US Approaches to Biodiversity Conservation

1
GAP Mapping of Predicted Species
Distributions Perspectives on Issues of
Statistical Inference
Gary J. Umphrey
Department of Mathematics and Statistics Universit
y of Guelph, Guelph, Ont., Canada N1G 2W1 3
August, 2002 Gap Analysis Program Meeting,
Shepherdstown, WV
2
Green - predicted distribution of gila
monster Blue - protected areas (Status 1 or 2)
3
GAP Modeling of Predicted Species Distributions

• Attempts to capture all available information
  to predict species occurrences.
• Information sources quite varied include
  species-habitat affinities, point locality
  records, range maps and expert opinion.
• Land cover classification a key predictor other
  predictors also condition model.

4
But how scientifically valid can GAP modelling
be?

• Sampling is biased, often blatantly so.
• How best to combine different kinds of
  information appears nebulous.
• It even uses expert opinion but how expert
  are the experts, and wouldnt a different group
  of experts give different opinions?

5
My objectives

• To explain why I consider GAP modeling to be
  inferentially sound.
• To discuss the interpretation of probability for
  a dichotomous presence-absence species map.
• To offer a few suggestions to guide future
  modeling and sampling.

6
Arthur P. Dempster (1987)
The accepted paradigm of statistical inference
is to draw inferences from random samples to
populations, emphasizing that only information in
the sample is to be used. I argue that this
paradigm is too narrow, in fact so narrow that
technical statistics risks dismissal as
insufficiently relevant to science, even in
situations where the main task is to draw
uncertain inferences from samples to populations.
In Probability and the Future of Statistics in
MacNeill Umphrey (eds), Foundations of
Statistical Inference, Reidel.
7
Dempster suggests thatR. A. Fishers concept of
Mathematical Probability permits the exact
reasoning of mathematics to be applied to the
fundamentally inexact topic of uncertainty.
8
How to lay a fair bet

• Suppose your model predicts the occurrence of a
  species in the presence area with a probability
  of 0.30 for a random spatiotemporal sampling unit
  of fixed size.
• You let someone (a skeptic?) bet either side --
  you take the opposite side.

9
How to lay a fair bet (2)

• Whoever bets on absence must put up 7/3 times
  the wager of the person who bets presence.
• For example, if the wager for choosing absence
  is 7, the fair wager for presence if the model
  is correct is 3.
• Expected winnings are 0 for each person you
  should break even (in the long run).

10
How to lay a fair bet (3)

• But choosing absence when the probability of
  absence is really 0.40 gives expected winnings of
  (7)(0.40) (3)(0.60) 1.

11
An analogy

• How does a blind person gather information to
  recognize a face by touch?

12
What do face recognition and mapping have in
common?

• Both seek information on an objective reality
  probability model can be calibrated and tested.

13
The logistic model isP(x) ea ßx/(1 ea
ßx), -8 0
An S-Shaped Curve
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
Spatial Probit Analysis

• Calibrate size of sampling unit required to have
  a k chance of species occurrence.
• Methods of probit analysis are extensively
  investigated.
• Allows flexibility for different kinds of
  biodiversity assessments e.g. for reserve
  selection vs biodiversity impact in nonreserve
  areas.

20
Could Karen Dvornich make a lot of money with
NatureMapping?

• It depends

21
(No Transcript)
22
(No Transcript)
23
(No Transcript)
24
Summary (1)

• Fishers concept of Mathematical Probability puts
  GAP modeling on an inferentially sound basis.
• Improving a map involves increasing the
  difference in occurrence probabilities between
  areas of presence and absence for a fixed-size
  sampling unit, subject to omission and commission
  error costs.
• BUT allocating sampling resources to maximize the
  difference may not be best.

25
Summary (2)

• Amount of change and effort required are measures
  of map quality.
• GAP maps should never be obviously wrong (same
  does not hold for ecological models).
• GAP projects need to be ongoing if maps are to be
  improved and calibrated.