“Early View” is like Christmas!

I’m extremely happy to say that the following papers are now out in early view – the first two papers are the results of Eryn Schineder’s and Kyle Rodman’s thesis work. For those who may not know, Eryn’s work focused on spatial patterns and reference conditions at the Barney Springs site south of Flagstaff, a pure ponderosa pine site on limestone soils that has managed to avoid being harvested. Truly a unique system to study… Kyle’s work also focused on spatial patterns and reference conditions, but in dry mixed-conifer sites along the Mogollon Rim. He presents a variety of reference attributes that will be interesting and applicable to many of you currently working in dry mixed-conifer forests (especially this findings regarding long-term changes in species composition). I’m am really proud of these two and both works are significant contributions to our knowledge regarding HRV and long-term vegetation dynamics. In case you’re wondering, Eryn and Kyle are both currently pursuing PhDs – Eryn with Andrew Larson at Univ. of Montana and Kyle at Univ. of Colorado at Boulder with Tom Veblen.

Lastly, the third paper presents an idea that Daniel Laughlin, Rob Strahan, Dave Huffman and I have been developing for a while now. In this paper we present a functional (species trait-based) approach to restoring resilient ecosystems in light of changing environmental conditions and explore it’s application in dry mixed-conifer forests (study sites at Black Mesa and on the north rim of Grand Canyon NP). Really exciting work that I’m happy to have been a part of!!!

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It’s been a productive year thus far…

I’ve been out of pocket for awhile on this blog, but it’s fir a good reason. I’ve been writing my butt off! Below are four manuscripts published in the last few months, all of which I was a part of… I’ll like the work speak for itself.

