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.
I thought the Skellam paper made some, what I think of as, pretty obvious observations. First that animal dispersal play a major role in oak dispersal and then that the rates of dispersal are important in secession order. Maybe I'm just biased by modern knowledge. I did really like that he included historical events like the most recent Ice Age, something Gleason and Clements pretty much completely ignored.
ReplyDeleteI really liked the Duckworth paper. When I think of range expansion I generally think about it in mostly abiotic terms. The temperature or rainfall has changed and thus the species must move to survive. I never really think about behavior or that behavior could facilitate dispersal.
-Miranda
DeleteI enjoyed these two papers, as they were some of the first we've read that have incorporated behavior instead of strictly treating organisms as particles which follow the rules of physics. Even the Skellam paper, which, as Lindsey describes treats individuals like gas particles, shows that interactions between species play a fundamental role in dispersal. Such interactions are a central part of ecology as we study it today.
ReplyDeleteI enjoyed the Duckworth and Badyaev paper, since it highlights how we cannot exclusively use principles from physics to explain dispersal
When reading the discussion of range dispersal in small animals in the Skellam paper, I kept thinking of human introduction of invasive species. In Skellam’s example of the wingless ground beetle, he estimated that it would take one million seasons for the beetle’s root mean square distance to increase to 290 miles. When looking at invasive species, humans can increase dispersal of a species by thousands of miles in a single day if an insect is unintentionally transported with international shipments. Skellam did highlight that displacement can occur due to “high gales, floating plant material, the muddy feet of birds and mammals,” but displacement caused by humans is more likely to have a much greater effect on dispersal than any of these non-anthropogenic displacement methods.
ReplyDeleteThe Duckworth paper reminded me of a study on cane toads at the invasion front in Australia (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5210690/). In both papers, the individuals at the invasion front were different from the individuals in the rest of the population. In the Duckworth paper, the invasion-front bluebirds were more aggressive. In the cane toad paper, there were morphological differences in the limb length of the toads at the invasion front compared to other toads in the population. Similar to the Duckworth findings, the cane toad study also concluded that the behaviors that were beneficial at the invasion front (aggression in bluebirds and long limbs in cane toads) are not as adaptive in the established populations.
I really liked the Skellam paper and the fundamental comparisons he drew between the random movement of particles and the movement of populations. However, I did wonder how you would account for the fact that numerous animal species tend to have a home range and – although their movements may be random throughout the day – these movements may take on a directionality later in the day (even if individual steps remain semi-random) as they return to their shelter/nest/den. Lyndsie’s point that so much of population modeling today emphasizes incorporating variation (among individuals/groups) also made me wonder how environmental variability, and the simultaneous range shifts we see occurring in multiple species occupying the same geographic locations today (as a result of climate, habitat fragmentation, competition) could be accounted for in his dispersion models. Skellam seems to touch on the overlapping population expansion aspect briefly with his section on “conditions at a common boundary”, but it still left me with questions on this.
ReplyDeleteThe Duckworth and Badyaev paper was very concise, and got at question that will continue to become very relevant under climate change: what are the mechanisms by which “invading” (range-expanding) species are able to displace “native” (naturalized) species? Their finding that short-term changes in behavior (aggression) across cohorts of males occurs upon establishment and colonization of a new area was really fascinating! However, since their test of aggressive behaviors was accomplished by assessing western bluebird reactions to a tree swallow – and not to mountain bluebirds, which are within their genus – I wondered if testing responses to intrusion of a less-related bird caused different behaviors to emerge than would be shown towards intrusion by a different species within Sialia.
I would like to start by saying I'm a big fan of the Duckworth and Badyaev 2007 paper. While the Skellam paper clearly laid out an important mathematical background, the modern paper provided some interesting insights into how the model has evolved. Additionally, the idea of behaviour as an adaptation (in this case aggression for those male blue birds with expanding ranges) was absolutely fascinating to me. I find phenotypic traits are often studied when it comes to adaptation and speciation (of course this is because I typically look at paleo studies where phenotypes are primarily what remains). To correlate aggressive behaviours and range expansion made for a fun read, especially with the context that range expansions are hard to observe in real time. In paleontology, we sometimes reap the benefits of dealing with large schemes of time where we can hypothesize about range expansion and speciaiton (a particular area of interest of mine because it was what I focused my Master's thesis around). The challenge in ecology seems to be observing this phenomenon in real time while also trying to understand the behaviours that can go along with range expansion.
