Schoener 1957 and Bailey at el. 2019

Schoener 1957 and Bailey at el. 2019

Blog Author: Annie Madsen

SCHOENER 1957

Main question: What is the currency of feeding strategies (what is maximized/minimized)?

4 strategies to optimize foraging:diet, space, period, group size

Optimal diet (M), a set of one or more items, can be predicted with a simple equation:
E = net energy
T = net feeding time
E/T = (potential energy-pursuit costs-handling and eating costs)/(pursuit time + handling and eating time)
This case does not incorporate search time (ambush predators or opportunistic foraging).

When considering search time, E/T is linear if: resources are equally distributed and replenish before predator returns, predator has complete knowledge of foraging grounds, and there is no prior investment required (travel/building a web).

Energy gain at different life history stages is relevant because energy allocation differs at those stages, especially when more/less energy intake during reproductive periods alters fitness. Animals must be able to gain energy above the baseline existence energy (the amount of energy required for basic cellular maintenance) to be able to allocate energy to storage, growth, or reproduction. Based on the literature, Schoener reviews how to calculate maintenance energy using metabolic rate and caloric content of food. He then discusses how animals can manage intake and allocation of energy through behavior and physiology. Schoener also mentions animals have to spend time to find mates and avoid predation, which compete with time spent foraging.

Using this background, Schoener presents a model (appropriately named the "general model") for optimal foraging that maximizes reproductive output. There are two special cases for this model: time minimizers and energy maximizers.

Optimal Diet
Schoener discusses the parameters that are usually incorporated into optimal diet models, reviewing equations from Laing, Holling, and others. The initially simple equation presented above is expanded to incorporate the specifics behind pursuit time (speed, distance, and fatigue), search and pursuit energy (metabolism and activity), handling and eating time (size of feeder, size of food, move to different location), pursuit and capture success (ratio of success:attempts), potential caloric content, and relative abundance of food items. The models vary from mechanistic representations of muscle movement to the different types of prey items. MacArthur and Pianka's equations regarding competition are also considered here. Two polarizing types of foragers are discussed: specialists vs. generalists (generalists favored during fluctuating prey abundance) and large vs. small prey. The feeding rates section addresses the functional response and maximizing fitness based on density.

Optimal Foraging Space
This section considers space and time as the relevant parameters, including home range, path of movement, and patch preference. Schoener first discusses how to estimate home range, which is a complicated enough problem that needs to consider food density, food preference, and metabolism. The path of movement is essentially the maximum distance a predator will move to eat a prey item and the patch preference perspective considers patch quality rather than item type. Here, Schoener mentions (without using this term) area-restricted search (ARS). He also mentions competition here in the form of territoriality.

Optimal Foraging Period
He says very little here, basically saying that no theory has been developed and no significant empirical work has been done.

Optimal Foraging Group Size
Foraging efficiency may decrease with group size if intraspecific competition increases beyond a threshold or if small costs of competition (or benefits of dilution effects) results in even larger group size. Conversely, foraging efficiency may not change with group size because animals distribute themselves equally across the prey distribution. Group size can increase efficiency through behaviors like flushing and pack hunting. Territoriality may again come into play here if the group cooperatively defends a patch. Community foraging (e.g., mixed species flocks) is also beneficial if there is little overlap in foraging preference among group members.


BAILEY ET AL. 2019

Bailey et al. present evidence for a specific case in optimal foraging literature: ARS. This foraging strategy is a non-random search pattern that involves biasing time spent in foraging patches based on encounter rates with prey items. It allows predators to forage more efficiently by spending more time in high density food patches. The authors tested whether two species of dolphins exhibited ARS using two hypotheses: Feeding increases feeding (positive feedback), foraging time increased in a patch after first encounter. They also looked for interspecific differences.

Using recording devices to detect increased echolocation use by dolphins (a reliable measure representing prey encounters), the authors defined separate encounters and used a Gaussian Mixture Model (GMM) to distinguish foraging clicks from other types of clicks. This type of model basically uses machine learning techniques to identify the foraging behavior instead of using an arbitrary cut off interval or eyeballing a spectrogram (this technique is also used to define foraging bouts in bird feeder studies; if anyone is interested, look up Wytham Woods studies). The "behavioral state transition" analysis tested whether feeding behavior led to more feeding behavior with any significance by comparing different behavioral states. The encounter duration was tested by defining a foraging patch, determining when the dolphins started foraging in said patch, and when they left the patch.

The behavioral state transitions were not significant. Dolphins were more likely to end a foraging bout (and therefore leave the area) if the foraging activity greatly increased between the first and last halves of the encounter.

