Measuring Biodiversity in Natural Systems
“If the traveler notices a particular species and wishes to find more like it, he may turn his eyes in vain in any direction. Trees of varied forms, dimensions and colors are around him, but he rarely sees any one of them repeated. Time after time he goes towards a tree which looks like the one he seeks, but a closer examination proves it to be distinct. He may at length, perhaps, meet with a second specimen half a mile off, or may fail altogether, till on another occasion he stumbles on one by accident.” –Alfred Russel Wallace
My project for the UF Biodiversity Institute involves investigating the relationship between biodiversity and ecosystem function in US forests. In order to understand this relationship, we need to understand what diversity is in the first place. The quantification of diversity has been a controversial topic in community ecology, and numerous diversity indices abound. We may intuit that diversity is an average property of a community but what is it an average of? As illustrated evocatively in the quote above from Wallace’s (1875) description of a tropical forest, a diverse community is characterized by having many rare species: you are unlikely to find two individuals of the same species unless you sample many individuals! Patil and Taillie (1982) were the first to recognize that diversity is a measure of the average rarity of species in a community. They found that all diversity indices are a weighted average of species rarity, weighted according to their relative abundance. All diversity indices meet the following criteria:
By modeling the waiting time for a conspecific encounter as a stochastic process with a geometric distribution, Patil and Taillie (1982) were able to derive the equations of the three most well-known diversity indices: species richness, Shannon index, and Simpson’s index. All three indices are from a family of indices called generalized entropies because they can all be defined by a single equation with different values of an order parameter, which defines the index’s sensitivity to rare species. Unfortunately, there are many pitfalls to using these measures (Chao et al. 2014a), all of which arise from their inability to obey the replication principle (explained in greater detail below):
Recently, Hill numbers have been proposed as the best choice for quantifying abundance-based diversity as well as a unifying framework for integrating species/taxonomic diversity, phylogenetic diversity, and functional trait diversity (Chao et al. 2014a). First discovered by Hill (1973) and later reintroduced in ecology by Jost (2006), Hill numbers are another a parametric family of diversity indices that can convert generalized entropy indices to effective number of species. Just as with the generalized entropy indices, Hill numbers define a rarity score for each species and average them in different ways that favor common vs. rare species, depending on the order parameter (Roswell et al. 2021):
Hill diversity is always expressed in terms of effective number of species, which is the same as the number of species in a completely even community with the same diversity score. As a result, regardless of how species rarity is averaged, all Hill numbers are expressed in the same units, which are readily comparable and interpretable. Moreover, Hill numbers obey the replication principle, meaning pooling assemblages with no overlapping species will result in a total diversity equal to the sum of the diversities of each assemblage. Hill number can also provide better cross-assemblage comparisons, as they can be partitioned into within- and between- group components (Chao et al. 2014a). The diversity profile of a community, given by the Hill diversity for different values of the order parameter, provides the same information as a species accumulation curve (Chao et al. 2014b), meaning it can be used to estimate “true” community diversity from sample diversity (Roswell et al. 2021). Hill numbers also can be generalized to phylogenetic and functional trait diversity (Chao et al. 2014a):
Linking biodiversity change to ecological mechanisms has remained elusive (Godsoe et al. 2021, 2022, 2023). It has been shown that an observed change in diversity is theoretically compatible with any type of biotic interaction. Biotic interactions change absolute abundances, but diversity only depends on relative abundances. Therefore, changes in diversity often reflect the success of rare species relative to common ones (Godsoe et al. 2023). But what about in biodiversity-ecosystem function studies, where biodiversity is posited to effect change in some ecosystem variable? Diversity indices are measures of average rarity, and as Patil and Taillie (1982) showed, the rarity functions can be a model of a waiting time stochastic process. Many advances in population genetics, phylogenetics, and stochastic population dynamics have come from modeling waiting time stochastic processes. By using modern model selection methods (Ponciano and Taper 2019) to choose the Hill number order parameter that best explains the data, could we gain insight into the stochastic processes that generate the data as well as the relative contribution of common and rare species?
Chao, A., C.-H. Chiu, and L. Jost. 2014a. Unifying Species Diversity, Phylogenetic Diversity, Functional Diversity, and Related Similarity and Differentiation Measures Through Hill Numbers. Annual Review of Ecology, Evolution, and Systematics 45:297–324.
