geometric differences

• If you are thinking additively, the differences between quantities are called arithmetic differences
• If you are thinking multiplicatively, the differences between quantities are called geometric differences
• Regular graphical plots display arithmetic (additive) differences
• Plots that use log-scaled axes display geometric (multiplicative) differences

Provinces of Canada

Provinces of Canada

Provinces of Canada

Examples

What would it look like if we added

• This classroom?
• The territories?
• The planet Earth?
• The planet Jupiter?

Dandelions revisited

Rabbits revisited

Gypsy moth time series

More on gypsy moth data

Different scales

• The log scale and linear scale provide different ways of looking at the same data
• Equally valid
• What are some advantages of each?

Advantages of arithmetic view

• When there is no natural zero (or the natural zero is irrelevant)
• Often the case for time or geography
• When zeroes (or negative numbers) can occur
• When we are interested in adding things up

Advantages of geometric view

• When comparing physical quantities proportionally
• When using population data to think about individual-level processes

References