The authors keep toting the novelty of their marine species study, which is a cool example, but I was hoping for other broader impacts for optimal foraging theory. I wish they had incorporated more social/spatial memory into the analysis, especially because they mentioned the impact of memory on ARS in the intro. However, I liked the use of localized interactions to model ARS because foraging is generally a mix of individual encounters, and the incorporation of pairwise associations was a welcome representation of the social interactions of a very social species. The authors go on again in the discussion to suggest that there is evidence to support ARS because of the likelihood to spend more time foraging in area after the first prey encounter. ARS is expected to occur when prey is not equally distributed across a patch (one assumption of classic optimal foraging models), which is consistent with their primary prey's schooling behavior. There may have also been seasonal variation in prey density that could have altered results.


Comments
I thought Schoener's approach to energetics was approachable because he eased us into the calculations with a well set-up background that was both relevant and easily digestable. I enjoyed how he integrated life history into energetics, which was consistent with how energetics has been presented to me in past lectures. However, the ending was a bit abrupt for me. I wanted a quick wrap-up at the end with some future directions and broader impacts. I was overall disappointed in the Bailey et al. paper because the intro set the story up to be really amazing, but I was a bit let down with the results and discussion that did not seem to broaden these results out to any other species or system. It left me wondering how much effect the charismatic species had on the publication process.

Ehrlich & Raven 1964 and Maron et al. 2019

Ehrlich and Raven (1964) and Maron et al. (2019) Blog Post 

Kat Jordan 

Foundations of Ecology Paper: Butterflies and Plants: A Study in Coevolution

Ehrlich, P. R. and Raven, P. H. (1964), Butterflies and Plants: A Study in Coevolution.     Evolution, 18: 586-608. doi:10.1111/j.1558-5646.1964.tb01674.x

Companion Paper:Plant–herbivore coevolution and plant speciation

Maron, J. L., Agrawal, A. A., and Schemske, D. W.. 2019. Plant–herbivore coevolution and         plant speciation. Ecology 100( 7):e02704. 10.1002/ecy.2704

Author Backgrounds:

            Paul R. Ehrlich is a population biologist from Stanford University in California. He is also the president of Stanford’s Center for Conservation Biology. He is perhaps most famous for his book (coauthored with his wife Anne Ehrlich who received no credit) The Population Bomb(1968) in which he discusses the potential ramifications of human overpopulation and proposes solutions to limit the population increase. Though criticized, the book created a dialogue regarding impacts of human overpopulation and climate change. 

            Ehrlich’s coauthor is Peter H. Raven, also from Stanford University. Raven is a botanist and an environmentalist who was once the director of the Missouri Botanical Gardens (beginning in 1971 after leaving Stanford). His primary research has been in preserving biodiversity in plants and species conservation. Undoubtedly, his most famous work is the one we are reading at present.
            The first author on the companion paper is John L. Maron from the University of Montana. His lab generally focuses on plant population and community ecology, although research topics have broadly included food web ecology, community assembly, and many others. 

Ehrlich and Raven (1964) paper: 

            The goal of this paper was to explore evolutionary interactions in a community ecology setting. Previously, much of community ecology had focused very on one group of organisms at a time, and had not explored the interactions of groups of species over time (i.e. their evolutionary relationships). To do this, Ehrlich and Raven focused on butterflies and their food plants, as the title eludes to. They attempted to answer four questions laid out in the beginning of the paper (paraphrased here): 

1.     What can be learned about the evolutionary relationships of intimate organisms? 

2.      Can one make generalities in community ecology? 

3.      Without a fossil record to rely on to determine time and rate of evolutionary change, can uncovered patterns be useful to understanding the evolution of either group?

4.     Is studying coevolution in groups useful for understanding their community ecology(-gies)? (see pg. 586, Ehrlich and Raven (1964) for original questions).  

            The authors began by examining the diversity of butterflies and their food plants. Much of the paper described butterflies, by family, and the food plants the members of the families utilize. To do this, the authors performed a very thorough literature review. After the descriptive section of the paper, the authors discuss any patterns observable in all the data. What was found was a relationship between biochemical aspects of some plants and the utilization of these plants by some butterfly groups. The evolution of plant groups used by butterflies lead to an evolutionary response by some butterflies to overcome obstacles in feeding on their preferred plant type (or made a switch to another plant type). Increased specialization would have been the result in some groups of butterflies (and plants), leading to the authors to comment on the role coevolution plays in increasing diversification. Consequently, some butterfly groups may have used the biochemical novelties in plants to change their coloration (i.e. their own defense against predators). The authors answer their questions one by one near the end of the paper: 

            1a.  Plant biochemistry has been a critical component in the evolutionary relationship of                     butterflies and their food plants. 

