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Behavioral Ecology Vol. 11 No. 2: 125-131
© 2000 International Society for Behavioral Ecology
Body size effects on locomotion and load carriage in the highly polymorphic leaf-cutting ants Atta colombica and Atta cephalotes
Department of Biological Sciences, Monash University, Wellington Road, Clayton 3800, Victoria, Australia
Address correspondence to M. Burd. E-mail: martin.burd{at}sci. monash.edu.au .
Received 9 July 1998; revised 18 May 1999; accepted 9 June 1999.
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ABSTRACT |
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Leaf-cutting ants reduce their walking speed under the weight of the leaf fragments they carry, an effect likely to have some consequence for the foraging performance of a colony. I manipulated loads carried by workers from two Atta species to determine how load mass and body size affect walking speed. A comparison of speeds before and after load manipulation indicates that change in load mass has a linear effect on velocity. Several different regression models of speed as a function of loads and body size have similar fit to the data, so a single best model cannot easily be identified. However, there is statistical evidence that the slope of the linear effect is more pronounced for smaller ants, an outcome most consistent with a regression model based on loading ratio, a metric that scales load mass relative to body mass. I then examined the effect of loading ratio on the leaf transport rate (the product of load mass and carriage velocity). It has been claimed that this rate is maximized over a range of loading ratios that is the same for all ants regardless of their size. However, I found that a latent body mass effect persists in the relation of transport rate to loading ratio, even though loading ratio is already scaled relative to body mass. The maxima seem to be reached only at artificially elevated loading ratios, so that transport rates with natural fragments tend to be sub-maximal. This conclusion is in agreement with analytical predictions of rate-maximizing load masses derived from the regression models. Thus, loading ratio does not adequately scale load mass relative to body size when used in this context (effect on leaf transport rate), and should be used cautiously. Ants are likely to accommodate loads through modulation of both stride length and step frequency, but precisely how this takes place requires future study.
Key words: ants, Atta, central place foraging, Formicidae, walking speed, scaling.
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Carrying leaf fragments is a central foraging activity of leaf-cutting ants of the genus Atta (Attini: Myrmicinae) (Hölldobler and Wilson, 1990
). Workers that transport fragments may vary by an
order of magnitude in body mass, and the fragments typically range from one to
several times body mass. Such heavy loads reduce locomotion speed
(Burd, 1996a;
Lutz, 1929;
Roces and
Núñez,
1993; Rudolph and Loudon,
1986) and increase energetic outlay
(Lighton et al., 1987) of
laden ants as they return to the nest with substrate for the fungal gardens.
Thus, foraging success of the colony would seem to be closely tied to load
size and locomotion. But despite much research on the load size-to-worker size
relation in attine ants (Roces and
Hölldobler, 1994;
Shutler and Mullie, 1991;
Waller, 1989; Wetterer,
1990,
1991,
1994;
Wilson, 1980), there is little
certainty about the functional significance of the relation.
The polymorphism of attine workers presents a difficulty for analysis and
interpretation of data. Many kinematic and metabolic features of locomotion
and load carriage are expected to scale allometrically with body size
(Schmidt-Neilson, 1984). It
seems appealing, therefore, to account for within-species polymorphism in
attine ants in some fashion that maintains functional similarity among workers
of greatly different size. However, it is not always a straightforward task to
compensate for body size variation in a functional or ecological analysis
(LaBarbera, 1989).
In this article I address two issues: (1) how does load mass affect the speed of laden ants? and (2) what effect does laden speed have on foraging performance? The influence of body size is a central concern for both questions.
Scaling of load with body size can be represented in several ways. Lutz
(1929) and many others have
represented load mass in relative terms by using the "burden" or
"loading ratio," L, defined by
 | (1) |
The main utility of the loading ratio in functional morphology derives from
the finding that the proportional increase in an animal's metabolic rate
during load carriage (measured as rate of oxygen consumption) equals the
proportional increase in total mass caused by addition of the load
(Lighton et al., 1987;
Taylor et al., 1980). For
instance, two animals of different size having equal loading ratios of 1.25
both experience a 25% increase in metabolic rate over their unladen travel.
