Judges’ Queries and Presenter’s Replies

  • May 20, 2013 | 08:42 p.m.

    Please explain how you deal with spatial scale when it crosses many, many orders of magnitude between environment and predator, such as centimeter scale for plants versus scavengers that might migrate thousands of kilometers seasonally.

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 21, 2013 | 04:46 p.m.

    So far, we’ve modeled scale disparities of up to 4 orders of magnitude between predators and prey, and it could be interesting to go further! In our simulations, the prey and the environment are always at the same scale, and the prey tracks the environment pretty closely (see the upper right graph). Predators only ‘perceive’ the environment via prey abundances. So when the entire range of environmental variation (in this case, the full sine wave) fits within a single cell of the predator lattice, predators only respond to the average value of the environment, as our example output suggests (center figure). Increasing the scale disparity between predator and environment shouldn’t change this result.
    ****
    That said, I’d also like to point out that we make the simplifying assumption that juveniles disperse, while adults do not; and that each time step encompasses one generation of each species. So our results say more about differences in home range size than about migration possibilities. To look at migrations specifically, we’d want to use a smaller time step and allow for adult dispersal. I think that we could deal with large-magnitude spatial scale disparities in the same way we do now, but we’d have to be thoughtful in choosing an appropriate temporal scale to report on.

  • May 21, 2013 | 11:27 a.m.

    Can you provide real-life examples that are consistent with your prey/predator and environmental pattern size interactions?

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 22, 2013 | 12:18 p.m.

    To answer your question, I’m going to concentrate on the prey-predator scale disparity here, because in all runs we’ve done so far, prey populations are at the same scale as the environmental variation. It would be interesting to change that in the future, because there are undoubtedly cases where a prey species can’t perceive all variation in its environment. I would expect the result to be similar to what we see for the predator under a scale disparity.
    ****
    It’s possible to get a rough estimate of whether our scale disparities are realistic, using home-range data for predator-prey pairs. For example, the average home range size of bobcats in central Florida is 1450 Ha for females and 2550 Ha for males (Wassmer et al. 1998). The average home range size of one of their main food sources, the marsh rabbit, is 3.96 Ha (Forys & Humphrey 1996). These numbers give spatial scale disparities of 1:366 and 1:643, which is comfortably within the range of disparities that we modeled (1:1 to 1:10,000).
    ****
    There is also some history in the literature of experimental manipulation in spatial scale disparities. Kawata and Agawa (1999) imposed scale disparities of 1:49, 1:196 and 1:441 in an algae-snail system by changing the size of the algae’s substrate plates. Interestingly, in the latter two cases, the snails responded to the algae as if it was homogeneously distributed.

  • May 21, 2013 | 05:38 p.m.

    The real strength of your combined presentation is that it makes the logic (and even a bit of the mechanism) behind grid-based spatial models intuitive. Pat yourself on the back for that. However, there is a huge literature on grid-based environmental models and cellular automata, including organismal dynamics. Can you state in a succinct way how or why your work is novel?

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 22, 2013 | 09:56 p.m.

    Thanks! It’s certainly a lot of material to communicate.
    To address your question: The previous work that we’ve seen tends to either model predators and prey on the same lattice (similar to our S1 simulation runs) or as a mean-field source of prey mortality (similar to our S100). Much of this literature also does not look at species interactions in the context of a spatially varying environment, as we do. Our work is novel in that it provides a way to study and compare the same-scale and mean-field extremes of scale disparity, as well as the entire range between them.

  • May 21, 2013 | 10:13 p.m.

    Dear Christine,

    Fun project! And yes, great way to explain theoretical ecology! Please give me a sense what you hope to ‘get’ in the end? What would be a really cool result or insight? Do you have a hunch (to avoid the pesky term hypthesis)? What are your expectations? How do you know if your study was succesful? When will you be done modeling? The “we are interested in …” statement on your poster is pretty open ended. Nothing wrong with pure exploration, but I do think a good set of predictions can help to sharpen any research project.

    Best,
    Volker

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 22, 2013 | 10:10 p.m.

    Thanks! You make a lot of good points, so I’m afraid you’re in for a long response.
    ****
    What we hope to get in the end is an understanding of how scale disparity in species interactions affects the patterns we see on the landscape.
    ****
    In our model, we assume that predators don’t respond to spatial pattern at any finer grain than that of their own lattice. So we expect that increasing the disparity between predators and their prey/environment would cause the distribution of predator populations to be increasingly spatially averaged compared to the prey/environment pattern. That’s what we see when we decrease the environmental pattern size with respect to the extent of the predator populations (center figure)- the differences between large and small predator populations decrease. We generally see the same thing as we increase the prey-predator scale disparity (bottom graph), although there’s a region where the 1:25 predators do worse than the 1:100 predators. We’ve got standard error on there (and it’s tiny!), so we’re still mulling over what this could mean.
    ****
    As for the prey, we expect all prey populations to converge to their carrying capacity in the absence of a predator, which we saw (result not shown). In the presence of a predator at the same scale as the prey, we expected the prey to be displaced from the ‘best’ lattice cells, because predators have access to all of the information about the prey’s spatial distribution in this case. We expected that this displacement would decrease with increasing scale disparity, because predation pressure would be spread over more populations. What we saw instead was that scale disparity didn’t have much of an effect at all (upper graph)! Changing the environmental pattern did have some effect even though the prey and environment are at the same spatial scale, because dispersal distances were constant.
    ****
    What would a cool result look like? It would be really interesting to find situations where predators track the environment more closely than their prey, despite not having direct access to environmental pattern information. We’ve had hints of this so far, both in our work and in the work of another team member who is applying this model to social evolution. It’s something we’re still exploring.
    ****
    For us, success would be a model that meets our expectations in known test cases (e.g. without predation, without dispersal, with minimal/maximal scale disparity), and in intermediate cases,
    tells us something new about how scale disparities between interacting species affect patterns we see in the natural world.