Taylor The Economics of Ecological Restoration and Hazardous Fuel Reduction Treatments in the Ponderosa Pine Forest Ecosystem
by M H Taylor, A J Sanchez Meador, Y S Kim, K Rollins, and H Will
Abstract: In this article, we develop a simulation model of the benefits and costs of managing the ponderosa pine forest ecosystem in the southwestern United States. Using the model, we evaluate and compare the economic benefits and costs of ecological restoration and hazardous fuel reduction treatments. Both treatment approaches increase the expected number of low-severity wildfires, which can promote postfire rehabilitation. Hazardous fuel reduction treatments are likely to reduce expected wildfire suppression costs, but not enough to offset the costs of implementing treatments. Conversely, ecological restoration treatments do not necessarily reduce expected wild-fire suppression costs but fully restore the ecosystem in more than half of the simulation runs, which lowers the need for future fire suppression and reduces the chance of conversion to nonforest, alternative stable states. We find that the choice between hazardous fuel reduction and ecological treatments will depend on the management objective being pursued, as well as on site-specific factors such as the wildfire return interval and the economic value of biomass removed.
 Stoddard Five-year post-restoration conditions and simulated climate-change trajectories in a warm/dry mixed-conifer forest, southwestern Colorado, USA
by M T Stoddard, A J Sánchez Meador, P Z Fulé, and J E Korb
Abstract: Some warm/dry mixed-conifer forests are at increasing risk of uncharacteristically large, high-severity fires. As a result, managers have begun ecological restoration efforts using treatments such as mechanical thinning and prescribed fire. Empirical information on the long-term impacts of these treatments is limited, especially in light of potential climate change. We assessed changes in forest structure and composition five-years following three alternative restoration treatments in a warm/dry mixed-conifer forest: (1) thin/burn, (2) prescribe burn, and (3) control. We used the Climate-Forest Vegetation Simulator (Climate-FVS) model to quantify potential forest trajectories under alternative climate scenarios. Five years following treatments, changes in forest structure were similar to initial post-treatment conditions, with thin/burn being the only treatment to shift and maintain forest structure and composition within historical reference conditions. By 2013, the thin/burn had reduced basal area (11.3 m2 ha-1) and tree density (117.2 tree ha-1) by 56% and 79% respectively, compared to pre-treatment values. In the burn, basal area (20.5 m2 ha-1) and tree density (316.6 tree ha-1) was reduced by 20% and 35% respectively, from 2002 to 2013. Mortality of large ponderosa pine trees (the most fire-resistant species) throughout the duration of the experiment, averaged 6% in the burn compared to 16% in the thin/burn treatment. Changes five years following treatments were largely due to increases in sprouting species. Shrub and sapling densities were approximately two to three times higher (respectively) in the thin/burn compared to burn and control and dominated by sprouting oak and aspen. Under climate simulations, the thin/burn was more resilient in maintaining forest conditions compared to burn and control which approached meager forest conditions (3–4 m2 ha-1). These results indicate that restoration treatment that include both thinning and burning can maintain forest integrity over the next few decades.
 Tuten Ecological restoration and fine-scale forest structure regulation in southwestern ponderosa pine forests
by M C. Tuten, A J Sánchez Meador, and P Z. Fulé
Abstract: Fine-scale forest patterns are an important component of forest ecosystem complexity and spatial pattern objectives are an increasingly common component of contemporary silviculture prescriptions in dry fire-adapted forests of North America. Despite their importance, questions remain regarding the assessment of silvicultural treatments designed to meet spatial objectives. We initiated a replicated silvicultural assessment of two forest management approaches commonly applied in dense ponderosa pine forests of the Southwest United States: historical evidence-based ecological restoration guidelines (ERG) and northern goshawk (Accipiter gentilis) foraging area management recommendations (GMR). We compared stand-level characteristics, global tree location point patterns and tree group-level attributes resulting from the marking of these approaches to current forest conditions and patterns of historical forest remnants in six, 2.02 ha stem mapped plots. We also assessed group-level Vegetative Structural Stage (VSS; a classification of fine-scale forest structural development used to regulate fine-scale spatial patterns in these forests). ERG and GMR-based treatments significantly reduced densities and basal area from the current condition, but did not significantly differ in density from historical forest remnant estimates. GMR-based treatments retained greater stand level basal area than ERG-based treatments, primarily in large, 28–48 cm tree diameter classes. GMR-based treatments approximated global tree location point patterns of forest remnants better than ERG-based treatments, primarily due to a 5–6 m minimum spacing of residual trees, but also likely due to specific aspects of ERG-based marking techniques. Despite this difference, both treatments resulted in group-level characteristics similar to those exhibited by historical forest remnants. Both treatments significantly altered group-level VSS area and reduced variation of tree diameters within classified VSS groups.
 Outzs Post-fire ponderosa pine regeneration with and without planting in Arizona and New Mexico
by J Ouzts, T Kolb, D Huffman, A J Sánchez Meador
Abstract: Forest fires are increasing in size and severity globally, yet the roles of natural and artificial regeneration in promoting forest recovery are poorly understood. Post-fire regeneration of ponderosa pine (Pinus ponderosa, Lawson and C. Lawson) in the southwestern U.S. is slow, episodic, and difficult to predict. Planting of ponderosa pine after wildfire may accelerate reforestation, but little is known about survival of plantings and the amount of post-fire natural regeneration. We compared ponderosa pine regeneration between paired planted and unplanted plots at eight sites in Arizona and New Mexico that recently (2002– 2005) burned severely. Two sites had no natural regeneration and no survival of planted seedlings. Seedling presence increased with number of years since burning across all plots, was positively associated with forb and litter cover on planted plots, and was positively associated with litter cover on unplanted plots. Survival of planted seedlings, measured five to eight years after planting, averaged 25% (SE = 8) and varied from 0% to 70% across sites resulting in seedling densities of 0–521 trees ha-1. Based on a projected 44% survival of seedlings to mature trees and target density of mature trees determined by historical range of variability and ecological restoration principles, four of eight sites have a seedling density in planted plots (125–240 ha-1) that will produce a density of mature trees (55–106 ha-1) close to desired levels, whereas seedlings are currently deficient at three planted sites, and in surplus at one site, which had abundant natural regeneration. Natural regeneration in unplanted plots during the first decade after burning produced seedling densities inconsistent with desired numbers of mature trees. Natural regeneration in unplanted plots produced less than 33 seedlings ha-1 at seven of eight sites, but produced 1433 seedlings ha-1 at one high-elevation site that supported a more mesic vegetation community before burning than the other sites. Our results show that current practices for planting ponderosa pine after severe fires in Arizona and New Mexico produce desired numbers of seedlings in approximately half of all projects, whereas natural regeneration rarely does within the first decade after burning.

 

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My script to install the “top” R packages

Here’s a script that I use to query the CRAN package download logs and figure out what packages are the “top” packages being used/downloaded. It borrows heavily from this post, which is badass… User be wary, as it download all of the logs for the specified date and creates a data.table to house this information (if you specify a large timeframe, this thing will be HUGE). To get around that, I randomly r sample the data.table for half of the entries and at the end, I’ve got a section to install these packages. However, it’s currently commented out.