Thus, loading ratios are an index of functionally similar burdens with respect
to relative metabolic rates. It does not immediately follow that the loading
ratio is also an index of functionally similar loads with respect to
locomotion velocity or foraging performance. Indeed, the analysis below
suggests that loading ratio can be an incomplete or even misleading metric of
relative load size.
Load mass is not the only variable that can be scaled to body size.
Locomotion velocity, usually expressed as absolute distance per second, might
be more appropriately measured in body lengths per second, or possibly defined
as the nondimensional Froude number
(Alexander and Jayes, 1983).
Yet another means of accounting for body size is to retain variables in their
absolute units but to include body size as an additional independent variable
in a statistical model. Body size, along with other independent variables, may
have linear or nonlinear effects on locomotion and foraging performance. It is
not easy to choose among these options in the absence of a strong theoretical
argument, but it is clear that the possibilities for data analysis are broader
than have been used in past studies of attine ants.
In this article I reexamine load carriage in two Central American attine species, Atta colombica and A. cephalotes. I begin with an "agnostic" view of locomotion in these ants by calculating six different regression models of laden speed in relation to other variables. No clearly best model emerges on statistical grounds alone, but experimental data in which I compare speed before and after manipulation of a load mass suggests that absolute load mass has a linear effect on laden speed. Why this should be so in biomechanical terms is unknown.
I also consider the locomotion data in relation to a measure of foraging
performance, the "leaf transport rate"
(Rudolph and Loudon, 1986), in
which locomotion velocity is a factor. Rudolph and Loudon
(1986) have claimed that the
leaf transport rate of Atta cephalotes ants is maximized under any
loading ratio from approximately 3.5 to 6.5, irrespective of the size of the
ant. My analysis reveals a more complex pattern in which the relation between
loading ratio and transport rate differs for ants of different body size.
Additionally, I show analytically that none of the regression models of
walking speed I examined is consistent with the Rudolph-Loudon range of
body-size independent, rate-maximizing loading ratios.
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METHODS |
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Sites and species
I studied a colony of Atta colombica Guérin on Barro Colorado Island (BCI), Panama, in September-October 1989 during the BCI rainy season, and four colonies of Atta cephalotes L. in the La Selva Biological Station (LS), Costa Rica, January-March 1998, during the LS dry season. Both sites contain lowland Central American rainforest (Leigh et al., 1982
; McDade et al.,
1994) and numerous Atta colonies. The BCI colony of
A. colombica foraged diurnally, and the LS colonies of A.
cephalotes foraged nocturnally in January and early February, with a
shift toward daylight foraging beginning in late February. Despite these
differences, the two species are ecologically and morphologically similar
(Weber, 1969).
Measurements
I measured walking speed of ants traversing 1-m sections of cleared, level
foraging trails during peak hours of leaf harvesting. The sections chosen had
smooth soil bases and were free of major obstacles. Air temperature during the
measurements on BCI varied from 25° to 28°C; trail temperatures during
measurements at LS varied from 24.5° to 27°C.
At BCI, the Atta colombica workers were transporting leaf fragments from a Cordia alliodora (Boraginaceae). I arbitrarily selected 100 laden workers, altered their loads by cutting the fragment with a small scissors or by adding a piece of aluminium foil, and timed to the nearest 0.1 s their transit over a 1-m segment of trail. Experimental manipulation of loads breaks up the natural covariance between ant size and load mass, an essential procedure to test load effects on performance.
At LS, I obtained data from 30 Atta cephalotes workers in a colony foraging nocturnally on an Ampelocera holteii (Ulmaceae), 15 workers in a colony foraging nocturnally on a Virola sebifera (Myristicaceae), 100 workers in a colony foraging diurnally on an Inga sp. (Mimosaceae), and 90 workers in a colony foraging diurnally on a vegetation source that was not identified. At LS I altered load masses to allow comparison of speed before and after the manipulation. Laden ants were timed with their natural loads over the first meter of a 3-m course. Upon completion the load was either reduced by clipping or increased by adding aluminium foil weighing approximately 5, 10, or 20 mg, and the ants were allowed to equilibrate to the new load in the second meter of the course. Transit time with the manipulated load was measured over the third meter.
