On
Optimal Use of a Patchy Environment
This work by MacArthur and Pianka is the first to explicitly
model the strategies employed by organisms to exploit the resources available
in their environment. In modeling these strategies, the authors state, “an
activity should be enlarged as log as the resulting gain in time spent per unit
food exceeds the loss.” This simple statement sets a straightforward economic
rule that guides their treatment of the problem. Through optimization methods
they attempt to identify the budgetary components that will increase and/or
decrease as certain activities are increased. The authors look specifically at
time spent per item eaten and divide that time into search time and prey
consumption time (pursuit, capture and eating time).
The economic approach taken by MacArthur and Pianka proves
useful in formulating a generalized view of what factors govern foraging
behavior. For example, increasing the number of prey species (i.e. moving from a
specialist toward a generalist) decreases the amount of time spent searching
while increasing the amount of time spent pursuing, capturing and eating prey.
This brought forth a number of evolutionary and behavioral implications, which
spurred further, more complex research in the field.
The authors employ similar methods in consideration of
patchy environments and produce similar results. In short, the addition of
patches with equally abundant prey items to a predator’s itinerary, will result
in more time hunting and less time traveling per prey item captured. This model
should generally hold true for adding patches that have unequal prey densities
as well. Moreover, spatial scale influences both travel time between patches
and how patches are used but should not change the amount of time spent hunting.
Lastly, competition is addressed. Regarding diet, the
introduction of a competitor will reduce the overall abundance of a prey item.
Apparently, this will not result in dietary changes. However, the introduction
of a competitor will cause an optimal predator to alter its use of a patch. It
is also evident that the patch structure of an environment imposes limits on
the degree of similarity between competing species. In general, given
sufficiently low travel time, a generalist can outcompete and replace a
specialist predator. However, a specialist may persist in the presence of a
generalist if the hunting rate of the specialist is greater than that of the
generalist.
Random
Dispersal in Theoretical Populations
In this work, Skellam is the first to utilize the random
walk principle in an ecological context. At the time this paper was written,
other biologists had used the idea of random walk and diffusion equations to explain
the process of genetic drift but had not gone any further than proposing a
general model for the spread of an allele through a population. Skellam
demonstrates the utility of diffusion equations in approximating many of the
key features of population spread. However, he also recognizes that it is a
somewhat simplistic model for explaining dispersal as it relates to actual populations,
in that populations in the real world do not disperse randomly.
In examining dispersal, Skellam cites the spread of Oak
trees and flightless in postglacial Britain. As a slow growing organism with a
long generation time and poor dispersal ability, the Oak has spread remarkably
fast. To account for this, Skellam posits that there must have been some
mediation of dispersal by birds or that the latest glaciation event was less
extensive than reported and that refugia persisted. Additionally, he provides
some insight into the mechanism of postglacial forest succession as it related
to seed dispersal ability. The muskrat, which was introduced to central Europe
in 1905, proved a useful case study as its spread following introduction
closely matched calculations for a theoretical population.
Skellam also introduced the concept of critical patch size,
noting that a particular region of favorable conditions must meet or surpass a
certain size threshold in order to support a viable population. Consequently,
populations in patches that fall short of this critical threshold should not
occur naturally. Skellams work has clearly paved the way for a lot of work that
has been done on populations and still has wide ranging implications in the
spread of invasive species and conservation biology.
Skellam Paper
ReplyDeleteWhile the dense math and associated text made this paper a bit of a drain to read, the explanations and justifications for the models were very useful. I particularly liked the oak tree example. It is interesting how this sort of paleo problem is relatable to so many other instances in the natural world. I also appreciate the extensive tie-in to other sciences like the gas particle theory. I feel like it kind of shows that other sciences were quicker to apply mathematical modeling to their systems. Ecology seems to have waited much longer (which has allowed lots of piggy-backing on other models). That said, ecological modeling requires far more complication than most other physical science type problems, and ecology is a young field.
MacArthur and Pianka
The predator prey dynamic presented in this paper seems to be a new way of modeling population dynamics at the time. I like how the authors frequently relate their model to economic theory, though some of their descriptions seem to display a much more “intelligent” natural word than we know to exist. Table 1 was very useful to me in understanding some of the conclusions reached. The specialization of use of larger patches was particularly interesting from a conservation perspective.
This paper highlighted the importance of prey – predator dynamics in fine and coarse enviroments, which are defined as “patchy enviroments”. The paper relies on the time spent per item eat . In fine enviroments the prey could be either equally distribute or not. Overall it might seen that that number or preys is larger and more available. In the other hand the time for catching and eating will increase. Somehow there will be a ratio between search time and pursuit time that is the optimal.