            2a.  Results cannot be predicted with great precision. In essence, weird things can                             happen. 

            3a.  The absence of the fossil record makes it incredibly hard to test predictions or further                   specify the relationships proposed in the paper. 

            4a.  Studying coevolutionary relationships among groups provides an excellent way to                        start understanding their community ecology. 

            In summary, the authors conclude that coevolutionary patterns have been vastly underrated especially when studying community ecology. Without taking into account organisms and their evolutionary responses to one another (i.e. predators and their prey), the study of community ecology is not quite complete. 

Moran et al. (2019) Companion Paper

            The Maron et al. (2019) paper is the most recent follow up to the Ehrlich and Raven (1964) paper. The paper begins by reiterating the latter paper and then proses that the role of plant defense in plant speciation is poorly understood. Maron et al. (2019) also present the shortcomings of the Ehrlich and Raven paper, such as the logical jump from appearance of the trait (i.e. chemical defense in plants) to the evolutionary response of their herbivore (butterfly) without discussing the mechanism in which allowed the trait to occur. The purpose of this study was to understand how the evolution of plant defenses can impact plant speciation. To do this, the authors expand upon six pathways prosed in Marquis et al. (2016). The pathways are as follows: 

1.     Herbivore defense and pollinator attraction 

2.     Coupled herbivore defense and phenological changes or resource allocation to pollinator attraction 

3.     Coupled defense and stigma-pollen interactions 

4.     Selection against hybrids in hybrid-zones 

5.     Defense evolution in parapatry

6.     Geographic mosaic selection in allopatry

            The authors then discuss the role of geographic isolation in leading to speciation They state that populations that become reproductively isolated and become specialized to a new geographic area. Increased specialization (i.e. specialized plant defense for local herbivores) may lead the plants to become more reproductively isolated since they are maladapted to other regions (i.e. restriction of gene flow). The authors then present three scenarios in which plant-herbivore interactions may contribute to speciation (see Figure 1): 

1.     Spatial differentiation in herbivores and herbivore pressures in an ancestral range can lead to different adaptation among plants based on what herbivores are encountered. Eventually, the divergence of these populations may be large enough to cause speciation. 

2.     Plants disperse into a geographic area with little to no herbivores so reduce their energy investment in defenses. This allows the plants to adapt to their new environmental conditions Eventually, herbivores will attack again and new novel defenses will evolve in the plants. 

3.     A new defense occurs (via mutation) and the plant population increases. Plants may expand into new areas where their ancestors could not. The result could be multiple speciation events. 

            Moran et al. (2019) summarize the paper by synthesizing this information into one key idea: these are possible mechanisms that Ehrlich and Raven did not mention in their paper. Further directions are proposed in which the authors report unanswered questions that still need investigating. 

My Thoughts:  

             Both papers provide a look into an area I am not familiar with: plants and their interactions with insects. However, I found both papers relatable to other aspects of evolutionary biology. That is to say, I believe these theories are broadly applicable to other living organisms and to understanding predator-prey coevolution. I liked working on the Ehrlich and Raven paper especially. As this class progresses (and as we move through the Principles of Ecology book), we are beginning to read papers where a lot more variables are taken into account when studying ecosystems. Instead of reading about single species and their interactions with their environments, we are now delving into a more complicated topic of the mutual history among different species (i.e. their coevolutionary history). I wonder if there have ever been discoveries about evolutionary relationships of more than two groups, but that is just a personal musing of mine. There are issues and questions I have, but I will save these for class. It will be great to hear others interpretations of the texts, especially those who have some more knowledge about plant or insect biology. 

Hairston et al. 1960 & Shochat et al. 2010

Blog Author: Elizabeth Chambers

Principles of Ecology

Hairston et al (1960) and Shochat et al (2010)

Citations:

 Hairston, N.G, et al. 1960. “Community Structure, Population Control, and Competition.” The American Naturalist. Vol. 94 No. 879: 421-425.

Shochat, E. et al. 2010. “Invasion, Competition, and Biodiversity Loss in Urban Ecosystems.” BioScience. Vol. 60 No. 3: 199-208

Author Background:

Nelson G. Hairston was an American ecologist who worked at the University of Michigan and later at University of North Carolina. He was interested in trophic interactions in ecological communities and was a major proponent of the concept of trophic cascades. Additionally, he served as a World Health Organization advisor for the United Nations, where his research focused on disease dynamics and the factors that contribute to the spread of human disease.