The timed ants and their loads were collected and stored in individual vials. Leaf fragments were weighed to the nearest 0.1 mg within 2-3 h of collection for BCI fragments and after overnight storage at 4°C for LS fragments. I weighed ants to the nearest 0.1 mg and measured femur lengths (suture with trochanter to articulation with tibia) to 0.05 mm (BCI) or 0.02 mm (LS) under a dissecting microscope with an ocular micrometer.
To determine the pattern of natural load mass carriage by ants, I made random collections of 710 laden A. colombica workers at 3 vegetation sources on BCI and of 1582 laden A. cephalotes workers at 5 vegetation sources at LS. Load masses, ant weights, and femur lengths were determined in the manner described above.
Statistical analyses
For each ant species I analyzed the following regression models relating
locomotion velocity to load mass and ant size (the error terms are omitted for
clarity):
 | (2a) |
 | (2b) |
 | (2c) |
 | (2d) |
 | (2e) |
 | (2f) |
In these equations v is velocity, vrel is
relative velocity in units of femur length per second, F is femur
length, the b's are regression coefficients, and the other terms are
as in Equation 1. Because all measured variables contained intrinsic variance,
ordinary least-squares (OLS) regression, which assumes that independent
variables are experimentally fixed and free of variance, is not the most
appropriate statistical technique to estimate parameter values
(LaBarbera, 1989;
McArdle, 1988). Instead, I
used reduced major axis (RMA) regression, a technique that is robust to
variation in the error structure of the variables
(McArdle, 1988). When
loge-transformed variables were used to estimate
parameters for models 2d and 2e, a correction factor,
exp(s2/2), in which s is the standard error of
estimate, was applied for back-transformation
(LaBarbera, 1989).
Using the same data, I calculated for each laden ant of each species its
leaf transport rate, defined by Rudolph and Loudon
(1986) as the product of load
mass and velocity, Mlv. I then examined
Mlv as a function of loading ratio, L, using
nonlinear regression (least-squares criterion of fit with Gauss-Newton
iteration) to fit the equation y = a(1 -
e-bx). This equation allows the regression curve to reach
an asymptote at a, with a more rapid approach to the asymptote the
greater the value of b. The square of the correlation between
predicted and observed values is used as the nonlinear regression
R2. I initially analyzed all data pooled across ant body
size and then analyzed separately three subsets of body size to determine if
the transport rate-loading ratio relations differ among size classes and in
comparison to the overall relation.
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RESULTS |
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Carriage velocity
Reduced major axis regression coefficients for the models in Equations 2a-f are presented in Table 1, along with the simple or multiple correlation for the variables involved. In each of the 12 regressions, the correlations are significantly different from zero (p <.0001), as expected. There seems to be no clearly superior model judging on the correlations alone, and certainly no single model that seems best for both species, although they are similar morphologically and might be expected not to differ much in the biomechanics of load carriage. Unmeasured factors such as intensity of trail traffic and number of collisions with other workers probably produce a scatter of data that allows a similar statistical fit to several models. However, experimental manipulation of loads provides more insight into Atta locomotion.
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Comparison of velocity before and after manipulation of load masses of Atta cephalotes workers shows that speed changes linearly with change in absolute load mass (Figure 1). Some of the scatter in the data of Figure 1 may be due to alarm or escape reactions after experimental manipulations, especially because adding weights required somewhat intrusive handling. The linear correlation for the data in Figure 1 is -0.76 (significantly different from 0 at p <<.0001). There is no suggestion of nonlinearity judging by the significance of quadratic (p =.26) or cubic (p =.37) terms in polynomial regression.
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Ma A linear effect of absolute load mass on speed is incompatible with Equations 2d and 2e but consistent with the other models. Equation 2a predicts that smaller ants suffer a steeper decline in speed with added load mass than larger ants, and equation 2f predicts the decline would be steeper for larger ants. Equations 2b and 2c imply that the effect of load mass on speed would be independent of ant size.
To test whether the pattern in Figure
1 is independent of ant size, I calculated a generalized linear
model of 
v as a function of Ml,
Ma, and the Ml x
Ma interaction. The interaction effect (evaluated after
Ml and Ma direct effects) was
significant (semipartial r2 =.024, t = 3.69, df =
221, p <.001), indicating that the linear effect of load mass on
speed is not independent of ant size. Inspection of
Figure 1 suggests that ants in
the smallest size class (Ma < 5 mg) display a steeper
slope, whereas ants in the largest size class (Ma 
15
mg) display a more shallow slope. Based on these results, Equation 2a is
supported as a model of laden locomotion. However, there are few data for the
largest and smallest size classes, and the apparent difference in slopes needs
confirmation from additional study.
