An Early Detection and Rapid
Assessment Network for Plant
Invasions
• Predictive Modeling of Species
Distributions and Early Detection
• A Regional Approach to Early Detection
and Rapid Response – IPANE
• An Information Network for Early Detection
and Rapid Response – Local to National
Levels
Predictive Modeling of
Species Distributions:
Applications to Invasives
Proteas from South Africa
http://protea.worldonline.co.za/default.htm
Protea Atlasing
Protea
altasing
in the
field
Field
forms
mapping
Protea Atlas sample sites across the
Cape Floristic Region
~60,000 sites, ~250,000 species-site records,
globally one of the most intensively sampled group of
species for any biogeographic region.
Cape Floristic (Biogeographic) Region
90,000 km2
9000+ plant species
70% found nowhere else
1400+ threatened or
endangered species
Objective: to develop Bayesian
hierarchical regression models to explain
and predict species distribution patterns
We use the Bayesian perspective to model
predictions:
•Bayesian inference answers the question:
“How probable are my hypotheses, given my
data?” (i.e. P(H|data)).
Rev. T. Bayes
•Versus the classical, frequentist perspective that
answers the question:
“How probable are my data give my (null)
hypothesis?” (i.e. P(data|H)).
Sir R.A. Fisher
How does the Bayesian perspective work:
1) We may have some prior expectations about the outcome of
an experiment, the parameters of the model, or the confidence
that an hypothesis is correct before any data are examined:
prior probability.
2) These probabilities are modified in light of the data available
providing: posterior probability or confidence in the
hypothesis.
3) Use Bayes theorem:
[posterior probability that the Ho is correct, given the data] ~
[probability that data would be observed, given the Ho] X
[ the prior probability that Ho was correct, before any data
were collected]:
p(Ho|data) ~ p(data|Ho) * p(Ho)
Simple conceptual example: predict the distribution of
spotted owls in the NW with some degree of confidence.
We know that owls are rare in the forested landscape; prior
experience may indicate that the probability of finding them in any
particular forest is .05
But, by including data on their ecology can we have increased
confidence in detecting their presence? For example we may
hypothesize that they nest in snags. We can evaluate this by
gathering observations p/a of owls in forests w/ and w/o snags.
Example forest survey data:
Snags seen in plot
Snags not seen in plot
totals
Owls present Owls not present
40
160
5
795
45
965
totals
200
800
1000
•Set up as a Bayesian model:
Posterior prob. of owls, given snags ~ prob. of snags, given
owls * prior prob. of owls:
P(O | S ) 
P( S | O)  P(O)
P( S | O)  P(O)

P( S )
P( S | O)  P( S )  P( S | NO)  P( NO)
For above example, the probability of finding owls in forests
given snags:
P(O | S ) 
(40 / 45)  .05
 .3
(40 / 45  .05)  (5 / 45  .95)
•Versus usual frequentest perspective:
There is a high probability that owls are not distributed at
random among forests (w/ and w/o snags) p<0.0001, or
that there is a strong relationship between no snags and no
owls.