Thursday, December 08, 2011

My "prior" brain has become Bayesian "posterior" mush

Wow, the months sure fly by. It seems like only days ago that I was trapping raptors during fall migration and performing my initial analysis on my goshawk season data. However, I have been very busy and have accomplished a great deal.
The most significant chunk of my time has been devoted to my research annual report. My agreement with the Forest Service requires me to submit an annual report of my study findings. Back in September, I provided a short report which included the status of our nest searches and general goshawk productivity, but much of the analysis came afterwards. By the end of the year I will submit a full report of my results. Before completing the report, I had to watch 3 months worth of nest camera footage and catalog all of the prey items. That was a pretty big time investment. Then came performing the statistical analysis and writing the report. While I could submit a report that just addresses the key questions the Forest Service is interested it, I chose instead to provide a complete report of all the work we performed which includes their key questions as well as the core and secondary questions of my thesis. Additionally, I had the option to submit the results in a general report format, but I chose instead to structure it as a full scientific paper or thesis. This work up-front will greatly streamline my effort when I get around to writing my thesis after my second field season. As a result, it took a lot of time to prepare. I am happy to say that I have submitted a draft to the Forest Service for their review and am awaiting the feedback. In total the document weighs in at 61 single spaced pages! However, I do include lots of photos and detailed maps of each goshawk territory.
The next chunk of my time has been working to figure out Hierarchical Bayesian Analysis. This has been a real challenge. It is not just learning a new statistical procedure, but instead requires a whole new philosophy and approach. As with many tools, the challenge isn't so much in learning the general concepts, but how to apply those general concepts to real problems you are trying to solve. Then, once you have solved the real problem, how do you know it's right? There is no one looking over my shoulder to point out the mistakes. They will all read my report expecting me to be the expert and to educate them. I still have a ways to go...
I am pursuing Hierarchical Bayesian Analysis to address two primary issues I have in my project structure that somewhat violate the assumptions of the frequentist procedures I have used so far. Not to get too alarmed, many papers have been published with these issues, but the right approach is to address them head on. In fact, most published papers have these issues, and only a few recent papers have addressed them. The first significant issue is that I classified historical goshawk territories as "occupied" or "not-occupied" dependent upon whether our search found goshawks nesting there. Of course, if we found a goshawk sitting on a nest, that is an absolute observation. But what about the territories where we did not find goshawks? I cannot say with the same certainty that they were not breeding there. In fact, my procedures have been shown by others to only be 70-90% effective at detecting nesting goshawks. The result is that I am reasonably confident that we missed occupied goshawk nests. Some may even have failed and were abandoned before we entered the field. Yet, they should be classified as occupied if nesting was initiated this season. Bayesian analysis will help me include the detection probability - or the probability that there are "false negatives" in my data.
The second issue is that I am using statistical procedures to produce an estimate of prey abundance in each goshawk territory. While the procedures provide a maximum likelihood value for prey abundance, the values have very wide confidence intervals. They are much more variable than point measurements. The frequentist model fitting procedures I have been using these values in assume a higher precision than this and also assume the error values are roughly normally distributed. These are weak assumptions at best. Those that use these procedures point out that the procedures are "robust" to minor violations to these assumptions. But how minor are they really? The Bayesian approach should help me to address these two issues.
My approach so far, as suggested by our department statistician, is to recreate my frequentist analysis using Bayesian methods. This is possible by building all of the frequentist assumptions into the Bayesian model as priors. Seems simple enough, but oh no... New procedures, new tools, tool integration, and the same old issue - I have to stop thinking about statistics in the same way... It's hard to break a mental model I have lived with for more than 25 years! Yesterday, I was finally successful. I have now recreated my frequentist analysis using Bayesian methods which builds confidence in the tools and the approach.
The next step in the process is to start modifying the assumptions. My response variable isn't normal it's actually a beta distribution. My prey abundance values aren't normal, but instead are gamma distributions. Can I use a single gamma distribution as the "prior", or are they different for each territory (requiring a heirarchical model). I believe I will end up with the latter. We will see where this continued journey takes me!
Oh yeah, I am also taking and teaching classes. My favorite class of my encore educational career so far has been Behavioral Ecology. The whole class has been fascinating, but my class project involved further depth in sex-ratio manipulation and sex-biased parental investment among various species. Last night I presented a paper on sex-biased filial infanticide (female Eclectus parrots killing their second-born male offspring when nesting is poor quality nest hollows). Fascinating stuff!
Moving forward, I am starting to get excited about year two of my study. I received word last week that it will be funded for another year! Many of my procedures will be the same as last year, but I will need to redesign a few of them. My rock-star field assistant is interested in another year as well. I can hardly wait!

