Blog author: Annie Madsen
Citations:
Nicholson, A.J. & Bailey, V.A. 1935. The Balance of Animal Populations. Proceedings of the Zoological Society of London, 105(3):551-598.
Okuyama, T. 2017. Egg limitation and individual variation in parasitization risk among hosts in host-parasitoid dynamics. Ecology and Evolution, 7(9):3143-3148. doi: https://doi.org/10.1002/ece3.2916
Background
Alexander John Nicholson was an Australian entomologist who largely studied population dynamics of insects. He studied zoology at the University of Birmingham and received an honorary D.Sc. from the University of Sydney in 1929. Much of his work regarded the Australian sheep blowfly (Lucila cuprina) and host-parasite interactions. Victor Albert Bailey was a British physicist who worked with population dynamics and ionospheric physics (regarding the transmission of radio waves). He earned his Ph.D. at Queen's College in Oxford in 1923.
Toshinori Okuyama is currently an assistant professor of Entomology at National Taiwan University. His research is self-described as meeting at the intersection of behavioral ecology and population biology and his research focuses mainly on species of jumping spiders.
Nicholson & Bailey
Intro
Nicholson opens with criticisms of previous mathematicians' work describing population dynamics (especially Lotka and Volterra). Main criticisms include former mathematical equations are too broad, do not test specific populations, do not consider competition, and disregard host-parasite interactions.
Section I
General assumptions by the authors included that animals require food, mates, and habitat, searching is always random, animals interact with each other and the environment, animals easily find mates at steady state of population density, and offspring do not search for food because they are born amongst an abundant food source (inside body of host). Animals also had the following properties: areal range, volumetric range, area of discovery, and power of increase.
The authors provided a differential equation describing how intraspecific competition resulted in diminishing returns, which was an improvement on Volterra's model that considered density to increase indefinitely. The authors next acknowledged that individuals likely differ in searching efficiency and that objects differ in how difficult they are to find, which contribute to the dimishining returns of the searching animals and dampened interspecific oscillations in the system. However, they excluded these factors from the model at first for simplicity's sake. Likewise, satiety and hunger may have influenced oscillations but are not considered until later.
Section II
The authors determined the steady state of a closed system for one host and one parasite. Other assumptions here include that egg supply is unlimited and the numbers of encounters is proportional to the number of hosts destroyed and number of offspring produced because these processes are coupled. The steady state is defined as the density of host species that can maintain a density of parasites which only destroy a surplus of hosts. The system is not dynamic under this definition and oscillation of the two species is considered unstable.
The authors also tested several conditions to understand various aspects of life history affect population dynamics, including fecundity, number of times a host can be attacked, juvenile ("fledgling?") success, demographic stochasticity of hosts, and the length and synchrony of the effective period of the parasite and vulnerable period of the host.
Section IV
This section investigates the population dynamics when populations are not at the steady density. The authors roll back the models to only include one host and parasite species again. The populations oscillated at a steady quarter period but the magnitude of the population density became greater over many generations.
These same relationships were then tested by adding more interactions including a specific condition with a hyperparasite and a general parasite with two different hosts. They discussed the oscillation process and were suspicious of the application of their simulations because the increased density magnitude over many generations did not describe what they considered to be actual population dynamics. The relative densities should have oscillated around the steady densities. The two-host system resulted in three different outcomes: oscillation increased, oscillation decreased, and convergence at the steady state.
Section V
The authors claim that continuous interaction with the host must consider both the time delay of food intake and the effects of age distribution (apparently this was Volterra's fatal mistake). With these conditions, the number of parasites needs to be either equal to or greater than the number of species of hosts in order to achieve a steady state.
Okuyama 2017
Egg limitation has been shown to destabilize consumer-resource dynamics, but can interact with individual variation in parasitoid foraging success to restabilize the system. Okuyama investigated a flipped perspective of this: the interaction between egg limitation and individual variation in host parasitization risk.