Eyal Shochat is an ecologist currently working at the Ben Gurion University of the Negev in Israel, and is also connected to Arizona State University as an independent researcher. His research largely focuses on how wildlife populations change in response to urbanization and other anthropogenic global change in their habitats, with a focus on bird populations in particular. 

Hairston et al:

The authors’ goal was to study what drives populations to be limited in their size. The authors note that previous studies had only focused on single-species populations and argue that it is important to study the community as a whole and to use a multi-species approach in analysis, taking into account the influences from different trophic levels on the system. The paper approaches the trophic levels by dividing organisms broadly into three groups: plants, herbivores, and predators. In modern ecological terms, these may also be described as primary producers, primary consumers, and secondary consumers, respectively. 

They observe that (almost) all energy fixed by photosynthesis conducted by the primary producers flows through the entirety of the biosphere and, as such, the totality of all organisms in a community will be limited by the amount of energy that is produced and which flows through the system. For the primary producers, they identify light and water as the limiting factors to their growth.

They argue that herbivores are generally not directly limited by the amount of food available to them, citing the vast amount of green plants and the rarity of these plants becoming depleted indicating that herbivores typically do not over-graze. Rather, herbivores are limited by predation and not resources. They use examples of insect and rodent outbreaks following predator removal as evidence of predation acting as a limiting factor upon the primary consumers. On the other hand, predators and parasites are food-limited, with their population sizes being limited by the number of available prey/host species in their community. Finally, decomposers are food-limited as well due to the finite amount of organic debris in a community. Their overall conclusion drawn from this discussion is that all terrestrial organisms “are resource-limited in the classical density-dependent fashion.”

                  They go on to describe the impact of these resource limitations as a cause of competition between species. Many different species may inhabit the same trophic level and will have overlap in their niche space. This niche overlap, combined with limited resources, will results in interspecific competition and attempting to out-compete other organisms which will drive natural selection and evolutionary change as species must adapt in order to survive in the competitive environment. 

Shochat et al:

This paper focused on urban environments and the impact that urbanization has at the community level, rather than simply focusing on the effect of habitat loss on the species level. Compared to wild areas, urban areas tend to have a higher population density of  total animals, but lower biodiversity. The authors wanted to determine what effect interspecific competition for resources had on biodiversity in urbanized environments and how this may explain the loss in diversity in cities. They hypothesize that urban environments have conditions which favor a small number of synanthropic or invasive species which can strongly out-compete other native, non-synanthropic species. The population size of these successful urban species will increase—leading to the higher total community population—while the species that cannot compete in an urban environment will see population crashes—leading to the lower overall species evenness.

Methods: The authors used two Long Term Ecological Research sites, Phoenix, AZ and Baltimore, MD for sources of population abundance data. Areas within the cities and suburbs were classified as urban, and undeveloped lands outside of the cities were classified as the wild habitats. The Arizona portion of the study focused on two different taxa, spiders and birds, while the Maryland portion just focused on birds. They analyzed species distribution rank of these two areas in order to determine the evenness and overall diversity of the communities. Additionally, they begin by tying in a brief review of other ecological papers and theories which back up their hypotheses in this article.

Results: In the wildland of Arizona’s Sonoran desert, species evenness of spiders and birds was greater than in urban Phoenix, while the city had a greater total population density for both taxa.  The study of Baltimore’s birds had very striking results following the same pattern, as just over half the total urban bird population was comprised of 3 invasives. Statistical testing showed that all of these results were significant. Optimal foraging studies previously done by Shochat show that common urban bird species are more efficient at obtaining food compared to desert species. This increased foraging efficiency allows the common urban species to out compete other birds and to dominate the city environments.  

Discussion: The authors stress the importance of considering species evenness and the community profile of environments rather than looking at the number of species present in an environment. Resources and predation can limit the populations of synanthropic species in the wild which maintains the evenness of the community. In urban environments, these pressures are lessened for the synanthropic species, which allows them to thrive and dominate their communities and competitively exclude others, leading to a loss of evenness.  

My Thoughts:

Both papers discussed the biodiversity of ecological systems, limiting factors for populations, and the effects of competition. Hairston et al really stuck out to me as product of its time – many of the general ideas are used in ecology today, but it was presented in a fairly simple manner and broadly lumped organisms into three big trophic levels, without going into detail on the effect of dynamics such as predators which are themselves prey to another consumer. This is a stark contrast to the more complex food webs that are discussed in ecology today. Shochat et al takes a heavy focus on the Anthropocene and how humans are changing communities in vast ways, in contrast to the more “hands-off” observational way that Hairston et al describe ecological communities. 