Geek+1

## Inspired and heavily dependent on the code Felix Schönbrodt
## http://www.nicebread.de/finally-tracking-cran-packages-downloads/

## ======================================================================
## Step 1: Parameterize the script with dates and the number of packages
## that we're interested in...
## ======================================================================

# My advice would be to set this to a day or a week. If you do 6-months like I've
# done here you better have the memory to support it!
start <- as.Date('2014-09-01')
end <- as.Date('2015-02-28')

# How many "top" packages are we interested in?
top.x <- 20

## ======================================================================
## Step 2: Download all log files for each week
## ======================================================================

# Here's an easy way to get all the URLs in R
all_days <- seq(start, end, by = 'day')

# If we were to look we'd  see a strong weekly pattern in the the downloads,
# with Saturday and Sunday having much fewer downloads than other days. This is
# not surprising since we know that the countries which use R don't work these
# days. Let's just look at MWF to be safe...
weekdays(all_days)
days.To.Keep<- c("Monday", "Wednesday", "Friday")
all_days <- subset(all_days, weekdays(all_days) %in% days.To.Keep)
weekdays(all_days)

year <- as.POSIXlt(all_days)$year + 1900
urls <- paste0('http://cran-logs.rstudio.com/', year, '/', all_days, '.csv.gz')

# only download the files you don't have:
missing_files <- setdiff(as.character(all_days), tools::file_path_sans_ext(dir("CRANlogs"), TRUE))

dir.create("CRANlogs")
for (i in 1:length(missing_files)) {
  print(paste0(i, "/", length(missing_files)))
  download.file(urls[i], paste0('CRANlogs/', missing_files[i], '.csv.gz'))
}

## ======================================================================
## Step 3: Load single data files into one big data.table and then clean
## up the files (delete them) once we're done
## ======================================================================

file_list <- list.files("CRANlogs", full.names=TRUE)

logs <- list()
for (file in file_list) {
  print(paste("Reading", file, "..."))
  logs[[file]] <- read.table(file, header = TRUE, sep = ",", quote = "\"",
                             dec = ".", fill = TRUE, comment.char = "", as.is=TRUE)
}

# rbind all of the files together
library(data.table)
dat <- rbindlist(logs)
# logs will likely be huge, so unless you have memory for days, we best delete it
# and free up that memmory
#rm(logs); gc(verbose=T);

#Let's make this data.table smaller, to save memory, and randomly sample half of it
dat<-dat[sample(nrow(dat), ceiling(0.5*nrow(dat))), ]

# define the remaining variable types
dat[, date:=as.Date(date)]
dat[, package:=factor(package)]
dat[, week:=strftime(as.POSIXlt(date),format="%Y-%W")]

# set the key
setkey(dat, package, date, week)

# Delete the files and thier directory (gots to keep our shit clean!!!!)
# Just comment this out if you don't want to delete the files (i.e., you
# might want them for later use)
#unlink("CRANlogs", recursive = TRUE) 

## ======================================================================
## Step 4: Analyze it!
## ======================================================================

library(ggplot2)
library(plyr)

# Overall downloads of packages
d1 <- dat[, length(week), by=package]
d1 <- d1[order(-V1), ]

# Build a vector of package names, to be  used later for install.packages
package.names<-as.character(d1$package[1:top.x])

# plot 1: Compare downloads of "top" packages on a weekly basis
agg1 <- dat[J(package.names), length(unique(ip_id)), by=c("week", "package")]

ggplot(agg1, aes(x=week, y=V1*2, color=package, group=package)) + geom_line(size=1) +
  ylab("Downloads") + theme_bw() +
  theme(axis.text.x  = element_text(angle=90, vjust=0.5))

## ======================================================================
## Step 5: Install them all (plus their dependencies)!
## ======================================================================

# Uncomment this line if you want to install all of the "top" packages
# install.packages(package.names,dep=TRUE)
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A little R love for my non-R friends…

Source: http://xkcd.com/1064/ There's even a package to make your figured in XKCD fashion! How awesome is that!??!??! http://stackoverflow.com/questions/12675147/how-can-we-make-xkcd-style-graphs-in-r

