Lepidoptera: Where They Are and
When They Fly
Roy Adams, UC Davis
Ryan Smith, Union College
Camila Matamala-Ost,Oregon State
Chris Mattioli, Providence College in Providence Rhode Island
Elizabeth Cowdery, Cornell
Grace Zalenski, Lewis & Clark
Lepidoptera
• Lepidoptera is second largest class in Insecta
• Approximately 600 species of moths occur in
the H.J. Andrews Experimental Forest
• Relatively little is known
Diverse Ecological Roles
Ecosystem Functions
Prey
Pollinators
Defoliators
Decomposers
Stages of lifecycle
Egg
Caterpillar
Pupa
Moth
Ecosystem connections
Prey
Rodents
Pollination
~570 vascular
plant species
Reptiles
True bugs
Spiders
Bats
Nematodes
Beetles
Birds
Assessing Environmental Impacts
Source of food, impacted by abundance of food source, sensitive to
changes in temperature and nutritional quality of plants .
Temperature
• Caterpillar growth rate affected
by temperature
• Caterpillar must reach certain
critical size to enter pupal stage
• Majority of moths in Pacific
northwest overwinter as egg or in
cocoon
• Many species won’t emerge
unless undergo period of cold
(dipause)
Plant Nutrition
• Sensitive to nitrogen and
water content
• High water content enhances
growth
• Theoretically, moth abundance
and/or emergence could be
linked to changes in nitrogen
and water content of plants.
Moth Sampling
• Universal Black light
traps
• 22w circular bulbs, 12v
batteries
• Set 1 – 2 hours before
sunset
• Moths attracted to light
and stunned by
insecticide and acrylic
veins
• Intervals of 1+ weeks
• Biased towards
phototatic night flying
moths (majority)
• Data not used this
summer, will be used in
island biogeography
study
Moth Identification
Moth Data Used in Modeling
• Sampled with same method by Jeffrey Miller 2004-2008
• Emergence uses data from 20 sites trapped 30+ times
• Moth Distribution includes data from biological inventory survey
• Almost 40% sites trapped only once
• More than half trapped either once or twice
Feralia deceptiva
Vegetation Sampling
Polystichum
munitum
• Purpose: Test hypothesis
that moths are distributed
near host plants by
contributing to a database
of vegetation data at moth
sampling sites
• 32 sites
• 100 meters in 4 directions
• All vascular plant species
except fern allies (except
horsetails)
• To learn more about
host plants
Phenology and Climate Change
•
“As difficult as it is to predict precisely how the planet will warm over the next century or so, it
is even harder to refine predictions of how those changes will affect specific species.”1
• What are the drivers of moth emergence?
– Moths are poikilothermic
• How will climate change influence moth
emergence?
– “Due to human induced climate change over the last decade, phenology has become one of
the leading indicators of species’ response to environmental change”2
• Will this have an effect on other animals?
1: Barringer, Felicity. “Trout Fishing in a Climate Changed America.” New York Times Green Blog 16/7/2011. 16/7/2011.
2: Roy, DB & Sparks, TH. “Phenology of British butterflies and climate change.” Global Change Biology (2000). 6, 407-416.
Emergence Objectives
• Improve on the previous model
• Create a model that can predict on which day
moths will emerge
• Use degree days instead of Julian days: GDD
for plants
Model Counts with Julian Days as the interval
Degree-Day Curve Model
Model Showing Counts with Degree Days
as interval
Degree Days
•
•
•
•
Took max temp. data from HJ Andrews
Assigned trap sites to Met. and Ref. Stands
Interpolated missing data
Discuss procedure for calculations
Thermal Climate of the H.J. Andrews Experimental Forest
PRISM estimated mean monthly maximum and minimum temperature maps showing topographic effects of radiation and sky view factors.
Provided by Jonathan W. Smith and EISI 2010
Formula:=IF(‘VANMET’!B4>0,’VANMET’!B4,0)+'VANMET DEGREE DAYS'!B2
The Model
• Uses abundance data from trapping
• Estimates parameters of emergence and abundance
curves from trap counts
• Optimizes parameter estimates to create emergence
and abundance curves
P(j,k)
• We assume we catch all moths flying at trap time
• P(j,k) is the probability that a moth emerges in
interval j and has a natural death time in interval k
• Measures abundance
Variables
Emergence time:
Lifespan:
• In original model, P(j,k) found by numerically integrating the
joint density
• Q(j,k) and qj successively computed
• Likelihood function uses qj to optimize parameter estimates
Obtaining our parameters
= Pr(moth caught by trap)
m = # moths flying
qj = Pr(moth trapped at tj)
Assume
(a constant)
Multinomial distribution
Convergence in distribution
As
and
, we assume
approaches some constant
(expected value of moths caught)
...
Where the Fi’s are Poisson random variables
Distribution, cont.
• m and alpha are unknown
– If m is large and alpha small enough, the likelihood
will be very close to Poisson
• The model uses the multinomial distribution :
Incorporating degree days
• Degree day values:
• Each moth has emergence threshold, D
• Now define
Changes
• Compute P(j,k) differently because Te is discrete
• Single set of parameters
for each
species, rather than separate for each trap and year
– AIC: measure of fit
3G
Days Since May 1st
3G
Degree Days
5O
Days Since May 1st
5O
Degree Days
Time calculation v. AIC
(high values)
Explodes to high value
59
Time calculation v. AIC
(mid values)
34
25
23
33
56
Time calculation v. AIC
(low values)
21
53
32
50
19
17
31
47
15
44
30
41
29
13
11
38
9
28
35
7
27
32
May Days
D.D. Jan
15E
26H
D.D. Mar
16M
23Q
D.D. Apr
May Days
D.D. Jan
5P
18A
18G
D.D. Mar
5O
28D
26B
D.D. Apr
5
May Days
D.D. Jan
D.D. Mar
D.D. Apr
28C
15D
39H
16B
23A
13B
3K
13C
3G
39B
Future Work
• Degree Days
– Revisit interpolation methods
– Experiment with different degree thresholds and
starting dates
• Model
– Multinomial v. Poisson
– Multiple traps for one year
• Take new data into account:
– Vegetation surveys
– Elevation, Aspect, Watershed, Habitat
Species Distribution Model
Applications
• Combine numerical
observations and relevant
variables (often environmental
and spatial) to predict species
distribution in space and/or
time
•
Why do this?