Moreover, Equation 2a contains an unlikely implication: if a load that slows an ant to zero velocity is taken to be the largest load it can carry, then Equation 2a implies that all ants reach v = 0 at the same loading ratio, L = -b0/b1, or 9.5 for A. colombica and 7.9 for A. cephalotes. However, my manipulations of load weight suggest that small workers more readily sustain high loading ratios than do larger ants (see Figure 2). Equations 2b and 2c are more realistic in this regard because they imply (upon solving for v = 0) that small ants can tolerate higher maximum loading ratios than large ants.
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Leaf transport rate
Figure 2 shows the leaf
transport rate, Mlv, of laden workers of each species as a
function of loading ratio. Figure
2a,b presents the data in the same fashion used by Rudolph and
Loudon (1986): mean ± 2
SE of Mlv is shown for unit intervals of loading ratio
(except for L 7). For both species, there appears to be an
approximate plateau in mean Mlv across loading ratios of
about 3-7 (with a possible decline for higher L). This broad maximum
closely resembles the pattern found by Rudolph and Loudon. Visual assessment
of this apparent plateau was the basis for their claim that leaf transport
rate is maximized by any loading ratio from 3.5 to 6.5, for ants of any
size.
Figure 2c,d displays the individual data underlying the means. Nonlinear regressions through these data produce curves similar to the putative plateaus of Figure 2a,b, but the scatter of data about the curves is obviously large (R2 is.28 for A. colombica and.34 for A. cephalotes). The data in Figure 2a-d are pooled across ants of all body sizes, thereby tacitly accepting the assumption that a 5-mg load on a 5-mg ant has the same effect on leaf transport rate as a 20-mg load on a 20-mg ant because the loading ratios are the same in both cases. Separate consideration of three distinct size classes in Figure 2e,f indicates that this assumption is not correct.
Figure 2e,f presents data for ants of 5-6 mg, 10-11 mg, and 15-20 mg (the last category is wider to include a sufficient number of points). Nonlinear regressions within each of the size classes of A. cephalotes and within the two smaller size classes of A. colombica show good fit to the data, with R2 values ranging from 0.60 to 0.87. [For the largest size class of A. colombica, nonlinear regression did not converge on a solution, and the linear relation is shown instead (R2 =.97).]
Two important patterns are evident in
Figure 2e,f. First, regressions
within individual size classes provide a much better fit to the data than does
a single regression that pools all body sizes. This suggests that the relation
of Mlv to L is not the same for ants of all
sizes. Indeed, the scatter of data in
Figure 2c,d is due largely to
differences among body size classes. Second, the regression curves do not
closely approach their asymptotes until loading ratios are large (particularly
for the larger ants). There is little support for the contention of Rudolph
and Loudon (1986) that all
ants, whatever their size, reach a performance plateau with loading ratios of
3.5-6.5.
Figure 3 shows loading ratio in relation to body mass for randomly collected laden ants of both species. The majority of loading ratios for 5- to 6-mg ants are below 5; for 10- to 11-mg ants below 4; and for 15- to 20-mg ants below 3. Thus, most natural loads are below the loading ratios at which their bearers come near the asymptotic maxima of leaf transport rates shown in Figure 2e,f.
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Analytical prediction of Mlv-maximizing loading
ratios
Another way of considering the question of rate maximization is to use the
regression equations for walking speed as functions for further analysis. Any
conclusion about leaf transport rate should be compatible with conclusions
about laden velocity, in that laden velocity is a factor in the term
Mlv. The data do not point clearly to a single best
regression model of velocity, but a single best model is not needed to
establish an important point: none of the alternatives examined is compatible
with the Rudolph and Loudon
(1986) claim of a universal
range of rate-maximizing loading ratios for all ants.