Chao, A., N. J. Gotelli, T. C. Hsieh, E. L. Sander, K. H. Ma, R. K. Colwell, and A. M. Ellison. 2014b. Rarefaction and extrapolation with Hill numbers: a framework for sampling and estimation in species diversity studies. Ecological Monographs 84:45–67.
Godsoe, W., P. J. Bellingham, and E. Moltchanova. 2022. Disentangling Niche Theory and Beta Diversity Change. The American Naturalist 199:510–522.
Godsoe, W., K. E. Eisen, D. Stanton, and K. M. Sirianni. 2021. Selection and biodiversity change. Theoretical Ecology 14:367–379.
Godsoe, W., R. Murray, and R. Iritani. 2023. Species interactions and diversity: a unified framework using Hill numbers. Oikos 2023.
Hill, M. O. 1973. Diversity and Evenness: A Unifying Notation and Its Consequences. Ecology 54:427–432.
Jost, L. 2006. Entropy and diversity. Oikos 113:363–375.
Patil, G. P., and C. Taillie. 1982. Diversity as a Concept and its Measurement. Journal of the American Statistical Association 77:548.
Ponciano, J. M., and M. L. Taper. 2019. Model Projections in Model Space: A Geometric Interpretation of the AIC Allows Estimating the Distance Between Truth and Approximating Models. Frontiers in Ecology and Evolution 7.
Roswell, M., J. Dushoff, and R. Winfree. 2021. A conceptual guide to measuring species diversity. Oikos 130:321–338.
Wallace, A. R. 1875. Tropical Nature and Other Essays. MacMillan, London.
Akshay Vinod Anand
A flicker on the adjacent hill, a beam of a flashlight. Humans. The distance, 10 km. But 50 feet up a rock face, with no moonlight, no water, no food and dense forest between us and the mysterious beam of hope, it was a losing battle. We watched the beam fade away into the loud darkness.
The Western Ghats are an ancient mountain range that runs along the western coast of the Indian subcontinent. Known for its incredible biodiversity and rain-soaked forests, these mountains are home to the charismatic Bengal Tiger, majestic Asian Elephant and a myriad other bird, insect, reptile, and plant species. I was on assignment to survey the northern regions of this beautiful mountain range for signs of large mammals to estimate prey densities for large carnivores. The northern Western Ghats are typically drier and hotter than the southern parts of the mountain range, characterized by thick scrub transitioning to moist deciduous forests. At the peak of the Indian summer, this landscape can be rather unforgiving, with temperatures exceeding 110 F.
It was early in May when I joined Mr. Sashi, the project lead, in the field. As a two-person team we were to survey close to 400 km of lowland scrub forest over the next month. This entailed walking 10 – 15 km line transects, on a daily basis, through this harsh terrain. We tried to use trails as often as possible, but being a fairly unexplored region of the Ghats, we would often end up using animal paths and dried streams to navigate through the forest. This might not have been the most ideal strategy (as we eventually found out), especially since those same paths were being walked by tigers and leopards.
This was just another day, another transect, another adventure. Or so we thought.
Sashi and I woke up rather lethargically, we had planned the day’s transect the previous night and it was going to be one of the easier ones. An approximate 8 km walk (piece of cake!). We packed our field bags and set off in our rickety old jeep. We were particularly upbeat this morning, after weeks of long and arduous surveys, this transect seemed like the perfect opportunity to enjoy the kaleidoscope of brown-green slopes that is the Ghats in summer. After a bump, a jump, and a push our jeep makes it to our starting point. We unloaded, got our bearings, and started the day’s transect.
Entering the forest is a lesson in time travel. The world around you cease to exist, the cities, the cars, the people all fade away. What is left is just you and your immediate surroundings. Time is almost nonexistent. The forest opens up and engulfs you in its calm, cacophony, and you exist as just another life form among the multitude of living energies around you. The trees lead the way, the insects laugh at you, the birds orchestrate the most beautiful symphony. Everything falls in place, like a jigsaw puzzle without its cracks.
We walk, in an almost hyperaware, meditative state. Every rustle of leaves, every twig breaking, sets off alarm bells. We play the role of a prey species, always on the lookout for danger.
The terrain is harsh, 60 º slopes, loose gravel, and a canopy 4 feet in height. A canopy of thorny shrubs. We crawl. Progress is slow. We are no longer on recognizable paths. We crawl some more. Progress is painstakingly slow. The sun is beating down and sweat drips through every pore, depleting vital fluids. The “easy transect” was proving to be anything but. We finally reach a clearing, and we take a much-needed break to plan the route forward. The GPS must be lying, it’s 3 o’clock in the afternoon and we have only done 3 km. WHAT?