• Ecological insight, further research
topics
• Land use management and
conservation planning
SDM’s and Machine Learning
• Supervised machine learning
– Use training data: {(x1,y1), (x2,y2),…,(xn,yn)} to
arrive at a function f(xi) ≈ yi.
• Split data into training, test, and validation
sets.
• Assume that if a moth exists at each site we’ve
trapped it at least once at that site.
SDM’s and Machine Learning
• Training set: half of the original data set used
in initially learning and fitting the function.
– Certain algorithms require their parameters to be
tuned for optimum performance. This is
accomplished by testing the model against a
validation set – a subset of the training set.
• Test set: half of the original data set separate
from the training set.
– After parameter tuning, the function’s accuracy
can be evaluated by running it on a test set.
Quantifying Accuracy
• The area under the receiver
operating characteristic
curve (AUC) is used as our
measure of accuracy for the
distribution maps.
• It is the probability that a
randomly selected positive
instance (moth presence) is
ranked higher than a
randomly selected negative
instance.
– AUC = 0.5 indicates a random
guess.
Learning Algorithms
Algorithms
• Random Forest
• Logistic Regression
• Support Vector Machines
• Generalized Boosted
Regression Models
Corresponding R package
• randomForest
• glmnet
• e1071
• gbm
Random Forest
• Ensemble method
• Grows decision trees by combining “bagging”
with the random selection of features.
– A decision tree is a model of decisions and their
outcomes. Internal nodes represent points where a
decision is made, and the leaves represent the
outcomes.
– “Bagging” is the process of randomly sampling with
replacement from the set of training examples, and
constructing a decision tree from the “bag”.
– Random forest also randomly selects features for each
training example rather using the whole of features.
Random Forest
Plant
#1
False
False
Plant
#2
Absent
True
True
False
Present
Pred
#1
Present
Temp
Low
Temperature Plant #1
Plant #2
Predetor #1
Moth
1 High
TRUE
TRUE
TRUE
Present
2 Low
TRUE
TRUE
TRUE
Absent
3 Low
TRUE
FALSE
FALSE
Present
4 High
FALSE
TRUE
TRUE
Present
5 Low
FALSE
FALSE
FALSE
Absent
True
Absent
High
Present
Tuning Random Forest
• After creating n bags, and growing n trees new
data can be classified by taking a vote of all
the trees’ predictions.
• The number of trees grown can be altered and
tuned as can the number of nodes of each
tree.
Logistic Regression
• P(y = 1|x) = 1/(1+e-t)
– Where t is (β0 + β1x1 +…+
βnxn)
• Attempt to find
appropriate β values to
weigh the covariates.
Tuning Logistic Regression
• It is oftentimes optimal to restrict the number
and size of these β values in regression. There
is a combination of penalty terms called the
“elastic net” to achieve these restrictions.
– Penalty term takes the form: λ[((1-α)/2)*|β|2 +
(α*|β|)]
• The parameters: α and λ are tuned.
– α controls which term is more important.
– λ controls the weight of the entire expression.
Support Vector Machines
• Non-probabilistic
classifier.
• Attempts to construct
an n-dimensional
hyperplane to separate
two possible classes of
data.
– The most desirable
hyperplane is the one
with the largest
functional margin.
Tuning Support Vector Machines
• Oftentimes data is not
linearly separable.
• Kernel functions map
the data unto a space
where a hyperplane can
be easily constructed.
–
–
–
–
Linear
Radial
Sigmoid
Polynomial
Generalized Boosted Regression
Models
• Ensemble Method
• Loss function: a measure that represents the
loss in predictive performance of a model.
• GBM’s construct an initial regression tree that
maximally reduces the loss function.
– A regression tree is a decision tree whose outputs
are real-valued.
Generalized Boosted Regression
Models
• To further reduce the loss function, new trees
are added.
– At the second step, a regression tree is fitted using
the residuals (variations in response) of the first
tree.
• The model now updates to contain two terms, and
residuals are taken from the two-term model. The
process continues in this stage-wise fashion until a
specified parameter – n.trees.
– Fitted values update with each new tree addition.
Tuning GBM
• Like the other learning algorithms, GBM also
has parameters to be tuned.
• The number of trees to be constructed and
added.
• The number of nodes in each tree (interaction
depth).
Logistic
Regression
Algorithm Performance
Random
Forest
Avg
AUC =
.607
Avg
AUC =
.605
gbm
SVM
Avg
AUC =
.606
Avg
AUC =
.505
Acknowledgements
• NSF
• OSU
• OSU Arthropod
Museum
• Matt Cox
• Steve Highland
• Tom Dietterich
• Dan Sheldon
•
•
•
•
•
•
•
Olivia Poblacion
Julia Jones
Desiree Tullos
Jorge Ramirez
John & Emily
Vera
Jeff Miller/Paul C.
Hammond