ReplyDeleteThe second case stressed the relationship between hunting time versus traveling time (spent travelling between suitable patches divided by the harvest). The patches are ordered by prey density. In this ratio really matters the predators itinerary among the patches available. This relationship can be seen in patchy enviroments of different sizes, which alter the dynamic and the optimal ratio.
MacARthur and Pianka: I thoroughly enjoyed this paper out of all of the papers we have read so far. I was able to correlate the theories presented here with similar archaeological theories regarding hunter-gatherer foraging behaviors. These models use behavioral ecology in order to examine prey choice, and hunting and gathering strategies employed in order to gain optimal benefits. One difference is that the use of these models in archaeology also consider the time spent in acquiring certain species for consumption, although they factor in the time spent in processing (butchering) certain animal species.
ReplyDeleteThat's cool Melyssa. I recall reading some stuff on the origins of agriculture that referred to foraging theory principles to figure when it made sense for people to switch from a hunting-gathering strategy to a agricultural strategy. I would imagine similar ideas have been applied to non-human populations to figure out conditions under which one or another resource acquisition strategy is optimal.
DeleteMacArthur and Pianka: This paper was an extremely interesting and enjoyable one to me. Thinking about the patterns in which predators and prey acquire their food based on the "patchiness" of an environment is the basis for many of the systems most of us study, whether it's animals, plants, or something else. The populations we see in the natural world are so dependent on the patchiness of other species around them and the competition this encourages or discourages. This paper seems revolutionary in the way it relates predator/prey populations and how they depend on the abundance or patchiness of their food.
ReplyDeleteSkellam: I found this paper to be enjoyable to read also. It seems like it was really the first paper to talk about random dispersal encouraging a whole new population of a species to spread. The symbiosis that exists with animals that depend on the seeds of plants and the respective plant is an inspiring one to me. Both species need each other, and through this paper, we can model and predict how much they benefit from that dependence.
Paper 12: MacArthur and Pianka – On Optimal Use of a Patchy Environment
ReplyDeleteThis paper explores the economics of foraging and the various adaptations that arise as a result. The fundamental concept that the behaviors and adaptations we find in nature have been selected for because there is more benefit than cost to them is one of the first things we learn in ecology and evolution. It is interesting to me the approach that they take in this study in trying to model these interactions. Search time is basically a measure of prey abundance and pursuit time is a function of the abilities of both predator and prey. Large patches consist of a more abundant prey population which results in smaller search time and thus produces a more restricted diet or specialized predator. So basically if there’s an adequate supply of one species in a localized area why spend more time searching for new species. However, in a paper we covered in macroeology last semester – Brown and Maurer 1989 Macroecology: The division of food and space among species on continents, they indicate that smaller species were more specialized in their use of resources than their larger relatives due to energy constraints. Larger animals were able to extract a greater fraction of nutrients and energy from their food than smaller animals and therefore they could feed on lower quality food and include a wider array of food items in their diet (generalist feeders). Conversely, smaller animals had to specialize on higher quality foods in habitats where they were sufficiently abundant to support the demand. In this case it seems to me that smaller animals become specialized not necessarily because food is abundant but because they have minimum energy requirements that dictate the quality of forage. So which comes first –specialization out of convenience or out of necessity? Or a happy coincidence of the two? And does the forage material make a difference – herbivores feeding on plant material vs carnivores hunting live prey vs omnivores, etc.?
Furthermore, I liked figures 1 and 2, although I am kind of confused with figure 1b, and how they illustrate the idea that after a certain number of species there is no further benefit in adding more. I also appreciated Table 1 and thought it did a nice job of summarizing.
Do the terms “optimal diet” or “optimal use” mean to suggest a situation where every prey item that was searched for and pursued was caught? And therefore this model wouldn’t account for losses or variations in success rate?
I also question what the authors mean when they state "optimal diet of a predator." I think Martina is correct in assuming that the optimal diet would be: every time a predator hunts, it catches its prey. It is a very black and white way to think about predator prey relationships. Going back to what we talked about in class last time, variation in diet can significantly alter these relationships. For example distinguishing between a generalist and a specialist can change the dynamics of a predator prey relationship. The generalist is not so heavily reliant on one single prey item, and if we introduce omnivores, the relationship only gets more complex. How would we measure this within MacArthur's models, and like Martina said how can we account for variation and success in hunting?