Okuyama translated the Nicholson-Bailey model into an individual-based model (IBM) to investigate individual variation. Parameters included number of eggs, mortality factor of eggs, host encounter rates, and the number of hosts in each generation. The foraging success of parasitoids was described by a negative binomial distribution and the parasitization risk of hosts was described by a multinomial distribution. Stability was quantified as the persistence of both hosts and parasitoids throughout the simulation.
Persistence and therefore stability in the system was not possible with density-dependent individual variation in foraging success, absence of egg limitation, and absence of variation in host parasitization risk. Egg limitation was shown to destabilize consumer-resource dynamics via the dilution effect (e.g., that parasitoids lose efficiency with increasing host density) but stabilized dynamics when there was variable host risk of parasitization.
Thoughts/Synthesis
The main difference between Okuyama's work and Nicholson & Bailey's foundational paper is the consideration of individual variation in behavior. Nicholson and Bailey assume within the construct of their model that individuals vary, but the variation is negligible at the population level. However, Okuyama tranforms the model by applying a more complex systems approach where he assumes that the population level processes are emergent from individual behaviors. Necessarily, Nicholson and Bailey (1935) is much more comprehensive because it pioneered the models of population dynamics in the more specific host-parasite system. Without being more immersed in the parasitism literature, I can't say definitively where and when these models and assumptions break down. However, the Nicholson and Bailey models are apparently used in predator-prey systems as well. The more specific cases of superparasitism and the proportional relationship of host encounter to egg success seem like they would break down in these cases, but the general functional response still holds some truth in modern systems.
The 2 papers incorporated mathematical models to study host-parasite and host-parasitoid interactions. Nicholson and Bailey built detailed mathematical equations and derived population density curves arithmetically on many different situations of host-parasite interactions. Okuyama added individual variation into Nicholson and Bailey’s model analyzed host-parasitoid interactions specifically under the assumption of egg limitation.
ReplyDeleteBoth papers described different host-parasite or host-parasitoid interactions based on some assumptions without listing any examples in nature, and then used mathematical equation to estimate the results. Compared with previous papers we read from the book, Nicholson and Bailey moved a step forward because their study gave us something we could test after collecting our own data. However, maybe because I am not familiar with host-parasite interactions and I am not working on mathematical modeling neither, I think my biggest concern about both papers is how applicable these situations could be in the real ecosystem. It is good that Okuyama cited some studies about superparasitism in the introduction, which provided some nature background of their model. But many other studies cited are also about mathematical modeling. In my opinion (maybe I am wrong), it is necessary to test whether these hypothetical host-parasite or host-parasitoid interactions exist, how often these incidents happen, and what are the most general situations in nature.
I've always enjoyed reading modern papers which directly build on work from several decades ago. It is neat to see that old ideas are still applicable and refreshing to see what a new perspective can do with such a classic paper.
ReplyDeleteOne of the assumptions that Nicholson and Bailey base their paper on stood out to me. They state that populations do not move systematically, but rather randomly, comparing organized but independent individuals to a fleet of ships. Perhaps I don't quite understand what is meant by "systematic", but I don't think populations necessarily move randomly while foraging. Highly coordinated flocks of birds and ants following each other's trails come to mind as examples. Both learning and social behavior could result in non-random motion. Although some number of assumptions are necessary for models, I think it crucial that these assumptions (at least somewhat) hold up.
I appreciated that the newer paper by Okuyama had a focus on making the ideas presented by Nicholson and Bailery more nuanced and applicable to a real system. I would be very interested to see an empirical test of the ideas presented in these papers!
I would have really like to read Lotka or Volterra before the Nicholson and Bailey. While I am familiar with the subject, I feel it would have given me a deeper understanding. I'm not sure why this paper is before them in the textbook. Additionally, it would have been nice if Nicholson and Bailey gave more explanation rather than assuming the reader is well versed in mathematical models.