Source: http://xkcd.com/1064/
There’s even a package to make your figures in XKCD fashion! How awesome is that!??!??! http://stackoverflow.com/questions/12675147/how-can-we-make-xkcd-style-graphs-in-r

***Update*** Maxwell Joseph 20+ R tutorials to YouTube for a new undergraduate course in Ecology and Evolutionary Biology at CU developed by Andrew Martin and Brett Melbourne, which are a nice place to start…***End Update***

The other day, a colleague/friend sent me a message asking how to go about learning R and specifically asked about online resources to help her lessen the learning curve. Since I knew she is a SAS user, I had some specific ideas of where I would point her, but I though I’d also post the guts of my response here…

So you’re interested in converting to R? That’s great and you won’t regret it…. As a former SAS user (and a general “new” R user), I usually suggest the following:

Many people recommend the R in Nutshell book from O’Reilly. It’s good, but it’s mostly a rehashing of available online help files: http://oreilly.com/catalog/9780596801717

Perhaps the best compilation of online video/tutorial type resources for learning R is this collection compiled by Jeromy Anglim: http://jeromyanglim.blogspot.com/2010/05/videos-on-data-analysis-with-r.html

As a former SAS user, I also suggest you start with Muenchen’s book  from Springer: http://www.springer.com/statistics/computational+statistics/book/978-1-4614-0684-6 He has an accompanying website with examples too that’s pretty useful: http://r4stats.com/examples/

It’s not to hard to find preview copies of the above mentioned texts online, but if you find them useful you really should support the authors and purchase a copy. As you progress, you’ll quickly outgrow any single book and then I suggest using the true power of R, the available online community and resources. Here are a few suggestions:

  • The R Project homepage. It really should be bookmarked. This is the place to come for official news from the R Project, plus links to documentation, mailing lists, and the official R FAQs
  • StackOverflow. Have a question about R? Search for questions tagged with “r” and you’ll probably find an answer. If not, post your question and I guarantee you’ll have an answer before you know it….
  • R bloggers. This is the first “news” feed I check every morning. It’s my go to for news, tips and articles related to R and is basically  a blog aggregator for posts from dozens of R bloggers, including the awesome work form the team at Revolution Analytics
  • #rstats on Twitter. This is pretty self explanatory (in 140 characters, no less). Just search for the #rstats hastag
  • If you find yourself still looking and desire some offline reading, the R Project has an extensive list of R books, as does the R Programming Language tag on Amazon.com

Hope this helps!

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Prezi on introducing spatial statistics

Last semester, I provided a couple of guest lectures in Margaret Moore’s Landscape Ecology class on spatial statistics. Spatial statistics, tools that hold a special place in my heart, are commonly used for understanding data distributed in a space where positions and distance have meaning; and are highly useful tools in forestry and ecology. This prezi is meant to be a brief introduction, and is expanded upon in my 599 class.
I had completely forgotten to publish the prezi, so here it is…. I hope some of you find it useful.

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Final thoughts on my F2F assignment in Nepal

When I decided to volunteer with Winrock International’s Farmer-to-Farmer program, I wasn’t sure what I was getting myself into, and while I was assured by a fellow volunteer that I would be taken care of, I never anticipated how great this opportunity could be. Upon arrival and throughout my time in Nepal, Winrock’s small (maybe 5 people) but dedicated team made me feel right at home, making it easier to focus on my task at hand – increasing the data handling and analysis capacity of young, experienced, faculties and selected post-graduate students through the application of R.

2014_04_16_07_50

Chhan and family invited me to have dinner at their home while in Kathmandu. It was, hands down, the best meal I ate while in Nepal.

My primary contacts in Nepal were Dr. Vrigu Duwadi and Mr. Chhan Bhattachan with Winrock, and Dr. Mohan Sharma, Professor and Continuing Education Center Director with the Agriculture and Forestry University of Nepal. I can’t say enough good things about these individuals. All of my activities while on assignment were coordinated through this team (with the invaluable inclusion of Krishna, our driver) to assure that we were delivering information that was pertinent to the audience and that facilities and logistics essential to the success of the training were available. In addition, all of these individuals had a hand in making sure I also got to tour campus, visit cultural and natural resources sites, and generally ensure that I received the best Nepali experience possible (which I think comes natural to them). I have to mention a special thanks to my friend, Chhan, who spent almost every waking hour with me and was largely responsible for how I experienced Nepal. You a competent statistician, an intellectual, and an exceptional host.