Sunday, October 09, 2011

Raptor Research Foundation - Duluth, MN

I just returned from a fabulous three days in Duluth Minnesota attending the Raptor Research Foundation annual conference. About 200 attendees from all around the world were there presenting their research and hearing about the work of others. I presented the preliminary results of my first field season in the form of a poster.

2011 RRF Poster (click to enlarge).

The poster session featured 24 posters, five of which were presented by Boise State Raptor Biology students! The session was well attended! I had a steady stream of visitors reviewing my poster and asking questions. Discussing my work with the top raptor researchers in the world was fantastic. I was discussing my findings with the people who know the Northern Goshawk as well as anyone. I discussed goshawk diet with falconers, statistics with statisticians, predator-prey relations with prey experts, owls with owl experts (regarding my recent video of a goshawk eating an owl), compared goshawk diets to Cooper's Hawk diets, the challenges of video recording systems, etc. I received strong confirmation of my work, but also great suggestions on how to make it better. It was definitely well worth the investment!

During the presentation sessions, I learned about the current state of pesticides and raptors (not pretty), the state of persecution against raptors (even uglier), the effect of wind farms on raptors (not as bad, but still a significant issue), new statistical approaches (cool, but maybe ugly for some...), and new monitoring techniques (unmanned vehicles!). As I have commented about other conferences, this whirlwind of information was cut down into 20 minute segments. My brain struggled to keep up and change from topic to topic. I have pages of notes to follow up on and have generated over 30 suggestions to integrate into my year one report and my plan for year two. Hopefully I will be able to attend again next year in Vancouver.

Special thanks to the Raptor Research Center at Boise State for partially funding my trip!

Saturday, October 01, 2011

Hard-wired!

One thing you quickly notice when working with predators is that many of them seem hard-wired to attack prey when the opportunity presents itself. This is especially prevalent in predators that do not have a regular feeding schedule. If you may not get another chance to eat in the next week, and there is easy prey in front of you, take it. Even if you have just consumed another meal and could not possibly eat more. This may seem nonsensical to some, but this "attack without thinking" approach is probably what has made many raptors so successful from an evolutionary perspective.
When trapping and handling the various raptor species we come to better understand the different temperaments of the species. While each individual exhibits its own personality, the personalities within a given species are highly similar. My primary study species, the Northern Goshawk, is in a genus known as Accipiter. The three North American species within this genus are reasonably high strung and reasonably hard-wired attack predators. As a result when we are trapping them, we often find that their crop, a storage place in their throat for food, is already full, yet they were trying to attack our lure.
This last Wednesday, while another raptor biology student (Neil) and I were trapping raptors at the Idaho Bird Observatory, Neil captured a hatch year (juvenile) Cooper's Hawk. The crop on the Cooper's Hawk was so full that it even had food in its mouth. Yet this bird was diving to attack a dove! Did it possibly think it could eat more. No, probably not, but it was hard-wired to take prey when it presents itself. Fascinating.
Cooper's Hawk with bulging crop (whole neck area) and a full mouth!

Monday, September 26, 2011

Falco columbarius

In my not so free time, I have been spending a couple days a week up at one of the two Idaho Bird Observatory raptor trapping stations. On one of the days it is quite crowded as I am participating as part of the "Applied Raptor Biology" course which is required for all Boise State University Raptor Biology students. The other day is my trapping day and if I have been assigned to the Boise Peak trapping station, then I will likely be there all day by myself. I really like Boise Peak and the solitude, but Lucky Peak tends to get more birds.