Hutchinson 1959 + Schneider et al. 2016

Blog author: Yuguo Yang

Citations

Hutchinson GE. 1959. Homage to Santa Rosalia or Why Are There So Many Kinds of Animals? The American Naturalist93: 145–159.

Schneider FD, Brose U, Rall BC, Guill C. 2016. Animal diversity and ecosystem functioning in dynamic food webs. Nature Communications7: 12718.

Author background

G. E. Hutchinson was a famous British ecologist and a professor in zoology at Yale University. He is highly reputed for his contribution on niche theory and species coexistence studies.

F.D. Schneider is an ecologist and environmental scientist at ISOE Institute for Social-ecological Research in Germany. He works on biodiversity valuation and ecological transformation. His recent studies focus on ecosystem degradation and biodiversity loss.

Hutchinson 1959

The goal of this paper was to figure out what drives the high richness of species in the world and what limits the species diversity. He derived his idea from Voterra-Gause principle that sympatric species evolve to occupy different niche (defined by food) due to natural selection, isolation, and invasion. He argued that the food relationship was not enough to explain the high diversity of species.

The theory of food chain was proposed by Elton (1927), in which species at the higher levels of food chain were larger and rarer than species at the lower levels. Hutchinson listed a couple of factors that would limit the length of food chains. First, it was assumed that no more than 20% of energy could pass through one link of the food chain. In this case, the food chain theory cannot support the high species diversity because of the length of food chains were strictly limited by energy. Also, the energy flow could not be higher because the increase of predators’ efficiency would cause the decrease of the prey population and ultimately extermination of the prey. Second, animals would change size during their life history, the term that he called “metaphoetesis”. In this case, animals may change their position in the food chain. He further argued that the diversity of plants (basal food source in the food chain) was not sufficient to explain the animal diversity because, in his point of view, the “kinds of food” provided by plants were limited.

Hutchinson started illustrating his ideas by introducing McArthur’s point of community evolution: more efficient species take over the less efficient one, but more stable community outlast the less stable one. In Hutchinson’s opinion, the reason for high species diversity was that diversified communities were stable and persisted longer than less-diversified communities. Then he also talked about the limitations of diversity: length of growing season, total biomass in the system, growth form of plants, environment rigor & stability, refugee availability in the harsh environment, etc.

3 main conclusions were drawn from his paper: 1. the reason for diversity is that a diversified community is stable. 2. Evolution of communities increase stability (a more complex system derives from the less complex one). 3. It is easier to have a high diversity for small than large organisms.

Schneider et al. 2016

Schneider’s paper focused on the consequences of animal species lost on ecosystem function. The authors tried to answer this question by studying what would happen after increased animal diversity. There are 2 theories of processes that counteract with each other: 1. Increased animal diversity will increase the complementarity of herbivores (herbivores become more exploitive to the resources), which has a top-down control of plant communities. 2. High animal diversity will increase feeding rates within the consumer guild (within animals), and thus release plants from grazing pressure. The goal of this paper was to investigate which of the processes is stronger after increasing animal diversity.

Methods

            The authors developed a dynamic food-web model using body mass as the only differentiating parameter for species feeding traits and physiology. i.e. it assumed that animals with the same body mass were identical. Also, the model assumed that most animals were omnivores (50% strict herbivory were tested as a comparison). The authors investigated 6 major variables in response to increasing animal diversity: total animal biomass, total intraguild predation, total animal metabolism, total plant biomass, total feeding on plants, and total plant metabolism. They also simulated the response of average body mass of plants and animals.

Results 

            3 main results were reported as the response to increasing animal diversity: 1. total plant biomass stayed the same. 2. animal metabolism increased, possibly due to increased respiration and intra-guild predation, and average animal body mass increased. 3. plant metabolism decreased but average body mass increased, indicating that more small plants were consumed than large plants.

Discussion

            The results of this study indicated that diverse animal species would gain more total biomass and become more exploitative on plants. But at the same time, high intra-guild predation existed. The diversified animal species would not reduce plant biomass (top-down control did not increase), assuming most of the animals are omnivores (when applying 50% of the animals to strict herbivores, total plant biomass decreased in response of increased animal diversity). However, the decreased plant metabolism and the increased average body mass indicated that plant communities shifted in favor of large plants.

