What is it about?

• What is an island?
• What is the expectation?
• Why does it matter?
  • theoretical interest (what determines diversity?)
  • conservation (habitat fragmentation…)
• How does it come about?

Explanations put forward

• Habitat diversity: greater in larger islands
• Equilibrium Theory of Island Biogeography:
  • colonisation vs. extinction events
  • speciation events
• Simple sampling effect (think quadrats of different sizes)

The Class Exercise: Stone Turning

Working in pairs, you will

• turn over stones,
• count the number of species present, and
• record the size of the stone.

Planning a Field Study

Be clear about the analysis before you start collecting data.

• What is my independent variable (predictor), \(x\)?
• What is my dependent variable (outcome), \(y\)?

What kind of variable? - and how will I test \(y\sim x\)?

Sampling Considerations

“Random sampling” and “avoiding bias” is drilled into you.

• What are you sampling here (what’s your ‘unit of replication’)?
• Is random sampling appropriate for this study?

The (in)famous Normal Distribution

• What will happen if you sample stones at random?
• Why is this bad?

Because of this…

You want this

What is the task ahead?

• Plot the data / relationship
• Formal test: is there evidence for our hypothesis?
• [What fits best?]

Shape of the relationship?

Beyond “it’s correlated,” what do we expect the relationship to look like?

• linear? — \(y \sim x\)
• log-linear (exponential)? — \(y \sim \log x\)
• log-log linear (power function)? — \(\log y \sim \log x\)
• sigmoidal?

Most common assumption

Number of species \(S\) follows a power relationship with area \(A\):

\[S = cA^z\]

which would give a straight line in a log-log plot:

\[\log S = \log c + \log A^z\]

\[\log S = \log c + z\times\log A\]

Sample distribution of areas (\(X\))

# calculate new column for stone area = width * length
SpA.data$area <- with(SpA.data, width.cm*length.cm)