Week 3: Bioenergetics and the Determination of Home Range Size
Paper for Tuesday
Authors of the Blurb: James H. Brown at the University of New Mexico & John L. Gittleman at the University of Georgia
These are two of the three coauthors of Foundations of Macroecology, the third, of course, being Dr. Smith. Dr. Brown is most famous for his work on body size and the metabolic theory of ecology, which directly relates to the paper we're reading.Dr. Gittleman received his Ph.D at the University of Sussex. His work relates to large scale macroevolutionary and macroecological phenomena, such as overarching phylogenies or the patterns and causes of biodiversity.
Author of the Paper: Brian K. McNab at the University of Florida
The focuses of McNab's research include macroecological trends in birds and mammals, especially tropical varieties. His work on bioenergetics was revolutionary because it unfurled into a whole new field of study. The authors of the blurb mention that, although later papers would go on to disprove the 1:¾ ratio that McNab derives for the log transformed relationship between body size and home range in favor of a 1:1 ratio, McNab still deserves a great deal of credit for coming up with the idea in the first place.Cliff notes of the paper:
Being aware that the basal rate of metabolism of an organism increases at an allometric rate according to its body size, McNab hypothesized that since the home range of an organism relates to how much it forages, and, therefore, how much it eats, the relationship between body size and home range might follow the same pattern.McNab compiled a large number of home range sizes and body weights for different mammal species from several different authorities: Burt, Fitch, Mohr, Blair, Calhoun and Casby, and Ingles. He notes that, while the estimations the various authorities give for body size and home range size are different, all the variation is within an order of magnitude, and therefore has no significant effect on the data after it has been log transformed. McNab divided his list of mammals into two groups, hunters and croppers, with hunters being mammals who seek out rare food items like prey items, seeds, or fruits and croppers being mammals who seek out common food items like browse or grass. This was done so that organisms which must have a larger range size in order to obtain the same amount of food as another organism of similar size with a smaller range could be considered separately. He then plotted a log transformed graph of the home range vs. body weight of his mammals.
The slope of the line, fitted by the method of least squares, was 0.63. McNab calculated the untransformed equation to predict the relationship between body size and home range as being R = 6.76 * W^0.63. In the paper, McNab says, "There is no significant difference between 0.63 and 0.75" ... "thus, the variability of the data is sufficient to allow W^0.63 to be replaced by W^0.75 and R = 8.51 * W^0.75" ~ I'm personally quite confused by this step.
This seems like clear evidence that, at least for mammals, the relationship between home range and basal metabolic rate is isometric, and that both of them have the same allometric relationship to body size. McNab writes, "[The size of the home range] is determined, mainly, by the amount of energy expended by the species." He also notes that the difference in foraging styles was important as well.
A later work by Thomas W. Schoener, 'Sizes of Feeding Territories among Birds, 1968' found that the relationship between home range and body size for birds had a scaling exponent closer to 1 than 0.75, and the blurb mentions that subsequent papers showed 1 to be the number for mammals as well.
Questions I had
1. How do ecologists approximate home range size for animals? Is there more than one method? What factors other than foraging type and body size affect home range size?2. Why did McNab get the scaling exponent wrong? Did it have something to do with his assumptions about the relationship basal metabolic rate had to range size? Was his data somehow flawed? His method?
3. How was McNab able to change 0.63 to 0.75? Was it a mathematically legitimate conversion?
4. For which animals does this trend hold true? It seems unlikely to be applicable to corals or clams, for example.
5. Do humans who hunt and gather in order to survive fit this trend? Do humans living in cities fit this trend?
After reading the paper it was interesting to see that Lucius first questions (1) were pretty similar to the ones I had… “How do ecologists approximate home range size for animals?” “Is there more than one method?” I found an interesting paper [Greenleaf, Sarah S., et al. “Bee foraging ranges and their relationship to body size." Oecologia 153.3 (2007)]” that following McNab concept calculates the “foraging range” for bees. I’m assuming that home range sizes are going to be obtain differently depending on the type of animal, but for bees, these techniques included mark-recapture (not recommended), genetic analysis, feeder training technique and others. They also recorded an estimated maximum foraging distance by another three different methods were bees are released at successive larger distances from the nest (or nest-feeder) until they no longer go back at them.
ReplyDeleteOn the other hand, I had a comment that I wanted to share with you about this paper. In page 136 of the paper, McNab talks about how they should have used total daily expenditure instead of BMR. A really important variable that affects energy exchange and has been omitted in this paper is temperature. McNab says that “a function relating the daily energy expenditure to weight would be temperature dependent” and later on he talks about “environmental fluctuations” and seasonal effects that to me are tidily related with temperature fluctuations but he never ends up adding this variable as part of the home range – body size equation.
I think, Lucius, that we have to remember that macroecology looks at such a broad range of variables in several magnitudes of order, that when you graph multiple magnitudes of order, the small amounts of variance between the individual data points becomes relatively irrelevant when you look for the trends. I'm not sure how they got the coefficients 6.76 in home range and the second coefficient 8.51, but they were comparing the power functions for both home range as a function of body mass and BMR as a function of body mass. The author saw that when they compared the two power functions, they did not find a sufficient significant difference between the two. Therefor, they could say, as I can understand, that the predicting power between home range as a function of body mass and BMR as a function of body mass both have the same predictive power. This means to me that home range and BMR scale together.
ReplyDeleteI can think of a few more factors that influence home range. Are we talking about animals that migrate or animals that stay in the same area for the entire year? What about resources that aren't simply energy resources? Water availability, minerals, mate availability, time of year (mating season? lean season?), all should influence home range too. But this just shows that the relationship of body weight to home range must be a very strong correlation in order to show a remarkable relationship even despite all the numerous variables I mentioned, and I believe that this is a statement to the power of macroecology.
Laura, that's a great point, TDEE should have been mentioned. The implications are that with this model, there is a very large disconnect between ectothermic and endothermic animals, I believe. Endotherms and ectotherms may have only one order of magnitude when it comes to BMR, but perhaps as great as 2 or 3 when it comes to TDEE. What is the TDEE to BMR ratio for a hummingbird, compared to for example, a snail of similar body mass? Or a large snake compared to an edothermic hunter such as a wild dog?
I'm a bit confused by that step as well, Lucius. I understand that there's no significant difference between the two powers, but how does McNab then come to a new constant using the same power (0.75) in Eq 3 as he did in Eq 1? Not sure if this is even an important part of the paper to dwell on.
ReplyDeleteOther factors that could affect home range, as McNab mentions, include water availability, soil conditions, quality of environment, and an increase in energy expenditure - as Laura mentions, McNab uses this possibility, although he never fully explains it in his math, although he relates it to metabolism.
I like Lucius's last question, and I think this could definitely apply to hunter-gatherers -- they're mostly nomadic ("highly mobile") and have a diverse diet (like all humans). McNab even mentions higher primates towards the end of the paper.
When I first looked at McNab's data, I thought that there might be some bias associated with it. Other than the Raccoon, Beaver, and Moose, all of his species weighed less than 6kg. This may be why he got more differing coefficients, even if they weren't significant from each other. (The supplemental figure that Felisa posted seems to show that more data better constrains the trend.)
ReplyDeleteWith reference to calculating range size, I would think that it doesn't really matter, since the plots are in log space. However, it would be much easier to get a more accurate figure today with the use of tracking collars.
In terms of total daily energy expenditure, I wonder if there would be any notable difference for animals that rest most of the day, but are briefly highly active vs animals that are constantly "active," but not extremely so (but that may be related somewhat to their feeding strategy.)