TSC project
Programs and what they do.
***Need to get to the essential question/problem. I cannot model EVERYthing, every
movement of an animal – or a person, for that matter - .
The essential question:
1. How to discriminate between a person moving along the path, in no fear of ambush, from
indigenous personnel or animals.
a. Want a probability that a particular movement falls into each of the categories.
b. Is speed of the essence? That is, does the radar operator need the algorithm to
quickly calculate and display the probability that the target is a bad guy or not?
Or, can a target be watched for a long time, while it covers a distance?
c.
2. There are in effect two questions, here: detecting real changes in position in noisy data,
and using the (estimated) real changes in position to identify the source of radar echoes.
3. ***Maybe instead of looking at distribution of velocity values, I should look at
location values? Maybe do that also?***
a. The idea here would be that you wouldn’t have to see them all the time; what
you’d be looking at would be the pattern of the target’s appearance/disappearance
and how that compared with patterns based on random motion.
b. For one thing, humans – especially bad guys – are more apt to stick to a trail than
most non-human mammals, which might use a trail for a while, but will fairly
quickly leave the trail to feed/forage. Trails, even game trails, are generally there
to make it easier to get from one place to another with minimal hassle & energy
expenditure. They’re rarely in/near good feeding locations.
c. How to generate a distribution of patterns of location? Do I need knowledge of
the location of any trails in the area of interest?
d. Manly (Chap. 4, p. 81) refers to the use of the bootstrap to test whether a set of
points is randomly distributed within a given region (Besag & Diggle, 1977.
Simple Monte Carlo tests for spatial pattern. Applied Statistics 26:327-333).
*** Besag has published a number of papers that may be relevant.***
4. ***Need to look at this: Nonlinear dynamics and target detection in cluttered
environments.pdf
Programs and what they do
1. TSC_project – does everything
2. add-error_1 – polynomial path with damped oscillations
a. Calculates radial component of velocity, plots with quiver.
3. add_error_2 – simple polynomial path
4. dot_product_example – calculates
5. human_path_2 – ***
6. human_path_1 – ****
7.
Pseudocode
8. Define a path with a function and numerically approximate its length, create a matrix of
(𝑥, 𝑦, 𝑙𝑒𝑛𝑔𝑡ℎ) data, and sample from that. Don’t worry about integrating to find a
segment length.
𝑓(𝑥) = 𝑒 𝑐5 +𝑐4 𝑥+𝑐3 𝑥
2 +𝑐 𝑥 3 +𝑐 𝑥 4
2
1
+ 𝑐6 𝑒 −𝑐7 𝑥 𝑐8 sin(𝑐9 𝑥)

𝑓′(𝑥) = (𝑐4 + 2𝑐3 𝑥 + 3𝑐2 𝑥 2 + 4𝑐1 𝑥 3 )𝑒 𝑐5 +𝑐4 𝑥+𝑐3 𝑥
− 𝑐6 𝑐7 𝑐8 sin(𝑐9 𝑥) 𝑒 −𝑐7 𝑥
2 +𝑐 𝑥 3 +𝑐 𝑥 4
2
1
+ 𝑐6 𝑐8 𝑐9 𝑒 −𝑐7𝑥 cos(𝑐9 𝑥)
9. Position unit at start of path.
10. Unit will walk along the path for a randomly-selected time.
11. The basic unit of movement along the path for humans will be the length of a single step
(step_length) taken by a human. This is not ∆𝑥!!!
(𝑥0 , 𝑦0 )
step_length
∆𝑥
∆𝑦 = 𝑓 ′ (𝑥0 )∆𝑥
(𝑥1 , 𝑦1 )
(𝐬𝐭𝐞𝐩_𝐥𝐞𝐧𝐠𝐭𝐡)2 = (∆𝑥)2 + (∆𝑦)2
= (∆𝑥)2 + (𝑓 ′ (𝑥0 , 𝑦0 )∆𝑥)2
= (∆𝑥)2 + [𝑓 ′ (𝑥0 , 𝑦0 )]2 (∆𝑥)2