Comments

Both papers studied the animal diversity and food webs. Hutchinson’s paper is more descriptive and qualitative about the ecological theories which helps me understand the background of these processes. However, I find it a little disappointed about his explanation of what drives diversity. To me, “stability” is the result of diversified communities rather than the cause. I would expect an explanation that focuses more on the process itself. 

            I chose Schneider’s paper as the companion paper because it covers a lot of similar concepts and the authors tested the balance of 2 processes using simulated data. The results were clear and impressive, although I expected more explanation on some of the details, such as why the diversified animal communities tend to consume more small plants than large plants. My another concern is the assumption that most animals are omnivores, which is not plausible, but I do not know a better way to modify this part of the model.

Skellam 1951 & Duckworth and Badyaev 2007

Blog Author

Lyndsie Wszola

Citations

Skellam, J.G. 1951. Random Dispersal in Theoretical Populations. Biometrika 38(1/2): 196-2018.

Duckworth, R.A., and A.V. Badyaev. 2007. Coupling of dispersal and aggression facilitates the rapid range expansion of a passerine bird. Proceedings of the national academy of sciences 104(38):15017-15022.

Author background 

John G. Skellam was a statistician and ecologist. He modeled populations using a novel stochastic framework called the reaction-diffusion model. In Skellam’s reaction-diffusion model, population dynamics give rise to the forward force of invasion fronts, depending on the species’ interactions with the environment. 

Renée A. Duckworth is an evolutionary ecologist and associate professor at the University of Arizona. Her research centers around understanding the evolution of complex traits, especially behavior, by studying eco-evolutionary feedbacks in range expansions through large-scale field and lab studies.

Skellam

The Skellam paper introduces the idea of the random walk as a way to study animal dispersal. Random walks are a path-dependent process where individuals move through space choosing each step according to either random processes or a probability distribution. Skellam considers the need for variation in random walk size steps, and uses the concept of the random walk to simulate a population’s range expansion as the population grows. Skellam portrays the expanding population much like gas particles moving through space, and provides a series of case studies, including acorns and small mammals, demonstrating that as populations grow, they must necessarily expand. He finally discusses limits on population growth and works to derive solutions for equilibria in populations. 

Duckworth and Badyaev

The central question in the Duckworth paper was whether behavior might help explain why western bluebirds have been expanding their range into landscapes traditionally dominated by mountain bluebirds. They conducted a large-scale field study in Western Montana assessing aggression and reproductive success in both species. Dispersal of western bluebirds into mountain bluebird habitat, and the resulting displacement of mountain bluebirds, was caused by an eco-evolutionary feedback between behavior and reproductive success. More aggressive male western bluebirds dispersed to the invasion front, where they displaced less aggressive mountain bluebirds. After the western bluebird population became established, aggression was less adaptive, and the population mean aggression declined. The paper concludes that this rapid cycling in adaptive behaviors is the driving force behind western bluebird, and perhaps other passerine, expansions. 

My thoughts

I think these papers form a fascinating counterpart to one another and demonstrate a central pattern in modern ecology. Traditionally, the study of population dynamics has treated individuals as uniform, much like the gas particles whose models give rise to our first dynamic population models. This viewpoint is strong in Skellam’s paper, which takes its central idea, diffusion, from physics and chemistry. In contrast, Duckworth’s paper demonstrates two increasingly central components of modern ecology: incorporating variation and eco-evolutionary feedbacks. I really enjoyed reading the two together because they demonstrate how incorporating variation in models can lead to more accurate predictions. 

Volterra 1926 & Scheuer and Stolzer 2019

Blog Author

Stella Uiterwaal

Citations

Volterra, V., 1926. Fluctuations in the Abundance of a Species considered Mathematically. Nature118, 558–560. https://doi.org/10.1038/118558a0

Scheuerl, T., Stelzer, C.-P., 2019. Asexual reproduction changes predator population dynamics in a life predator–prey system. Population Ecology61, 210–216. https://doi.org/10.1002/1438-390X.1017

Author background:

Vito Volterra was an Italian mathematician who worked developed new mathematical analysis methods, applying them to physics and biological mathematics. He was also in the Italian air force during World War I and fought against fascism in the 1930s – the last years of his life. In ecology, he is best known for his work on predator-prey models.  

Thomas Scheuerl is an evolutionary biologist with ties to the Imperial College London in the UK and the Unniversity of Innsbruck in Austria. He works primarily with bacteria and rotifers. His work typically focuses on questions around adaptation and the benefits of sex.

