Associate Professor of statistics Lisa Madsen and statisticians from the United States Geological Survey (USGS) have come together to develop methodology to estimate the total mortality of bats, birds and other small creatures on wind farms and solar facilities. The Endangered Species Act requires that wind farms pay particular attention to endangered or threatened species such as golden eagles, brown pelicans, whooping cranes, condors and Indiana bats, which are killed when they accidentally collide with turbine blades.

“We want to keep track of our natural resources. We don’t want to end up depleting them, because we can’t tell we are taking too much.”

Monitoring fatalities at wind energy facilities can help government agencies, such as the U.S. Fish & Wildlife Service and the Bureau of Land Management, make better decisions about species management. Developing statistically accurate fatality prediction and estimation tools and monitoring protocols can also help agencies ensure that renewable energy facilities developers design operations to minimize the impact to wildlife, thus reducing environmental damage. “Fundamentally, what people want to know is ‘how many?’. This idea of keeping count and our desire to know ‘how many’ are important for conservation,” Madsen said. “We want to keep track of our natural resources. We don’t want to end up depleting them, because we can’t tell we are taking too much.”

## How many? The missing bats and birds

Madsen’s collaborators, Manuela Huso and Dan Dalthorp, from the USGS Forest and Rangeland Ecosystem Science Center in Corvallis are contributing new statistical models, estimators and software tools to improve bird and bat fatality estimates at solar and wind power facilities. Huso initiated the research 10 years ago to come up with improved models and methods of estimating the count of carcasses. Dalthorp joined her shortly thereafter; Madsen began collaborating with the USGS team in a more substantial capacity during her sabbatical two years ago.

Last year, the team along with collaborators from consulting firm, Western EcoSystems Technology, Inc, data science lab DAPPER Stats, the Swiss Ornithological Institute, and Duke University developed a software package called GenEst (a generalized estimator of mortality) — a suite of statistical models and software tools specifcally designed for estimating the total number of creatures arriving in an area during a specific time period when their detection probability is unknown but estimable. The latter can also be used more generally to estimate the size of open populations with imperfect detection probabilities.

However, as Madsen’s research on fatalities at wind farms shows, estimating an accurate count is anything but a straightforward process. In the case of wildlife fatalities due to collision with wind turbines or solar panels, carcasses invariably go missing, carried away by scavengers or fall in areas inaccessible to searchers. Therefore, simple counts of carcasses found at wind farms do not reflect the actual number of fatalities.

Madsen and her colleagues have developed complex statistical tools that estimate the actual number of carcasses when they are undetectable for any reason by taking into account a host of predictor variables such as searcher efficiency, variations in plot sizes and location of inaccessible areas.

Madsen developed a model to use data from field trials to estimate searcher efficiency. This model is incorporated into the larger GenEst model framework. “My collaborators are working on other aspects of the problem: getting a count of missing carcasses by estimating the amount of time a carcass is likely to stay before getting carried away by a predator. It is a highly involved project, where we put all the pieces of the puzzle together along with the uncertainty associated with all of these aspects,” explained Madsen.

“I think that non-statisticians could benefit from learning some statistical principles such as the concept of uncertainty, collecting useful data, and applying appropriate data analysis tools in a given situation.”

The software package, created by the team, will be utilized by government agencies as well as Western EcoSystems Technology, Inc., which has already begun to implement the software to assist their clients. The project has also attracted attention from environmental and government agencies in Canada, South Africa, Portugal and Scotland among others. In addition, the USGS statisticians have conducted workshops demonstrating how to use the software to estimate animal mortality at wind and solar energy facilities. “The methodology is generally applicable to any situation where you want to count something where the detection is not perfect,” said Madsen.

## The path to ecological statistics

After graduating from the University of Oregon with a master’s degree in mathematics, Madsen taught mathematics in a community college in New York. She wanted to get a doctorate in math education because she enjoyed teaching the subject. But she quickly discovered it wasn’t an ideal academic match for her. In the meantime, her husband suggested she try a statistics course. Madsen enjoyed the experience and switched to the Ph.D. program in statistics at Cornell University.

She also obtained a minor in natural resources at Cornell, which inspired her to apply statistics to ecological problems. In recent years, Madsen has also worked on numerical models of geological data to estimate the risk of environmental disasters such as leaking oil wells and other phenomena.

Madsen excels at teaching courses on statistical methods to non-statistics students at the graduate and undergraduate levels. She enjoys helping her students develop a statistical mindset as they learn about extending statistical methods to different disciplines.

“I think that non-statisticians could benefit from learning some statistical principles such as the concept of uncertainty, collecting useful data, and applying appropriate data analysis tools in a given situation,” Madsen remarked.