To some degree, I approached this assignment expecting very little, and being totally prepared to “wing it” if need be. Everything I read about traveling to Nepal was that most non-Nepali visit to trek in the Himalayas, but it’s generally not the place you just up and decide to visit. Essentially, most people traveling here, plan, save an prepare for months. This was a little unnerving for me, but I think it added to my experience and alleviated many preconceptions or unreal expectations.

Given all of these factors, I’ll summarize my time in Nepal by listing a few things I learned on this trip (in no order of importance and they’re not all serious):

  1. We, as Americans, should be grateful that we have clean water and a dependable power supply. We should also be thankful we have food security, transportation safety regulations, and a well-developed sanitation system.
  2. I’ve said this before – that a good driver is worth their weight in gold – but the exchange rate has gone up after my trip to Nepal and especially during my time in Kathmandu. A good driver is worth 6x their weight in gold.
  3. I really do love American food (and craft beer) and missed it greatly. I’m especially grew tired of lagers and missed American ports and brown ales. I also missed eating raw greens…
  4. Kathmandu, and some of the larger cities like Bharatpur are extremely polluted. It doesn’t take away from its beauty, they’re just polluted. People here at home have been asking what it was like to see the Himalayas, and I have to explain that due to the smog, I never saw them. Not once. It’s sad, but the Nepali people’s sewage and waste infrastructure has failed to keep up with their urban expansion, leaving them with a serious problem. Crossing a Bagmati river in Kathmandu revealed piles of floating garbage (not a new issue) and the lack of pollution or emission standards is readily apparent as mini- and micro-buses, bikes, and all forms of vehicles constantly pump black fumes into the atmosphere.
  5. Gender equality (albeit still a work in progress) is a beautiful thing and it’s good to seen Nepal making positive strides in this arena
  6. It’s impossible to talk about the effects of disturbances in mixed-conifer systems when the other party’s talking the importance of increased crop yields to feed the hungry or integrated pest management to reduce the impact of pesticides on human health (think DDT concerns in the US, circa 1940s only with humans). Some of the professionals I spoke with expressed interests in deforestation and land degradation, largely anthropogenic in nature, so I was able to see how my work might apply there… but it was a stretch. I also saw and read about numerous wildfires that were burning in community forests and near-by National Parks, but few seemed to think it was an “interesting” issue.
  7. The United States of America is not as cool as it thinks it is… we have no native monkeys for crying out loud! Two words – Rhesus macaque
  8. I loved “having tea” and now see how it facilitates conversation and idea sharing. I wasn’t prepared for the fact that “having tea” doesn’t mean you’ll actually be drinking tea. It could be eating dal, having cookies and coffee, or any variety of thing. Essentially, it’s a break and an excuse to chat.
  9. Apparently, everyone outside of Kathmandu has a water buffalo or two. I don’t think they “own” them.
  10. The widespread use the internet and availability of information at a moment’s notice has changed our lives forever. Not everyone has this luxury. They might have smart phones and access to the internet, but I don’t think everyone uses it to empower and educate themselves quite like the I (we?) do. I hope I’m wrong on this one… My time in Nepal assured me that the people there have the intellectual capacity, but the resource limitations limit how they might achieve success.
  11. Facebook really has made the world smaller. I think my friend list doubled after this trip and I’ve corresponded with several participants over pictures, data, analysis, and all sorts of things.
  12. In a country where more than 70 percent of the population depends on agriculture for its livelihood, Nepal has done a superb job of recognizing the importance of community management and conservation of its forests. Bravo!
  13. Nepal’s flag is the only national flag in the world that is not rectangular in shape and is considered to be the most mathematical flag. Hell yeah! Go Math!
    The Nepali love football, but they LOVE cricket!

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Completion of my assignment in Nepal with F2F

DSC_0868

Myself and the participants in the 2014 workshop in Bharatpur, Chitwan, Nepal – Provided by Winrock Intl. and USAID.

This morning we met with the USAID staff here in Kathmandu, Nepal and debriefed them on my assignment, signaling the end of my work here. Though I only spent six full days with the host institution at AFU, this experience has been a great opportunity. I truly feel that I’ve helped a developing country (a little) to increase their capacity to do agricultural and natural resource research, albeit indirectly through introducing them to R.