Volterra

Volterra’s system has a resource and a consumer. The resource reproduces indefinitely by itself. The consumer would die by itself but can feed on the resource. As the consumer populations increases, resources are more likely to get eaten. As the resource population increases, resources are less likely to get eaten. Populations of the resource and consumer can be described by two equations, which are periodic functions of time with equal periods. 

Volterra describes two types of systems: conservative and dissipative. A conservative system neglects the actions between conspecific individuals while in a dissipative system population increases are dependent on population size. He uses a three species system (resource, herbivore, predator) to illustrate these ideas. If that system is conservative, the predator cannot exist and the resource and herbivore cycle. If that system is dissipative, either the predator goes extinct and the herbivore and resource cycle, both animals die and the resource is left, or all three species coexist and cycle. 

Scheuerl & Stelzer

The rotifer Brachionus calyciflorus can either reproduce sexually (here called a cyclical parthenogen (CP)) or asexually (obligate parthenogens (OP)). The two clones differ in sexual propensity and therefore possibly also differ in population growth rates, since reproduction is not limited by sexual induction in the asexual clones. The authors studied how this may affect predator-prey population dynamics at three different nutrient levels using the algae Chlamydomonas vulgarisas prey.

To do this, the authors set up chemostat populations containing rotifers, algae, and nutrients. An automated sampling system counted predator populations and algal populations were measured using a photometer. They found that asexual populations had greater variance around the mean (that is, higher amplitudes), but other parameters were similar between the two clones. They further found that differences between population dynamics of sexual and asexual rotifers was highest at low nutrient levels. 

My thoughts

I enjoyed reading Volterra’s classic paper after reading many other papers that are based on his work. I also found the additional complexity of sexual versus asexual reproduction to be a thought-provoking twist to the rather basic population models presented by Volterra.  Volterra’s work appeals to me because, although it is much too simplified to accurately represent real populations, it is a great way to visualize the forces that play into population fluctuations. It is also easy to add complexities (and therefore reality) to the model, such as the inclusion of sexuality. 

MacArthur and Pianka 1966 & Rodriguez et al. 2019

Blog Author: Crystal Uminski

Citations: MacArthur, R.H., and Pianka, E.R., “On optimal use of a patchy environment.” The American Naturalist, Vol. 100 No. 916 (Nov-Dec 1966), p. 603-609. 

Rodriguez, J. et al., “Does optimal foraging theory explain the behavior of the oldest human cannibals?” Journal of Human EvolutionVol 131 (2019), p. 228-239.

Authors: 

Robert MacArthur (1930 – 1972) was an American ecologist who is noted for his work in niche partitioning. (We’ll be reading his paper on niche partitioning in warblers later in the semester.) MacArthur is credited with establishing the use of the hypothetico-deductive (H-D) method (a process of testing predictions based on existing theory) in the field of ecology. MacArthur was considered a pioneering leader in establishing hypothesis-driven science and worked to provide other ecologists with examples of how H-D science should be conducted. MacArthur first used the H-D method in his 1957 paper, “On the relative abundance of bird species.”  In the six years prior to MacArthur’s paper, Fretwell (1975) estimated that only 5% of papers published in Ecologyinvolved testing a hypothesis. MacArthur helped to steer ecology away from observation-based work (such as the style used by Clements) and towards experimentation. Eric Pianka (b. 1939) is an American evolutionary ecologist who completed post-doctoral work with Robert MacArthur at Princeton University. Pianka has published over 200 scientific papers and is noted for his work on desert lizards. Pianka has been a faculty member at the University of Texas at Austin since 1968.  

Jesus Rodriguez is a Spanish biologist who specializes in the paleoecology of European Pleistocene mammals. He has researched the evolution of mammalian community structure and the influence of climate change on the extinction of megafauna, but now studies human-carnivore interactions using mathematical models. Rodriguez is currently a curator at the National Research Center on Human Evolution in Spain.

MacArthur and Pianka (1966): 

MacArthur and Pianka created mathematical models to determine the optimal utilization of time and energy budgets for a species. Their work is the foundation for optimal foraging theory. In “fine-grained” environments (where the prey species are located in the proportion in which they occur), the time predators spend eating each item is divided into search time (T_N­­^S) and pursuit time (T_N­­^P). When additional prey items are added to the diet (N+1), the change in search and pursuit time can be calculated. When predators increase their diet to include a larger number of prey options, search time can be reduced but pursuit time can increase (some of the additional prey items may be more difficult to find or catch). Figure 1 shows that in a hypothetical predator in a fine-grained environment, the optimal diet contains 4 prey species. Increasing the number of prey species would cause a greater increase in pursuit time than a decrease in search time (which is not beneficial to the predator). The S’ curve in Figure 1 represents a scenario where the density of the prey species is reduced by half. The inclusion of S’ shows that the number of prey species in the optimal diet is not static – in the S’ scenario, the optimal diet includes 5 prey species. 