Last week while at Boise Peak by myself, I trapped my first Merlin (Falco columbarius). I had been working to trap an Adult Red-tailed Hawk which had taken an interest in my lures. He/she had been by twice, but just wouldn't commit. He/she finally landed in a tree in front of the blind and just watched as I tried everything I could to lure him/her in. Nothing worked. Then I noticed a small raptor was mobbing the Red-tailed Hawk. If the Red-tail wouldn't commit, then maybe this bird would. One quick pull on the sparrow lure and I would have my answer. In a flash the raptor turned and like a bullet hit my net. I ran out to retrieve what I must embarrassingly admit I thought was a female Sharp-shinned Hawk. No, it was none other than a Merlin! My first!

 Hatch year Merlin, Taiga subspecies (Falco columbarius columbarius)

The trappers all like to catch Merlins as they are fairly rare. They do not breed in our area, but do arrive during the fall migration and stay through the winter. We may catch a dozen or so during a season between our two trapping stations. In this areas we have the opportunity to see all three sub-species, although the Taiga sub-species is the most abundant.

Hatch year Merlin, Taiga subspecies (Falco columbarius columbarius)

Do you know how hard it is to take raptor photos by yourself?

Just two days later I was at Lucky Peak with our raptor class. Neil was trapping, but I was assisting with the sparrow. We saw a bird in the distance and Neil lured him in closer with our larger lures. As he entered the "station" (trapping area) I noticed it was a smaller raptor and pulled the sparrow. Same as before, it turned on the sparrow and hit the net at full speed. Merlin #2! Neil with the assist!  I immediately noticed that this bird was considerably darker than the first. Could it be the dark Merlin sub-species (Falco columbarius suckleyi)?

Dark Merlin??

Upon closer inspection and consultation with the IBO Research Director Jay, we determined it was still a likely Taiga subspecies, but could be a hybrid between the Taiga and Dark sub-species. The face looks dark enough, but a true Dark Merlin would not have visible stripes on its tail.

Merlin, Taiga subspecies (Falco columbarius columbarius),
possible hybrid with dark Merlin (F. c. suckleyi)

I have no complaints. While they are the same sub-species, I trapped two Merlins in three days. Not bad. There is still five weeks of trapping to go. Maybe another Merlin sub-species or higher on my wish list, a large falcon (Peregrine or Prairie). I'll keep you posted...

Monday, September 05, 2011

Celebrating Vultures Through Art

Karyn and I had the honor of volunteering at the Peregrine Fund's World Center for Birds of Prey on International Vulture Awareness Day. Karyn was contacted for her artistic skills and abilities, I was merely there for additional support. We were asked to lead a children's activity of a group painting of a vulture (each child paints a bit of the painting). For those of you who know the two of us personally, working with a large group of children was a terrifying prospect.

It all began a few months ago when our friend from Nairobi Kenya, Dr. Munir Virani, contacted us asking if we would participate (check out his amazing photography at his link). He would be in Boise for the event to talk about the huge decline in African and Indian vulture populations. He was interested in modeling a children's art project after a very successful program that was implemented in Kenya. We happily agreed, and then wondered what we got ourselves into!

Karyn performed all of the prep work in acquiring all of the supplies, sketching out some initial designs, and putting together a plan of how it would all work! The sketches were based on initial photographs provided by the Peregrine Fund. Neither of us knew what to expect and what the finished product might look like. We also didn't know how many paintings might be needed. Karyn decided to produce three sketches, we started with a California Condor in flight.

Initial sketches.
California Condor. The first strokes by a 2 year old.
Karyn with our first artist!

One of the challenges was to assign painting tasks to the various abilities within the groups of kids. The younger ones focused on the broad painting tasks like the sky, while the older ones filled in the detail.

Karyn had the original reference photo available and also a small rendition that she painted to help guide the progress, but all of the paint on the canvas was put there by the kids themselves.