ReplyDeleteThe Skellam paper, on the other hand, was a bit dense, but it provided many important ideas about random walk and range expansion which are still used today. There was one point of confusion for me in the Skellam paper. On page 198 (not the book's numbering, but the original paper's numbering), Skellam says that a slight systematic drift is ultimately the most important cause of displacement. I was unsure if he meant displacement geographically speaking (i.e. the cause of a range expansion) or displacement in some other sense (e.g. mathematically or genetically). There is a chance my mind is too focused on the evolutionary idea of allopatric speciation via geographic boundaries, so there's a chance I completely misinterpreted his meaning.
I really liked the Skellam paper. Although a lot of it is almost taken as a given with modern ecological knowledge, it was very interesting to see how this was brought together into these basic fundamental concepts regarding dispersal.
ReplyDeleteI did find the exclusion of variation in the population to be an issue in the older paper since he did seem to treat the populations as relatively homogeneous entities, rather than having differenign characteristics within a certain range. Assuming homogeneity on your population is a big assumption to make, and it can leave out a lot of key ecological processes affecting the model when it is done. The importance of this variation was strongly exemplified by the Duckworth paper - without incorporating the variation in aggression into their study, there would be a much weaker explanation of why exactly the range expansion occurred.
- Elizabeth
Stellam’s paper is a pure mathematical modeling paper about random dispersal. I like the way the author define those symbols he used at the second from the last section, but he did not do that for the previous equations, which makes it a stretch for me to follow, especially when he used those symbols in the context directly to describe the processes. Also, I do really like that the author moved back to the biological discussion at the end. He talked about the limitations of the random dispersal assumption and that local irregularities won’t have a big difference than randomness. I partly agree with that, but I think it still depends. It is true if the irregularities are resources distributed in “patches” or “mosaic”, while it might not be true if the “irregularity” is something that has strong influence on the dispersal, such as a small river near the focal populations.
ReplyDeleteThe companion paper is interesting to me because I do not know that there could be a coupling between dispersal and behaviors before reading this paper. I am especially interested the trade-off between reproductive success and the male aggressiveness, and I am not totally convinced by the authors’ explanation on that.
I’m not familiar with spatial ecology, so I thought Skellam’s result that the rate of radial expansion of a population is constant was a cool result especially since it was supported by the muskrat data. However, I couldn’t follow most of the analysis in Skellam, so I’m not sure how he arrived at that finding.
ReplyDeleteI thought the Duckworth Badyaev paper was fascinating and it raised a lot of questions for me. First, I didn’t notice mention of female dispersers. Obviously, dispersal of males alone cannot result in species range expansions so it would be interesting to know more about female behavior. Second, the findings made me wonder how aggression is maintained in populations. Are there historical differences between mountain and western bluebirds that could explain why aggression is maintained in some species but not others?
- David
I appreciate that the Skellam paper starts ou by going into mathematical details about fundamental concepts such as random walks and diffusion. I think concepts like the kinetic theory of gases are helpful for visualization of the movement of animals and Skellam (1951) is a great reference. However, unlike most experimental physics, ecological studies do not happen inside a vacuum, so I think in this way the beginning perspective greatly limits one's ability to describe and predict the dispersal of most species. I think taking something as complex as animal behavior and trying to boil it down to fundamental physical laws is intrinsically flawed because they cannot account for complex behaviors such as territoriality, migration, and delayed dispersal. Skellam does include population growth equations as the paper continues and begins to incorporate other types of interactions between animals and habitat to account for more complexity, such as competition and habitat quality. All in all, I thought this paper was very advanced for its time.
ReplyDeleteI enjoyed the Duckworth and Badyaev paper because it filled gaps in the Skellam paper that are vital to understanding ecological systems. I loved learning about the influence of aggression on dispersal and the range expansion of western blue birds. It was fascinating to see how they were able to tie the predisposition of highly aggressive males to having longer dispersal distances. I also thought it was interesting that aggressiveness was more constant in individuals than in the population, so that even if aggressive males were not great fathers (not much help at the nest), the population was still able to expand and stick around in the newly expanded areas because less aggressive males from new generations could stay, inherit territory, and successfully help raise chicks.