If velocity is related linearly to loading ratio (Equation 2a), then
Mlv would be greatest at
 | (3a) |
 | (3b) |
 | (3c) |
). The locomotion Equations 2d and 2e predict that
Mlv reaches a maximum only at infinite load mass
(appendix, case 4). Equation 2f is largely uninformative with respect to an
optimal loading ratio because relative velocity, vrel, is
not a term in Mlv. Consider what these alternative Mlv-maximizing optima indicate. Equation 3a gives an optimum loading ratio that applies to all ants regardless of body size, but the optimum is a single value of L (for a given set of regression parameters) and not a broad range. For the parameter estimates obtained in this study (Table 1), Equation 3a implies rate-maximizing loading ratios of 5.2 for Atta colombica and 4.5 for A. cephalotes. In contrast, Equations 3b and 3c imply that transport rate is maximized over a range of loading ratios, but, because the body size variables Ma or F appear in the right-hand side expressions, the predicted optima necessarily depend on the size of the ants involved. The infinite optimal loading ratios implied by Equations 2d and 2e are biologically meaningless, and Equation 2f is inapplicable to the problem at hand.
Thus, none of the locomotion models is compatible with a single broad range
of rate-maximizing loading ratios for all ants regardless of their size.
Either laden speed follows peculiar rules which these equations do not even
approximate (unlikely, given the reasonably high correlations in
Table 1), or the Rudolph and
Loudon plateau hypothesis is incorrect. Curiously, Rudolph and Loudon
(1986) report laden locomotion
using a regression model like Equation 2c (except they use head width rather
than femur length as the size measurement). Thus, their locomotion model and
their plateau hypothesis cannot both be correct.
Figure 3 shows the rate-maximizing optima from Equations 3a-c (using parameter values from Table 1) superimposed on the random samples of laden ants. No matter which locomotion equation is used to predict peak performance, the majority of loads for both species are below the theoretically optimal sizes. Equations 3b and 3c seem to form an approximate upper boundary for the scatter of natural loads, but this may be fortuitous.
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DISCUSSION |
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The results of this study confirm that intraspecific variation in body size affects both laden velocity and leaf transport rate in Atta ants. Six locomotion models that account for body size variation in different ways were analyzed for each species (Table 1). Judging by the simple or multiple correlation among the variables involved, all six models are reasonably successful at explaining laden walking speed. However, speed changes after experimental load manipulation suggest that load mass has a linear effect on speed (Figure 1). A statistically significant interaction effect, in which the linear relation is steeper for smaller ants, is most compatible with the model in Equation 2a, which scales loads to body size by use of the loading ratio. However, Equations 2b and 2c give a more realistic prediction about maximum possible loads, if we assume that maximum loads slow an ant to zero velocity.
Although loading ratio rescales load size relative to body size, it does
not completely incorporate all body-size dependence in the relation between
fragment size and leaf transport rate
(Figure 2e,f). Indeed, by
pooling ants of different body size, as in
Figure 2a,b and in Rudolph and
Loudon (1986), the latent
body-size dependence is obscured, leaving the incorrect impression of a single
plateau in leaf transport rate for all ants. Plateaus in transport rate may
occur, but Figure 2e,f shows
that it is not the same plateau for large and small workers.
I have used leaf transport rate in the present analysis to allow comparison
with other literature on attine foraging, but it may not be an appropriate or
useful measurement of foraging performance. The quantity
Mlv has some appeal because the units can be interpreted
as the leaf biomass carried a given distance per unit time. But these units
are different from the more conventional foraging measure of (gross or net)
gains per time, and the two measures do not predict the same optimal load
masses (Burd, 1996a). One
problem with Mlv is that it pertains only to an ant's
return laden journey, although the outbound journey and leaf cutting are time-
and energy-demanding components of a foraging excursion. Furthermore, the leaf
transport rate takes no account of the way in which large numbers of workers
interact to collectively yield the colony level rate of resource acquisition.
Thus, despite the common use of leaf transport rate to measure attine
performance, it may at best serve an heuristic function in foraging
studies.
If, as Figure 3 implies,
natural loads are too small to maximize Mlv or to maximize
the gross rate or energetic efficiency of tissue delivery to the nest
(Burd, 1996a), does this mean
the ants are not foraging optimally? Two hypotheses have been offered to
explain how suboptimal individual performance of Atta ants may be a
component of optimal group foraging. Roces and
Núñez
(1993) proposed that small
loads allow laden ants to return more quickly to recruit nest mates, thereby
increasing the rate at which the whole colony exploits a resource. However,
rapid return to the nest would seem irrelevant for the majority of foraging
time when nearly continuous flows of outgoing and returning traffic
prevail.