Progress.

Another activity for the kids was to create vulture masks. Here we have a vulture painting a vulture!

Vulture painting a vulture!
More progress.
Starting to come together!
Progress.

It was very manageable when only one or two kids were working at a time. Then a rush of 6 to 8 at a time! Trying to make sure they had mixed paint available, didn't destroy the painting etc. was a challenge. Many were painting over other's work. In most cases it improved the overall presentation!

Five brushes at a time!
Amazing progress!
Finishing Touches.
The completed work! AMAZING!
The artists and their ages.

Near the end of the day we started the second painting. This one would not be finished, but it was great to have another one to work on.

Painting #2.

It was a hectic and stressful day. Both Karyn and I were exhausted at the end of the day. Of course, I was only the assistant. This was mainly Karyn's show as the photos illustrate. By all accounts it was a tremendously successful event. I believe everyone had a great time and learned a lot about vultures in the process.

Other events during the day included presentations by Chris Parish on the California Condor program, Dr. Virani on the African Vulture program, and flight displays of many live raptors including a Harpy Eagle, Peregrine Falcon, Gyrfalcon and Aplomado Falcon. The Peregrine Fund put on a great educational event, which I hope will further the cause to help protect these fabulous creates. I am glad that we were able to contribute to the cause. You can too by educating yourself on the plight of vultures around the world and consider donating to The Peregrine Fund. They have a proven track record in achieving results on the ground (or I should say in "in the air")! I thank them and all of the families that participated!

Luigi - The Harpy Eagle with trainer.
Juvenile Aplomado Falcon in flight.

Monday, August 29, 2011

The Great Escape

This video captures a mistake by an adult goshawk. The female goshawk delivers a Belding's Ground Squirrel to the nest. Upon arrival she sees an uneaten bird waiting. She feeds the bird to the nestlings, then flies off leaving the dead Belding's Ground Squirrel behind. One problem - it isn't dead. (video plays in double time. female leaves at minute 2:30)

Monday, August 22, 2011

False Negatives

I continue to analyze the data gathered in my first field season studying Northern Goshawks in the Sawtooth National Forest as a part of my Masters program in Raptor Biology. This is a continuation of my first post on the analysis process. I actually received requests from MULTIPLE people asking me to continue blogging on the analysis phase of my project. So, hold on tight and stick with me, I will try to make this as painless as possible!

First nest discovered with nestlings!

In the first post, I illustrated using straight-forward confidence intervals that avian abundance was a significant predictor for goshawk nest occupancy and success. Here I will highlight another more sophisticated approach to arrive at a very similar answer. Then I will discuss the problem with these two approaches and why these are no longer valid for this particular case and l talk a little bit about where I will be taking it from here.

In the previous post I introduced the concept of AIC based model selection. I mentioned that in ecological studies it is now a foundational expectation for data analysis. Here I will illustrate analyzing nest occupancy and success using AIC model selection.

The first step is to hypothesize which variables should be predictors for nest occupancy and success. An important constraint is that you need to limit the number of possible explanatory variables, based on the sample size. There are different rules of thumb, but one is that you must have 10 samples for each variable, some say five. I am going to stretch this a bit and try three variables for 24 samples. I predict that Avian prey abundance and Mammalian prey abundance, are significant predictors. I also want to include the percent of the territory in sagebrush habitat (versus forested habitat) as I believe that has affected my abundance measurements. The first step is to ensure that none of the predictor variables are overly correlated. For this I will set a threshold for the correlation coefficient greater than 0.70.

Graph of relationships with correlation coefficients.

