Lepidoptera: Where They Are and When They Fly - PowerPoint Presentation

Slide1

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 & ClarkSlide2

Lepidoptera

Lepidoptera is second largest class in

Insecta

Approximately 600 species of moths occur in the H.J. Andrews Experimental Forest

Relatively little is knownSlide3

Prey

Defoliators

Pollinators

Decomposers

Diverse Ecological

Roles

Egg

Caterpillar

Pupa

Moth

Ecosystem Functions

Stages of lifecycleSlide4

Pollination

Rodents

Reptiles

Bats

Birds

Spiders

Beetles

True bugs

Nematodes

570 vascular plant species

Ecosystem connections

PreySlide5

Assessing Environmental Impacts

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 cocoonMany 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.

Source of food, impacted by abundance of food source, sensitive to changes in temperature and nutritional quality of plants .Slide6

Moth Data and Sampling Slide7

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 studySlide8

Moth IdentificationSlide9

Moth Data Used in Modeling

Sampled with same method by Jeffrey Miller 2004-2008Emergence uses data from 20 sites trapped 30+ timesMoth Distribution includes data from biological inventory survey

Almost 40% sites trapped only once

More than half trapped either once or twice

Feralia

deceptivaSlide10

Vegetation Sampling

Purpose: Test hypothesis that moths are distributed near host plants by contributing to a database of vegetation data at moth sampling sites32 sites

100 meters in 4 directions

All vascular plant species except fern allies (except horsetails)

To learn more about host plants

Polystichum

munitumSlide11

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.”1What 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”2Will 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.Slide12

Emergence Objectives

Improve on the previous modelCreate a model that can predict on which day moths will emergeUse degree days instead of Julian days: GDD for plantsSlide13

Model Counts with Julian Days as the interval

Degree-Day Curve Model

Model Showing Counts with Degree Days as intervalSlide14

Degree Days

Took max temp. data from HJ AndrewsAssigned trap sites to Met. and Ref. StandsInterpolated missing dataDiscuss procedure for calculationsSlide15

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 2010Slide16

Formula:=IF(‘VANMET’!B4>0,’VANMET’!B4,0)+'VANMET DEGREE DAYS'!B2Slide17

The Model

Uses abundance data from trapping Estimates parameters of emergence and abundance curves from trap countsOptimizes parameter estimates to create emergence and abundance curvesSlide18

P(j,k)

We assume we catch all moths flying at trap timeP(j,k) is the probability that a moth emerges in interval j and has a natural death time in interval kMeasures abundanceSlide19

Variables

In original model, P(j,k) found by numerically integrating the joint density Q(j,k) and q

j

successively computed

Likelihood function uses

qj to optimize parameter estimates

Emergence time:

Lifespan:Slide20

Obtaining our parameters

= Pr(moth caught by trap)

m

= # moths flying qj = Pr(moth trapped at tj

)

Assume

(a constant) Slide21

Multinomial distributionSlide22

Convergence in distribution

. . .

Where the

F

i

’s

are Poisson random variables

As and , we assume (expected value of moths caught) approaches some constantSlide23

Distribution, cont.

m and alpha are unknownIf m is large and alpha small enough, the likelihood will be very close to PoissonThe model uses the multinomial distribution :Slide24

Incorporating degree days

Degree day values:Each moth has emergence threshold, DNow defineSlide25

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 fitSlide26
Slide27
Slide28
Slide29

3G

Days Since May 1

st

3G

Degree DaysSlide30
Slide31

5O

Days Since May 1st5ODegree DaysSlide32
Slide33

Future Work

Degree DaysRevisit interpolation methodsExperiment with different degree thresholds and starting datesModelMultinomial v. PoissonMultiple traps for one yearTake new data into account:

Vegetation surveys

Elevation, Aspect, Watershed, HabitatSlide34

Species Distribution Model Applications

Combine numerical observations and relevant variables (often environmental and spatial) to predict species distribution in space and/or timeWhy do this?

Ecological insight, further research topics

Land use management and conservation planningSlide35

SDM’s and Machine Learning

Supervised machine learningUse training data: {(x1,y1), (x2

,y

2

),…,(

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.Slide36

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.Slide37

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.Slide38

Learning Algorithms

AlgorithmsRandom ForestLogistic RegressionSupport Vector MachinesGeneralized Boosted Regression Models

Corresponding R package

randomForest

glmnet

e1071gbmSlide39

Random Forest

Ensemble methodGrows 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.Slide40

Random Forest

Plant #1

Pred

#1

Present

Plant #2

Temp

Absent

Present

False

False

False

Absent

Present

True

True

True

High

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

AbsentSlide41

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.Slide42

Logistic Regression

P(y = 1|x) = 1/(1+e-t)Where t is (β

0

+

β

1x1 +…+ βnxn)Attempt to find appropriate β values to weigh the covariates.Slide43

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.Slide44

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.Slide45

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.LinearRadialSigmoidPolynomialSlide46

Generalized Boosted Regression Models

Ensemble MethodLoss 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.Slide47

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.Slide48

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).Slide49

Algorithm Performance

Logistic RegressionRandom Forest

gbm

SVM

Avg

AUC = .605

Avg

AUC = .505

Avg

AUC = .607

Avg

AUC = .606Slide50

Acknowledgements

NSFOSUOSU Arthropod MuseumMatt CoxSteve HighlandTom DietterichDan Sheldon

Olivia

Poblacion

Julia Jones

Desiree TullosJorge RamirezJohn & EmilyVeraJeff Miller/Paul C. Hammond