ReplyDeleteThe one major issue I had with the Nicholson and Bailey was the statement that populations move randomly. For on thing, the logic they use makes no sense. If individuals move non-randomly than why and how does that result in populations moving randomly? They also completely disregard any social behaviors. Flocks of birds and packs of wolves most certainly do not move randomly. While this assumption may be need for the simplicity of the model, they state it as though it is fact.
I found the Okuyama very simple. And while he has an interesting result, I'm not sure if it worthy of whole paper. Empirical data would have made it much stronger.
-Miranda
I liked the general philosophy behind the approach in Nicolson and Bailey (NB). Namely, that they explicitly described their ecological hypotheses about how animal interactions happen and then used mathematical reasoning to deduce the implications of their hypotheses. I think this approach has two main benefits:
ReplyDelete1. It is clearer than purely verbal reasoning;
2. Rigorously identifies the possible outcomes of
hypothesized ecological processes. This can be helpful for designing empirical studies to identify what processes generate real-world patterns.
For instance, because of the first benefit, it’s easier to notice that their premises may be flawed, e.g., “the searching of animal populations is always random” (I am also confused by their justification). As to the second benefit, this is illustrated by the predictions made in both NB as well as Okuyama. While Okuyama is too recent to expect tests of his predictions, NB has been assessed by fields tests.
I (very briefly) glanced through the first paper with field tests of NB’s predictions (Varley 1947), and the author did find that NB’s predictions were useful. However, I’m not familiar enough with this literature to know what the current consensus is on NB’s model and predictions. Interestingly, Varley argued regular or damped oscillations were more likely than the unstable oscillations predicted by NB, and identified variation in parasitism risk as a process that could stabilize host-parasite population cycles. This process is one of things Okuyama studied in his paper.
- David
Although the Nicholson and Bailey publication and Clements’ paper were published only a year apart, the difference in style between the authors is apparent. While Clements’ work was mostly based on his observations of species, Nicholson and Bailey were strictly within the realm of modeling and included very few (if any) connections to how their modeling connected back to observable interactions of actual species. Following up on David’s comment about the Varley paper, the Nicholson and Bailey models weren’t put into a “real-world” context with species for over a decade.
ReplyDeleteNicholson and Bailey operated under the assumption that egg supply in parasites is unlimited. They even included a statement justifying their assumption, stating that “the egg supplies of parasites are seldom, if ever, very small.” The Okuyama paper acknowledges the Nicholson and Bailey model and mentions that the model assumes that nE is equal to infinity, however, in his own model, Okuyama sets nE to values in the range of 3 to 15. I am very unfamiliar with the world of parasite ecology, but I cannot think of an example of a parasite that would fall into the “egg limitation” category. Again, I’m unfamiliar with the literature of the field, but the extreme difference between 3 eggs and an infinite number of eggs feels a bit dissonant.
It was really neat to read the argument (and see the math behind) one of the earliest frameworks for thinking about parasitoid-host (or predator-prey) density-dependence and population fluctuations in the Nicholson and Bailey paper. I tend to disagree with their second fundamental hypothesis that the searching of animal populations is always random. We now know that there certainly is a degree of randomness, but organisms use various stimuli and environmental cues (scent, pheromones, sound, etc.) when searching for food, shelter, etc. While some organisms are less organized and sensitive to such cues than others, we have discovered much more detail about the complexities of animal communication since they published in 1935. While it is necessary to make some assumptions in developing a model, I think their assertion that it can be assumed parasites have unlimited egg supplies is too broad and does not account for the wide range of differences in reproductive potential among individuals within a population (or body size constraints that affect fecundity, for that matter). When the authors discuss the scenarios that occur when parasitism (or predation) and destructive environmental variables coincide, they conclude that host densities will be minimally affected by the environmental factor. I really think that this scenario is situational and will be influenced primarily by whichever variable is less avoidable (or more detrimental) in a particular system, for a particular host. For example, if the host is in a sheltered, protected environment, it is likely to be more vulnerable to parasitism, whereas if the host is also mobile and foraging, it might be more susceptible to flash flooding or high wind speeds than a chance encounter with a parasitoid.