The graph indicates a low amount of correlation between the predictor variables (0.24, -0.29, 0.34). This was a surprise as I expected the mammalian abundance to be highly correlated to the amount of sagebrush habitat (seemed that we saw more mammals in open habitat). But, low correlation coefficients are good. I have then calculated the AIC values (actually AICc values which are AIC values adjusted for small sample size) for each of the eight combinations of these three variables as predictors for nest success, including the null model (no predictor). There are ranked based on the lowest AICc values. This analysis indicates that the model using mammalian abundance and avian abundance best explains the data, although the model using only avian abundance is very close (within 2 AICc can be assumed roughly equivalent). There are various approaches to moving forward from here: 1. Use the top model; 2. "Model Average" those within 2 AICc; 3. "Model Average" those within 4 AICc; 4. "Model Average" all eight models. Some have even recommended model averaging within 10 AICc. Here I will simply take the top model, create coefficient estimates, and 95% confidence intervals for the coefficients. If the confidence intervals do not include 0, then we can assume that predictor to have a significant influence.

From this we can take away that a model of both Mammalian prey abundance and Avian prey abundance best predicts nest occupancy and success, and that the influence of Avian prey abundance is significant (confidence interval does not overlap with zero). Hmm, that was the same answer as the previous analysis!

The Problem

But, there is a problem with both of these analyses. They both have an issue of "False Negatives". In these analyses, I had 8 successful nests and 16 failed or unoccupied nests. The issue is that I don't know for sure that there was not a successful nest in one of the 16 territories that we failed to discover. The "No Nest Detected" territories could have one of three values: 1. There was no occupied nest there; 2. There was a nest there but it failed before we detected it; 3. There was a nest there and it was successful, but we failed to detect it. Of course, this last category is very troublesome. For large conspicuous creatures, you might assume this probability is very, very low. For goshawks it is not low. We have walked right under nests without seeing them. We know this as we discovered it later.

Rosenstock et al. (2002) analyzed 224 papers published in nine different journals between 1989 and 1998 and found that only 13% of these studies acknowledged and addressed the case of false negative detections. The bar for publication is clearly higher today.

The Solution

The solution to this issue is to include the detection probability into the analysis. Essentially, instead of saying a territory is "not occupied", we say the territory has a X% probability of being occupied and successful. The whole statistical approach changes. The challenge is determining whether the detection probability is constant, what it is, and what it depends upon. There are a number of ways to generate this, which I am still investigating. At a minimum I will use the values provided by Woodbridge and Hargis (2006), who have analyzed the discovery method I utilized in the field and determined it has a 90% detection rate. I should say that having used the methodology in the field, I believe that they are being quite optimistic!

That's it for now. Thanks for sticking with me. More to come. I welcome your feedback.

Friday, August 19, 2011

The Hunt for Wolverines in Glacier National Park

This last year, Karyn and I read a book titled, "The Wolverine Way".

This amazing book provides some great insight into the behavior of this very elusive creature that most of us will never see in the wild. It also highlights some of the conditions which the researchers must face to study an animal which spends its life in the very high rugged terrain which is not very hospitable to humans. Any time I am having a bad day in the field, I think of what these guys had to face on a daily basis and that helps to reset my expectations. I highly recommend this book for research, wildlife lovers, or anyone who just appreciates a good story.

Anyway, reading this book inspired us to return to Glacier National Park, even though we might have just as good of an opportunity to see a Wolverine in Idaho. We have visited Glacier on a few occasions in the past. First as a bike tour we traveled from Missoula, up and over Logan Pass and into Waterton Canada and back. Later we returned for a hiking trip. This years trip would be focused solely on hiking with an emphasis on trails will the highest chance of seeing a Wolverine. We wouldn't find any wolverines, but the trip was spectacular. (click on any photos to enlarge)

Sunrise on the East side of Glacier National Park.
View over Redrock Lake toward Swiftcurrent Pass

The Hikes

The Highline trail is one of the most popular trails in the park for serious hikers and those. The trails is relatively easy if taken from Logan Pass to the Loop, where you can catch a park shuttle back to the top. This path is 11.5 miles, only gains 800 feet, but drops close to 3000 feet. However, the 0.75 mile side trip up to the Grinnell Glacier Overlook is strenuous, but HIGHLY recommended. With the side trip it finishes at about 13 miles. The trip is spectacular with amazing vistas and great wildlife - goats, sheep, eagles, marmots, etc. It is clearly my favorite trail in the park.