In patchy environments, the hunting time (H) increases when the predators are in less-suitable patches. Delta H represents the increase in hunting time per item when an additional patch of environment is added to the predator’s itinerary. The optimal diet in patchy environments is determined by comparing the change in hunting time to the change in travelling time (T) per prey item caught. Figure 2 shows that in a hypothetical predator in a patchy environment, the optimal number of patches in the itinerary is 3. Increasing the number of patches would decrease the travelling time but increase the hunting time. 

MacArthur and Pianka concluded that in productive, fine-grained environments, predators with low search/pursuit ratios should be more restricted in their diet, but this conclusion does not hold in patchy environments where predators spend most of their time searching. Predators with large pursuit/search ratios should show restricted patch utilization in productive environments where food is dense. Optimal predators that have competition for food sources will shrink patch utilization but not the number of prey items in the diet.

Rodriguez (2019):

Rodriguez uses the framework of optimal foraging theory, as well as the lens of human behavioral ecology, to explain cannibalism in an ancestral human species. Rodriguez’s paper relies on the assumptions in MacArthur and Pianka’s paper about prey choice and prey availability and aimed to answer whether humans were a high- or low-ranked prey type in the diet of ancient hominins. If humans were a high-ranked prey type, this would support the theory of nutritional cannibalism, but if the humans were a low-ranked prey type, this indicates a scarcity of the higher-ranked prey types and that cannibalism was a last-resort mechanism for survival. 

The different prey species in the ancestral human diet were accounted for in the remains identified at an archaeological site. The seven sets of human bones at the site that had “anthropogenic modification” were considered the cannibalized humans. The remains of 9 other mammal species that were larger than 5 kilograms and had evidence of anthropogenic modification were classified as the other prey types. The caloric content of human and non-human prey types was calculated. MacArthur and Pianka’s model assumes that the predator encounters the resources at random in proportion to the resource abundance in the environment, so the amount of each prey type at the archeological site is assumed to be in proportion to the amount of that prey type in the environment. Rodriguez used a random encounter model to predict theoretical prey densities. 

Rodriguez found that rhinos and bison were high-energy prey and that human individuals provided a “moderate amount of energy” (about 13% of the accounted calories). Compared to other prey species, the humans represented a high-ranked resource. Following the Prey Choice Model, high-ranked prey are harvested on encounter. The lower-ranked non-human prey were consumed in proportion to their abundance in the environment, but the high-ranked human prey were harvested in a proportion higher that expected based on estimated abundance. Humans were positively selected as a prey option. Rodriguez proposes that even though humans were a lower-calorie food source, there was a low cost of acquisition, which made humans a higher-ranked prey option. 

The nature of human behavior may have violated the assumptions of random encounter, which contributed to the higher-than-expected number of human prey at the archaeological site. The human victims may have been individuals of the same group as the cannibals and died of natural causes (and if this is the case, the energetic cost of “hunting” this prey is zero). Rodriguez concluded that ancestral humans followed the principles of optimal foraging theory and that cannibalism can be thought of as an adaptive strategy. 

My thoughts:

After reading a biography of MacArthur which emphasized his importance in the movement of hypothesis-driven science, I was a surprised to see that this paper was so heavily grounded in theory. MacArthur did hint at a need for experimentation, indicating that the delta P value “must be empirically determined” for each species, but other than a brief mention that there is “evidence for this from herons,” MacArthur uses mathematical models to explain optimal diets of predators rather than empirical data collected from experimentation. 

I am not very familiar with the field of archaeology, but I did question whether Rodriguez’s results could have been affected by a preservation bias in the fossil record? Were human fossils more prevalent because human fossils were more likely to be preserved than other species? 

In most of the papers that we have looked at in class so far, humans are considered exceptions to the ecological frameworks. It is interesting to see how human behavior (even if it is an ancestral species of human) can fit into the principles of optimal foraging theory. Although modern humans don’t necessarily “hunt” for food, can optimal foraging theory still explain some of our food-seeking behaviors today? There’s a whole host of socioeconomic factors that contribute to the “food desert” effect in urban areas, but can some of the concepts of optimal foraging theory be applied to explain why low-cost, high-calorie, processed foods are so prevalent in certain areas?