ReplyDeleteThe Okuyama paper was similar in that it addressed parasite-host population dynamics and the stability of these populations, but an individual-based modeling approach was used to assess the both the interaction between egg limitation and host variation, and each variable independently. One of the assumptions that the author makes – that the number of eggs for each parasitoid is infinite (i.e., all encountered hosts are parasitized) – contradicts his previous statement (that the number of eggs is limited and parasitoids may decide not to parasitize, given smaller number of eggs). While it is almost impossible to develop a robust model that can be extrapolated to the population-level without making some assumptions, this struck me as an oversimplification when dealing with a complex, density-dependent biological system (especially because egg limitation is of particular interest for parasitoids). Overall, he expanded upon Nicholson and Bailey’s models primarily by placing emphasis on individual-level variation that has radiating effects on a population. I would have liked to see more examples of the “testable predictions” he alluded to in the discussion, as he did not give many clear examples of where his models would be most applicable in the future (though we could extrapolate).
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ReplyDeleteThe two papers work well together. Specifically, the Okuyama paper discusses egg limitation which was mentioned in the Nicholson and Bailey paper, but never tested. It is interesting to see the modern paper build on the original paper (using the same equation and variables too). My one major comment (perhaps more of a personal preference) was that the Nicholson and Bailey paper would have benefited from some real-life examples. Though the paper accomplished something important in the field of ecology (i.e. provide a mathematical framework for looking at competition among parasites and hosts), it would have benefited from at least one example. This may be because I am unfamiliar with a lot of the terms/concepts presented in the paper. I always resonate more when an example is provided. This would have also deconstructed the mathematical model down into something more tangible/observable. Are the oscillations presented in the Nicholson and Bailey paper actually happening in a real world setting? That is what I wanted to know when reading this paper. This is not to say that their verbal reasoning did not seem logical (I have come out of this paper pretty convinced), but without a tested example, the paper is all model. It seems to demand a follow-up paper with some tested examples.
ReplyDeleteThe Okuyama paper made me question superparatism. This is a concept I have never heard before and I find it fascinating. How do parasites detect this phenomenon? I did not have any issues with the Okuyama paper, though I find reading the graphs personally challenging. Overall, I found both papers very interesting and the conclusions seemed to make logical sense.
It was very interesting to read a paper from the 1930s that raised criticisms of Lotka & Volterra. The ideas in Lotka & Volterra are taught often in ecology courses, and while I have read and been taught about the limitations of the model and the assumptions it entails, I was unaware that a critical lens had been put on it at a relatively early time period in the history of ecology.
ReplyDeleteAlthough Nicholson and Bailey were critical of some of these assumptions, it was odd that they believed the movement of populations was random -- this is a big assumption to make and as a result will have an impact on how well the model represents nature. There is a degree of randomness in animal movement, but assuming randomness to always be the case does not match up for social/pack animals or in the case of learned behaviors informing movement. I found it strange that the authors would raise the point of limitations in Volterra but still make a large, potentially limiting, assumption for their own model.
Okuyama's paper was an interesting application of the ideas raised in Nicholson and Bailey, although very strongly based purely on the mathematics. I would find it useful to use this paper as a sort of stepping-stone, a point that indicates possibilities for future studies, that is: testing the modeling results published here with a real system and comparing the empirical outcomes in order to get an idea of the accuracy of the modeled results to what we see in nature.
- Elizabeth
The papers form an interesting contrast in their views on complex behavior in biological systems. In the Nicholson and Bailey paper, the authors present mathematical models as a way to parse the "random" or "disorganized" patterns arising from the interaction of multiple organize or directed processes enacted by individuals.
ReplyDeleteIn contrast, the Okuyama paper is an excellent example of how multiple individual-level processes can give rise to emergent behavior of systems. The two papers, when viewed together, tell the story of how ecology as a field is moving from trying to minimize individual-level behavior in analyses to seeking to understand the nature of emergent processes from individual variation.