Early in Highline Trail Hike. Going-to-the-sun road is visible below.
Beargrass looking back toward start of Highline Trail.
Karyn at Grinnell Glacier Overlook.
Grinnell Glacier from Overlook.

Many of the trails were closed due to bear activity. On our hike into Trout Lake we were turned around after meeting a couple that had just had a very close aggressive encounter with a Grizzly Bear with a cub. They were actually charged by the female. Ptarmigan Tunnel, Iceberg Lake and Grinnell Glacier trails were also closed. From Many Glacier only two of the longer day hikes was available - Cracker Lake and Swiftcurrent Pass. We chose the pass.

Swiftcurrent Pass trail heads up from Many Glacier, past a number of lakes and crosses over Swiftcurrent Pass just above the Granite Chalet (on the Highline Trail). Thus, we would end up less than a mile from where we had been a few days before. The trail was once again filled with wildlife including our own bear encounter, although this one was a black bear at about 100 yards. We easily slipped by and continued on our way. The trail passes a few lakes before hitting the head of the canyon and turning into switchbacks. Each switchback provided a new more amazing view until we made it to the summit at 6.8 miles. This trail was an out and back so we were able to enjoy the views again on the way back down along with answering everyone's questions about how much further it was to the top. Quite a few people were headed up behind us as this was one of the few trails still open.

Head of Swiftcurrent Canyon. Where is that wolverine???
View from where we came (started the day 5 lakes down valley).
Virginia Falls, short hike.

On the final day in the park we enjoyed the short trail from the top of Logan Pass, opposite the Highline Trail, which heads into Hidden Lake. The early morning lighting provided fantastic scenery and up-close encounters with wildlife.

Clements Mountain from Hidden Lake Trail
Hidden Lake from Hidden Lake Overlook.
Beargrass.

The Wildlife

While the wolverine remained elusive, we did see lots of other wildlife. Here is a sampling from the week. A Golden Eagle amazed us on the Highline Trail as it pursued Ground Squirrels and Hoary Marmots. As multiple species alarm calls echoed across this landscape this guy flew in and dove toward the prey, but came up with empty talons. It isn't often you get to watch raptors from above!

Golden Eagle approaching prey on Highline trail.
Golden Eagle coming around for a second chance (Highline Trail).
Golden Eagle, Highline Trail.

It's fun to watch people in the parking lots look through binoculars at mountain goats a mile away. Just a short distance down a trail and you sometimes have to leave the trail to get around them. On the highline Trail we came face to face with a mountain goat. It was clear he had no intention of leaving the trail. We stepped to the outside, but he would not pass. I realized this would box him in. We stepped to the inside and he marched right on by, almost brushing up against us.

Mountain Goat demanding the trail (Highline Trail).
Mountain Goat (Highline Trail).
Mountain Goat sleeping ON Hidden Lake Overlook platform.

Bighorn Sheep aren't quite as conspicuous, but we still saw them on many occasions.

Bighorn Sheep (Hidden Lake Trail).
Bighorn Sheep (Going-to-the-Sun Road)

One of my favorite animals, is the Hoary Marmot. These large rodents really show their personality when you watch them. They are also an important prey species for the Wolverine! We found them at the higher elevations on most of the trails we hiked. A number of juveniles were out and about as well.

Hoary Marmot (Highline Trail).
Hoary Marmot (Highline Trail).
Hoary Marmot (Highline Trail).
Juvenile Hoary Marmot (Hidden Lake Trail).

I was hoping to see White-tailed Ptarmigans, but they too remained elusive. Of course, we weren't allowed to hike the Ptarmigan Tunnel trail, I am sure we would have found them there! On the Swiftcurrent Pass hike we did find three families of Dusky Grouse (right near the bear).

Dusky Grouse.

It was an amazing trip with the Highline Trail hike being the favorite. I highly recommend it and can't wait to go back to this amazing place.

Maybe a white-faced meadowhawk? Dragonflies are not my thing...