During my brief time here, we manage to cover:

  1. Getting started with R (What is R, an overview of R-project.org resources, installing and running R, walkthroughs of using the Comprehensive R Archive Network (CRAN), accessing internal and external help, documentation, an overview of packages and their use, and detailed applications of RStudio)
  2. Data management (reading and writing data, data types and factors including: vectors, matricies, arrays, lists, text and characters, dates and time, and dataframes)
  3. Basic statistics (summarizing a sample, summarizing categorical data, comparison of samples, relationship between variance, association between categorical variables)
  4. Calculations and manipulation (calculations, defining subset of data values, sorting data, forming factors)
    Syntax and data entry (reading data, syntax of commands, logical operations, building and using sequences, handling missing values, testing and coercing classes, and generation and use of random numbers)
  5. Hypothesis Testing (testing difference in variances and means, t-tests, tests of distributions, interpreting output)
  6. Modeling (fitting a line, fittings non-linear curves, multiple regression, regression with grouped data, interpreting output)
  7. Analysis of variance (specifying the treatment, syntax of model formulae, analysis, designs with several error terms, saving information from the analysis, other facilities, advanced designs, summarizing results and interpreting output)
  8. Advanced graphing (scatterplots, boxplots, histograms and bar charts, time series, pie charts, and saving plots in both the base plot and ggplot2) and
  9. Programming  in R (developing custom functions, object structure, and “for”, “while”, and “repeat” loops, ifelse statements)

On a personal note, this was my first trip to Nepal, let alone south Asia and it’s been hugely eye opening. I now clearly see the need for further technology transfer and assistance, so that developing countries can benefit from global advancements and increase their own capacity. Activities such as those I’ve been engaged in here in Nepal are key to empowering local people to solving their specific problems. I firmly believe that the countries of the developed world cannot solve the problems in the developing world by giving physical of fiscal goods to them, but we can lessen the learning curve and empower individuals by providing help understanding technology emerging practices and removing barriers.

We need to promote the sharing of technology and information so that people and communities in developing worlds are aware of the resources that are available to them and thus may become self-empowered.

Next stop, Bangkok and then a short hop back to the States!

 

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On assignment in Nepal with F2F

 mapIn my previous post, I said I was headed to Nepal for a couple of weeks for an USAID assignment for the John Ogonowski and Doug Bereuter Farmer-to-Farmer Program, coordinated though Winrock International. My trip here was largely uneventful, and I am now writing this from my hotel room in the Royal Century Hotel in Bharatpur, Nepal (the blue dot above). So far, I’ve traveled quite a but (US to Kathmandu (the red dot), then to Bharatpur), ridden elephants on a jungle safari in Chitwan National Park, eaten lots of authentic Nepalese food, partaken of many beers (Everest, Tuborg and Carlberg), seen numerous research facilities around the Rampur Campus of AFU, and had many great conversation about the culture, ecology, political and socioeconomic issues facing Nepal. I didn’t really realize how far the country has come in the past decade.
I’ve begun teaching R, and while I know I don’t have enough time to teach them everything, I hope that they learn enough to be able to advance independently once I’m gone. That and I hope the power holds up…

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Farmer-To-Farmer in Nepal

DSCN0477Tomorrow morning, I leave for Nepal for an USAID assignment for the John Ogonowski and Doug Bereuter Farmer-to-Farmer Program, coordinated though Winrock International. The assignment is with the Agriculture and Forestry University (AFU) in Rampur, Chitwan (Baratpur Campus, actually) which was founded in 2010.

The details are not all that interesting, but AFU requested USAID (via subcontractor, Winrock) provide statistical expertise to conduct a comprehensive workshop introducing and applying an “easy to run and simple statistical system” that could help “researchers to summarize and analyze information with a computer.” I was told that AFU students and faculty were currently using SAS and Genstat (a UK-based, commercial package) but lacked expertise to teach one another. It may go without saying, but structuring the workshop around R was an easy sale and the rest is history.

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Great Post Over at Flowing Data on Histrograms…

Histograms
Flowing Data is a blog I visit daily and I own and often cite both of Nathan’s books in my classes. One of his most recent tutorials focuses on histograms, their use, and their implementation in R. Seeing how size distributions (often represented by histograms) are the backbone of forestry and most quantitative ecology studies, I thought this tutorial deserves a repost. As always, you wont be disappointed in reading the post…

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