  • May 21, 2013 | 11:17 p.m.

    The video animation explanation was wonderful. I would love to show it in my Biology 110 ecology lab. The poster schematic was very effective. Can you please operationally define the term “prey fidelity” for me and give an example?

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 22, 2013 | 08:21 p.m.

    I’m glad you enjoyed the video, and hope you find it useful! All we mean by ‘prey fidelity’ is how well the distribution of prey populations tracks environmental variation. Our environmental pattern is represented by values defining the prey’s carrying capacity in every cell. So any process that reduces the prey populations in each lattice cell from that carrying capacity will reduce the fidelity of the prey pattern to the environmental pattern.

  • Further posting is closed as the competition has ended.

Presentation Discussion

  • Icon for: Brian Drayton

    Brian Drayton

    Faculty
    May 20, 2013 | 10:02 a.m.

    Loved the video, and found the model very interesting. Did you have a particular experimental system in mind when building the model?

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 20, 2013 | 05:04 p.m.

    Glad you liked the video!

    Because of the huge variety in scale-disparate processes that occur in ecological systems (and beyond), we set out to make our model as general as possible. For example, our code allows the user to define the order in which the population processes are executed. We also coded for the possibility that the prey is at the larger scale- which would be the case if you were studying, say, carnivorous plants.

    We’re currently collaborating with another student who is modifying this model to study questions in social evolution. Right now, she’s looking at the consequences of disparities between the size of villages and the governments that oversee them.

  • Icon for: Andrew Tyre

    Andrew Tyre

    Faculty
    May 21, 2013 | 03:13 p.m.

    Fantastic video explanation of the LV equations!

    In your figure showing the disparity between predator and environment, the “worst case” of 1:10000 shows a similarity of 0.8 — what is the lowest value your metric can take? I’m having trouble wrapping my head around the Fourier transformation bit.

    Have you thought about generating environmental lattices with fractal properties? What about swapping out the LV equations for, say, Rosenzweig-Macarthur models? LV has some dynamics that aren’t very realistic.

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 21, 2013 | 05:33 p.m.

    To answer your first question, the minimum for our metric is 0.75 (when the environment is made up of a single sine wave, as it is here). We used the 2D Fourier transform in our analysis because it explicitly pinpoints the different scales that make up spatial patterns. Because our environment is sinusoidal, its transform only has peaks in the center and at n steps away from the center, where n is the number of periods in the region. All patterns can be expressed as a sum of sine waves, so any reduction in the ability of our simulated species to track the environment shows up in the Fourier transform as the appearance of peaks at other frequencies. Our metric compares the location and size of peaks in the Fourier transforms of the environment and species lattices.
    ****
    So far, we’ve just stuck with simple environments, but I can certainly see the draw of a fractal environment. We use continuous boundary conditions, so one advantage to the sinusoid is that we can avoid discontinuities at the ‘edges’. As for the dynamics, we wanted to start with something as linear as possible in order to get a good understanding of our model before complicating it. Our future choices of dynamics will definitely depend on what our next questions are!

  • Icon for: Rosemary Le

    Rosemary Le

    Trainee
    May 23, 2013 | 08:19 a.m.

    Great video! I loved the visuals.

    Does your model include or have you tried to model instances where the prey, predator, or resources are wiped out by some external force to see how this affects the environment or track the movement of prey or predator? In the event that there is no predator, and the prey population increases, do the prey have to move to new areas to access more resources?

  • Icon for: Christine Dumoulin

    Christine Dumoulin

    Presenter
    May 23, 2013 | 01:03 p.m.

    Hey, thanks!
    So far, we’re only modeling populations at equilibrium across the region. We do have the capacity though- we’d just have to initialize the model with populations in only one or a few cells. A constant proportion of individuals disperses from their home cell every generation, so we would definitely see the prey spreading out to new areas in the absence of predation.
    As for external forcing, one thing I would love to do would be to shock the environment with either a resource pulse or a localized catastrophe, to see how long the disturbance in the predator and prey patterns lasts.

  • Further posting is closed as the competition has ended.

  1. Christine Dumoulin
  2. http://www.igert.org/profiles/4498
  3. Graduate Student
  4. Presenter’s IGERT
  5. University of Tennessee at Knoxville
  1. Austin Milt
  2. http://www.igert.org/profiles/5367
  3. Graduate Student
  4. Presenter’s IGERT
  5. University of Tennessee at Knoxville

How do cross-scale interactions mediate species’ ability to track resources?

Ecosystems are made up of interacting species that respond to the environment at different scales. The amount of space that members of a species can use is limited by characteristics such as movement ability and body size. Plants, for example, often draw resources from a smaller area than the herbivores that graze on them. Such cross-scale interactions are common in nature, and they may enable species to respond to environmental patterns at scales that they would not otherwise ‘see’. If so, local disturbances could indirectly alter ecosystems over larger areas, and vice versa. Here, we explore how a simple predator-prey interaction affects both species’ ability to follow environmental resource patterns across a region. To answer this question, we developed a computational model that simulates environmental patterns, predator populations and prey populations using three stacked grids or lattices. Grid cells in the prey and environmental lattices are always the same size, and we study the repercussions of predators’ ability to act at a different scale by increasing the cell size in the predator lattice. As those grid cells become larger, predators lose the ability to distinguish between areas that attract prey and those that don’t. Our simulations reveal that as the difference in predator and prey grids increases, the predators become more evenly distributed across the region. The prey’s ability to follow environmental patterns is hindered by the presence, but not the scale, of the predator. Scale differences can be important, but they need not affect both species equally.