DeleteMacArthur and Pianka was pretty interesting - I especially like the consideration of spacial heterogeneity. I'm was wondering if the first, simple case of search and pursuit time in a homogeneous environment is assumed to be nested within the patches of the second, patchy resource case with hunting and traveling time. I'm also curious whether the prediction of more productive environments having more specialist consumers actually holds. The positive relationship between productivity and diversity would make me think that it might be beneficial to be a generalist in a productive ecosystem.
ReplyDeleteI thought the comparison between the two papers was interesting because they seem to be presenting opposite concepts on how an organism disperses to new areas. MacArthur and Pianka suggest that how an organism picks an environment to use/occupy or disperse to is rather calculated based on the resources available in that environment, whereas Skellam claims that at a population level dispersal is random even though there may be some choosiness, that can mainly be ignored, that is similar to a gravitational effect. Both ideas seem fundamental to our current understanding of why organisms are where they are an how they got there. I have to say I am more drawn to the Skellam paper though because of the several nods and citations of Fisher, Haldane, and Wright since I have more of a genetics background. The modeling in the Skellam paper for population dispersal is very similar to how alleles act in population genetics.
ReplyDeleteMacArthur and Pianka’s model on the economical use of resources is simplistic. I can see the value of this study because this is a simplistic model of energy dynamics between predator and prey. The major assumptions of this study are: natural selection as an active force on the system and fitness is directly correlated with the economical use of resources. I agree with the assumption that natural selection acts on the efficiency of an animal, but fitness’ relationship is not only influenced by the economical use of resources. For instance, fitness can also be influenced by sexual selection which is not taken into account by this simplistic models. I think this is an overall good model of economical use of resource behaviors, but also believe that introducing additional factors (like adding more than one prey/predator) would make this system more dynamic and less straight forwards as this model suggests.
ReplyDeleteSkellam provides a simplistic diffusion model of random dispersal. Like Skellam points out, this is obviously a simplistic view of dispersal, but it provides a basic dispersal model that others have expanded on since then. I find it interesting that Skellam’s Oak example is a direct rebuttal to his own model, and thus acknowledges the limitations of the model. As the introduction states, the model is not defined by its assumptions of random dispersal, rather it is valuable because the diffusion model is able to describe "prominent features of population spread" using a simplistic model.
My favorite quote from the introduction is: “Therefore, the selection regime for dispersal is shaped by, and in turn shapes, the scale of environmental variation facing the species” (p. 188).
MacArthur and Pianka proved a valuable contribution by basing their optimization model on economic theory, allowing them to draw conclusions about predator specialization. I agree with Sami and Martina that the model seems oversimplified. However, it does make sense to me to start with an economic model, since money is one of the main forms of trophic transfer we're familiar with in human societies. Regarding Dunbar's question about homogeneous environments: I wonder if a fine-grained habitat would be essentially the same as a patchy habitat, if the grains were large enough?
ReplyDeleteI'm impressed by Skellam's image of the advancing wave front of a spreading population, resulting from an analog of Brownian motion. The example of the spread of muskrats in Europe since 1905 stands out--since there is an almost exactly linear relationship between years and the square root of the area inhabited. As Schuyler has pointed out, this is the first author in our sequence to take evolutionary genetics seriously, and to mention gene flow in the context of speciation.
One of Skellam's most dramatic results is that spatial limitations alone can account for the carrying capacity in the logistic equation, completely aside from availability of food supply.
Skellam, while difficult to follow in places, was also really impressive in the wide range of earlier concepts it draws on, both ecological and non, as well as in some important ideas touched on that have become more important since.
ReplyDeleteLike MacArthur & Pianka, and to some extent Nicholson & Bailey, spatial concepts are central. Skellam covered both continuous and discrete population growth, as well as competition. It was neat how he showed the conditions under which species could coexist when one was a superior competitor and the other a superior disperser, and how this depends on initial densities. This was a neat extension of Gause's work.
Section 3 was particularly challenging to follow - a lot the math terms were not well-defined. I didn't really see how the conclusion of minimum necessary area size was reached. Maybe we can cover in class.
Like Sami, I was intrigued by the notion of dispersal as a strategy of hedging for environmental heteoreneity, which I wish Skellam had gone into more.
I'm also interested in the importance of rare, long-distance dispersal events that Skellam touched on. These seem like they could be very ecologically important (potentially "black swan' type) events that could facilitate invasion/colonization and greatly affect community dynamics and succession