Dr. Teresa Fidalgo Fonseca is a Professor of Forest Science at the Universidade de Trás-os-Montes e Alto Douro (UTAD) in Portugal, where she studies forest resources engineering and silviculture, focusing on the practice of aligning woodlands growth management with community values and needs. She serves as Division 1 Deputy Coordinator for Silviculture at the International Union of Forest Research Organizations (IUFRO) and Guest Editor of academic journals *Forests* and *Frontiers in Forest Management*.

Her recent publication, Management of Maritime Pine: Energetic Potential with Alternative Silvicultural Guidelines, was co-authored with José Lousada and published in *Forest Biomass: From Trees to Energy* in February 2021. In it, Teresa presents new guidance for managing maritime pine species, developed and verified using simulations in her ModisPinaster model. Ultimately, the results of this study, when implemented, have the potential to optimize yield of biomass, a cost-effective and sustainable source of renewable energy.

A statistical evangelist, Teresa has used JMP for many years, both in the classroom and in her own research.

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**Forest of maritime pine in Portugal where data for statistical analysis and modeling is collectedMeg: Which came first – your interest in forestry or your interest in statistics?**

**Teresa: **There was an excellent forestry engineering course of dendrometry I took as an undergraduate student at UTAD that was taught by a brilliant professor who introduced me to forest biometrics and modeling. At the time, I’d been feeling that I very much enjoyed statistics, and it was so exciting to find out that I could apply statistics in forestry!

After graduation, I completed my MS in forest resources engineering and worked on modeling stem taper of eucalyptus [the diameter of a tree’s bole as a function of height above ground]. Then I did my PhD – also in modeling – and created a model, now freely available through the French platform Capsis, that simulates the dynamics of maritime pine, including mortality, growth and diameter distributions.

That model, ModisPinaster, came about in answer to a problem: at that time we did not have a forest model for the most represented conifer species in Northern Portugal that could be used for forest planning! We implemented several permanent plots in the field, collected data and then I developed it into what was at first a conceptual creation. Now it is not just constrained to Portuguese forests but can be used by other researchers from other places.

**A design plan for ModisPinasterMeg: What do you see as the potential impact of implementing the silvicultural guidelines you used ModisPinaster to develop? **

**Teresa:** Forest management should always be based on science. Traditionally, managers have used guidelines derived from empirical studies that do not have the strength we can provide with statistical modeling. In the case of [my recent paper in *Forests*, Size–Density Trajectory in Regenerated Maritime Pine Stands after Fire], our model shows how to best manage naturally originating pine stands affected by forest fires through natural regeneration.

This model allows forest managers to identify the optimal standard density of plants along with development stages for the species. It’s so important that managers not base their work solely on numerical targets like “how many trees should we have?” but instead on a very good data set and appropriate models, which might be simple as a linear or a quadratic model, of which the description of the maximum-density line is an example.

I’ve always really enjoyed connecting my research with practical use, and whenever I can, I try to build models that will benefit forest managers…. If we can provide them with good support for forest management, I'm positive that this will bring impact on sustainability of forest resources.

**Example of ModisPinaster interface showing output options and simulation of growthMeg: What are some of the other research questions you’re using the model to investigate?**

**Teresa: **Most recently, my colleagues and I have been analyzing the radial diameter growth of another pine – the European black pine, which is not native in Portugal. We had data from six different locales and, using the Schumacher growth equation, we looked at the differences between the black pine populations. We wanted to understand the expected behavior of the species outside its natural range, and modeling was a crucial way of achieving this.

With modeling, we can do so much more than just calculating averages and standard variations. First we graphed the dispersion of the diameter with tree age and then fit the model to identify some differences by site. As you can see, I am always smiling when I talk about modeling because it's really something I like!

When I identify a pattern, I could easily spend seven days a week, 24 hours a day modeling. It is so nice to think about all the information that can be generated from good data and how we are able to summarize it in a mathematical equation providing information that can be important for forest managers.

**Examples of visual data analysisMeg: How can you be sure your data is good? **

**Teresa:** First of all, I’m very rigorous with data because I believe you can’t have a good model if it is not well supported by good data. It’s important to have adequate measurement and data selection criteria so that your data is highly representative of the sampled population, such as the conditions for a species’ natural regeneration in one of the examples mentioned.

There is a rather long list of challenges we face when it comes to data quality. When I was doing my PhD, I had an experience where I found an error, but only after building several models. I had to refit all of it, which took me some time, so now I very carefully analyze the data before modeling anything!

And there is one more very important thing: you need to analyze the quality of the model. You have to see if it performs with the assumptions and when. I say this to all my students: we are responsible for providing a good model, so we have to ensure that the model goes through all the right statistical tests and analysis.

**Typical datasets: Anscombe´s quartetMeg: What kind of checks do you use to determine whether a model is good or not?**

**Teresa:** I usually do visual analysis, with different graphs to check not only the relationship between the response variable and each factor, but among all the factors. I often suggest that my students use colors because sometimes, just by using a different color to separate a data set, we can better understand both the overall and individual patterns.

As for data cleaning, any outliers or influential observations – as long as they are not errors – need to be kept in the data set in order to provide information about the process. One time, I had an outlier related to an unusual number of maritime pine trees, but it was a true value as I measured it in the field. Being so different from the other data points, I was aware that it would influence the results. I built several models – one with the total data set and another I tested without the outlier. Ultimately, however, I did not exclude it because, as I said before, good models require good data sets, including any outliers that represent true variation in a sample.

**Meg: What misconceptions do students have when it comes to statistics?**

**Teresa:** Some students think that modeling is just about creating some trends in the data. Other think it is too complicated. They’re not well prepared at first, but once I teach them more about statistical analysis, they realize the potential of modeling. It might take a lot of time and practice to build a very good model, so I always try to motivate the students to come with me, step by step, on this modeling journey! In fact, I’ve had students who continue to do modeling even after finishing the course – which, for me, is very rewarding.

**Students in the Forest Management course at UTAD working with ModisPinasterMeg: It must be! No doubt it helps to have a professor like you whose passion for statistics is infectious. And to learn statistics in an applied setting like forest science where it’s not just pure modeling, but where you can see the real-world applications. **

**Teresa:** Applications are so important. The course I teach is based on JMP, and the first few lectures are about how to use the software. Once students are acquainted with JMP, they start creating small models that are used in forestry. From there, I slowly increase the level of difficulty. For example, I start with linear regression modeling and by the end of the course, I’m teaching nonlinear models. As the topics grow more difficult, it’s important that my lectures are not just theoretical, but practical with real scientific examples.

The first lecture is the most important because that’s when I capture students’ interest in data. At first, it’s not an interest in modeling – it’s an interest in data analysis. I provide them with graphs from my research or available on the web and ask them to analyze what they see without knowing anything about statistics or modeling. At first, students may not think they see anything, but after we discuss it, they start to see the trends emerge. (Sometimes, before showing the graphs, I present an alphabet soup, to get the students involved and also to train their eyes.)

One of the most important things I tell them is that in the future, we will only use more data in scientific fields. The next generation will rely more on statistical analysis and modeling than I do. So we need to invest in providing future scientists with the skills they need to build models. It’s incredibly important to promote statistics as part of science. Not just science, not just data analysis, but both.

We have to engage students in developing fundamental skills for dealing with data – get them to understand the potential of data analysis to simplify the world through discoveries that were never possible before.

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