I have proposed (Burd,
1996b) that ants engaged in cutting hinder their nest mates'
access to leaf margin. By taking smaller fragments they relinquish the
resource more quickly and allow more workers to obtain fragments per unit of
colony foraging time. A model of this process based on queuing theory
predicted load sizes for optimal colony performance that correspond well to
natural load sizes (Burd,
1996b), but the detailed behaviors assumed in the queuing model
have not been tested.
Schmid-Hempel et al. (1985)
have suggested that small nectar loads taken by honey bees (Apis
melifera) maximize the ratio of energetic gains to energetic expenditure
of foraging. This strategy would maximize the total energy delivery of a
worker over its lifetime if it could spend only a fixed amount of energy, but
whether such considerations are important for walking, rather than flying,
insects is not certain (Fewell,
1988; Weier et al.,
1995).
There remains the biomechanical issue of why load mass affects velocity in
the linear manner indicated in Figure
1. A simple explanation would be that load mass has a linear
effect on either step frequency or stride length alone, without affecting the
other. However, loading is unlikely to alter an ant's gait in so simple a
fashion. Step frequency in crayfish is reduced by loading (walking on land
rather than in water), due to increased duration of the power stroke during
which legs are in contact with the ground
(Grote, 1981). But loads also
cause postural changes (legs tucked more closely under the body to provide
greater mechanical advantage against the load), and these changes reduce the
stride length. Similarly, in hermit crabs
(Herreid and Full, 1986) and in
painted turtles (Zani and Claussen,
1995), velocity during load carriage is related to modulation of
both stride length and step frequency. In ants, maintaining laden speed seems
to depend largely on the ability to maintain balance, with relatively long
legs being advantageous (Nielsen et al.,
1982). Leaf-cutting ants holding fragments in their mandibles must
experience considerable rotational force, and they generally position
fragments above their backs in an apparent attempt to improve balance. The
gait changes imposed by gravitational and rotational forces may be the
fundamental cause of the load effect on velocity in attines, but this awaits
detailed kinematic study of these ants.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONAPPENDIXREFERENCES |
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Case 1
Assume that locomotion follows an equation of the form v = b0 + b1L. Substitution for v in Mlv yields Mlv = Ml(b0 + b1 L). Because Ml = Ma (L - 1) by the definition in Equation 1 of the main text, further substitution into Mlv yields
 |
Differentiating the above equation with respect to L produces
 |
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2Mlv/L2 =
2b1Ma, is negative if
b1 is negative (higher loading ratio decreases velocity),
indicating that Equation 3a specifies a maximum.
Case 2
Assume a locomotion equation of the form v =
b0 + b1Ml +
b2Ma. Substitution of this and of
Ml = Ma(L - 1) into
Mlv yields
 |
Differentiating this equation with respect to L results in
 |
 |
2Mlv/L2 =
2b1Ma2, is negative
provided the regression coefficient b1 is negative, so the
critical point in Equation 3b is a maximum.
Case 3
Assume a locomotion equation of the form v =
b0 + b1Ml +
b2 F. By a derivation similar to that in case 2,
the critical point is found to be
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Case 4
Assume a locomotion equation of the form v =
b0Mlb1
Mab2. Substitution into
Mlv as in the previous cases yields
 |
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When the above equation is set equal to zero, a solution occurs only at
L 
, provided b1 is negative. If the
locomotion equation is originally based on F rather than on
Ma (Equation 2e), then
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As before, when the above equation is set equal to zero, a solution occurs
only at L .
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ACKNOWLEDGEMENTS |
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I thank the Smithsonian Tropical Research Institute and the Organization for Tropical Studies for making their field stations at Barro Colorado Island and La Selva available, and the responsible ministries of the governments of Panama and Costa Rica for permission to conduct the research. Susan Giles provided unflagging assistance with the field work at La Selva. I thank N. Aranwela, I. Cuthill, G. D. Sanson, and three anonymous reviewers for helpful comments on the manuscript. This study was funded by the Australian Research Council.
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