No more stops, we need to motor ahead if we’re going to have any chance of making it to our destination before sundown. We rehydrate, and head north. There is approximately 4 hours of daylight and 5 km to cover. A steep, “uphill” task. We walk, the terrain is no different, thorns, gravel, sun. It’s 6 o’clock now and we are defeated. We’re down to the last liter of water, although the end is in sight. Our GPS (that sly, untrustworthy GPS) tells us that we are just 2 km from the end point. What it doesn’t show is between us and our destination, are two steep ridges, the latter with a 150-foot rock face.
We push, one ridge down, 7 o’clock, light is fading.
The thought occurs to us that we might not make it. We motor up the last ridge, as we reach the top we are confronted by a thicket of Karvy (a small shrub that grows in dense thickets, making it nearly impossible to move through). I look at Sashi, “What now?” We push and shove our way through the Karvy, as it stands there smirking at us like a headmaster whose just caught you cheating on a test. We finally break through the Karvy. The sun has set, we have about 20 minutes of ambient light and in front of us is a 150-foot, sheer rock face.
By now we are running solely on adrenalin. We decided to climb, I led the way. No way.
Rim rocked: “The state of being stuck on a rock face, with no possibility of going up or down.”
The light had faded completely, and so had the adrenaline. We were rim rocked. I spotted a ledge nearby, about 3 feet wide and 10 feet in length. We had no other option than to camp there for the night.
We settled in, coming to terms with the situation we had gotten ourselves into. As the light faded to pitch black. It started. The forest yawned, stretched, shook itself and woke up. The night had begun, and the forest was alive.
We sat in silence as the cacophony of crickets enveloped us. A concert of chirps, clicks and buzzes intertwined into a divine symphony, of which Bessie, Bach or Beethoven would be proud. The music spread like waves, rhythmic, constant, calm.
We just sat there in awe, listening, thinking, being. There was a soft rustle of the undergrowth to our right. There had been many such sounds over the last few hours, but somehow this felt different. What followed was a sound I will never forget. It was soft at first but grew in amplitude until it resonated in our bones. The low, thunderous, rumbling of a panting leopard. It was a guttural sound, propagating from every cell of the animal’s body. The panting got louder and louder; it was moving towards us.
I could feel my heart racing, until it was thudding against my ribcage. The adrenaline, that I thought was completely depleted, started coursing through my veins again. We looked at each other, frozen. You never really understand what it means to fear for your life, until you are face to face with an animal of this caliber. Leopards are expert climbers, with an acute sense of smell and hearing. The odds were stacked against us. The panting neared, till it was just below us. Then there was sniffing. We listened as the animal circled below us. Then, silence.
The next hour was the longest of my life. Every second was an eternity.
Mud and rocks come cascading down the rock face and we hear something walking above us. The leopard. My heart is in my mouth. Silence.
Panting and sniffing below us, an hour had passed. A shower of mud and rocks an hour later. This animal was having fun, “scare the pesky little humans” was the name of the game. Although, I presume it was just investigating the new smell in its territory.
The leopard eventually moved on, but not before shaving off a good 5 years from both of our lives.
We didn’t sleep a wink that night. We just drifted with the multitude of life around us, somehow incorporated into this system, like a cell performing its function to keep the entire body alive.
Sometime during the night, we saw humans on the adjacent hill. Probably the rest of our team worriedly searching for us along motorable roads. Unfortunately, this searching strategy proved to be rather ineffective.
Before we knew it the eastern sky stared to fade into existence, sunrise. As the sun emerged, and washed the forest with light, so did a pair of Langurs. They were sitting on a branch opposite us, at eye level, looking at us quizzically. Had they been there the whole night, watching us in amusement like a late-night sitcom. The expression on their faces said yes.
We decided to climb down and find a way around the rock face. We were drained, the night had taken its toll on us. I turned around and looked up one last time. To that little precipice where I lived a lifetime, in 8 hours.
gy Information. https://www.ncbi.nlm.nih.gov/.
Vanessa Luna Celino
Science Communication Efforts to Promote the Conversation on Fire Management in Peru
My doctoral research and practitioner work focuses on community-based fire management and stakeholders’ perceptions of fire governance in Peru, my home country. My research advances our understanding of the human-fire relationship by bringing theoretical and methodological approaches from multiple disciplines (ecology, geography, political sciences, and anthropology). Research and practitioner work on these issues, which are unique for the country, expects to contribute to policy making through crucial scholarship and collaborative activities with local partners. In my last in the Ph.D. program, I have been working on results dissemination by elaborating peer-reviewed scientific papers and science communication efforts. The later included the filming of a mini-documentary about my research (see below), and participatory workshops and symposia in November 2023. These efforts were possible thanks to the SNRE’s Robin E. Nadeau Ecology Graduate Research Award.
Research context and motivation:
Fire is an essential tool in tropical subsistence agriculture and is a traditional, intergenerational, and cash-free way of releasing nutrients, controlling pests and weeds, and preparing new farmland. However, agricultural burns and other ignition sources have increasingly affected fire regimes -frequency, intensity, severity, and seasonality- in most tropical ecosystems. Some agricultural burns result in accidental or escaped fires, where secondary outbreaks unintentionally affect surrounding areas, especially when strong winds are combined with droughts. Concurrent changes in global and regional climate also accentuate the increase in fire frequency.
Globally, societies have responded to escaped fire threats with some degree of fire suppression and prevention strategies. More recently, there has been a call for new practices and paradigms on fire management: a call that incorporates traditional ecological knowledge from indigenous and local peoples, avoids the overcriminalization of fire-related practices, and promotes bottom-up fire management. Fire governance involves decision-makers engaging with key actors to determine fire’s social and ecological role and how to manage fire. Understanding key actors’ perceptions is the first step in fire governance and can be applied to understand policy context, facilitate communication and transparent decision-making, and manage conflicts.
Specifically, the Peruvian Andes has a long history of anthropogenic fires, which have shaped the natural landscape over millennia. Here, too, fire is an important agricultural tool in local communities and the most affordable way to open farmlands and control undesirable vegetation and pests. However, as in many other tropical countries, agricultural burns are prohibited and are a significant problem when not adequately controlled. There are also interesting examples of local communities self-organizing and adapting their fire-related practices to get the most benefit from their burns and reduce wildfire risk. Yet, bottom-up fire management initiatives require the recognition of multiple actors involved in decision-making on fire related policies.
Science communication for environmental policy change:
For the dissemination and validation phase of my doctoral project, I organized and facilitated two workshops and two symposia. In collaboration with a local nonprofit organization, CEDES Apurimac, the organization of two workshops on ‘Locally-based fire management in the Peruvian Andes,’ targeted local stakeholders representing the regional and local government, nonprofit organizations, volunteer firefighters, local communities, and researchers, many of whom participated in previous phases of my doctoral research. One workshop was held in Kiuñalla campesino community and another in Abancay city.
Having my doctoral results as a starting point of discussion, participants discussed what actions were needed to promote effective fire governance in the Peruvian Andes. Overall, these workshops promoted the reflection on various current and potential fire management strategies, such as community brigades, law enforcement, fire awareness campaigns, safe agricultural burns, and landscape management.
The two symposia targeted ~250 undergraduate students from local universities in the regions where my research was conducted and aimed to promote the dialogue on fire management in Peru. In Abancay city, the symposium ‘Prevention and control of wildfires from rural communities’ brought together representatives of government, non-profit organizations, and campesino communities to discuss farmers efforts in community-based fire management. In Cusco city, the symposium ‘Research on wildfires and local prevention efforts,’ brought together fire researchers and regional practitioners in the aim to promote more wildfire research and innovative fire-related actions in Peru. Both symposia were free of charge for any attendee.
Wildfires are an issue increasingly affecting every corner of the world. The focus of my research and practitioner efforts in fire governance and management is intentionally geared towards aiding decision-making through an integrated and adaptive approach to fire management. This stands in contrast to the prevailing emphasis on wildfire suppression and prevention strategies currently implemented in Peru. My main goal as a doctoral student has been to promote the bridge between research and action through science communication and spaces of social learning on effective fire-related practices and policies. This is why the organization of workshops and symposia were extremely relevant to the success of my doctoral project. Following the completion of my doctorate, I intend to persist in collaborating with rural communities, whether in academia, government, or within a non-profit organization. My goal is to devise solutions that enhance human well-being and contribute to the preservation of natural areas in tropical regions.
Mini documentary: https://www.youtube.com/watch?v=a8JfpR0qxg0
Symposium in Abancay: https://sites.google.com/view/conferenciafuegocusco/simposio-abancay?authuser=0
Symposium in Cusco: https://sites.google.com/view/conferenciafuegocusco/inicio?authuser=0