(∆𝑥)2 + [𝑓 ′ (𝑥0 , 𝑦0 )]2 (∆𝑥)2 = (𝐬𝐭𝐞𝐩_𝐥𝐞𝐧𝐠𝐭𝐡)2

(∆𝑥)2 {1 + [𝑓 ′ (𝑥0 , 𝑦0 )]2 } = (𝐬𝐭𝐞𝐩_𝐥𝐞𝐧𝐠𝐭𝐡)2

(𝐬𝐭𝐞𝐩_𝐥𝐞𝐧𝐠𝐭𝐡)2
∆𝑥 = √
{1 + [𝑓 ′ (𝑥0 , 𝑦0 )]2 }
a. How do I handle step length for animals?
b. step_length could be allowed to vary some to allow for normal variation in step
length.
c. Reduce step_length (for animals) when animal is foraging, and allow it to be
negative.
d.
12. The radial/tangential velocity question
13. Basic movement patterns:
a. Bad guys stick to the path, maybe stop to rest once in a while.
b. Indigenous humans & other mammals mostly stick to the path, every once in a
while wandering off to forage
i. Maybe have canids wander back-&-forth across the path as they progress.
c. Prey species (ungulates, etc.) apt to show a stop-&-start movement pattern, as
they stop to listen/smell for predators.
i. Humans concerned about being ambushed will behave this way, too.
d. ***
14. According to Allan, the accuracy of the radar is “meters” radially, “tens of meters”
tangentially. So, how to deal with this? Possibilities:
a. First approximation: sample bivariate normal distribution with different
variances?
b. Need to ‘generate’ the variances in the radial and tangential directions then
‘translate’ them into a motion in what direction?
i. Along the path – NO
ii. ***
c.
T
𝒅𝒚
R
V= 𝒇 ( )
𝒅𝒙

(0,0)
15. Get a random variate representing the time the unit moves along the path until a ‘stop’,
when it ‘decides’ whether to continue along the path or move off the path to exploit a
patch..
a. If it’s non-human or a local inhabitant
i. Keep it on the path until a stop, then let it turn off the path at some userspecified (random?) point? Let it
ii.
b. If it’s a transient
c. ***
16. Patch behavior
a. Move orthogonal to path? We’ve got the
derivative:
∆𝑦
∆𝑥
Want:
1.
2.
Have
1.
2.

1.
∆𝑥, −∆𝑦, or
−∆𝑥, ∆𝑦
(𝑥, 𝑦)
𝑑𝑦
𝑑𝑥
Pick random ∆𝑥, corresponding
𝑑𝑦
sign for ∆𝑦 = ∆𝑥 ∙ 𝑑𝑥
b. Once an animal gets in a patch, should it be able to move directly to another
patch? – NO.
c.
17. At a distance of 10 km, an error of 10 m  error of 0.0573o.
18. The radar can only detect moving targets, so the errors must be added to the animal’s
motion.
a. The errors should be calculated parallel and perpendicular to the radar beam, then
‘translated into ∆𝑥, ∆𝑦 values that are added to the target’s position?***
y
tangential
x
radial
To
Detector
b. If I’m generating the errors by random sampling of a bivariate normal
distribution, the semi-major axis of the points should coincide with the tangential
vector and the semi-minor axis should coincide with the radial vector.
c. If you have a vector 𝐕 = [𝑥, 𝑦] (starting at the origin), then orthogonal vectors are
given by [– 𝑦, 𝑥] and [𝑦, −𝑥].
d. Set the magnitude of the velocity vector equal to the walking speed. Then
y
T
V
R
x

(
𝒅𝒚
)
𝒅𝒙
e. What do we have? What do we want?
𝑑𝑦
i. Have 𝑦 = 𝑓(𝑥), 𝑑𝑥 , ‖𝐕‖
ii. Want 𝐑, 𝐕 so I can translate the random variates from the bivariate
distribution into ∆𝑥, ∆𝑦 values for errors the particle’s motion.
iii. How would I actually do this? Sample the bivariate distribution for a
pair of random variates…should the magnitude of these then be mapped
onto 𝐑 & 𝐕, then converted to (∆𝑥, ∆𝑦) values to reposition the particle
along the path?
iv. I think I just let the particle move along the path, keeping track of its
position, then at each step add a random error to the position at the end of
each step.
1. The only correlation will be between the positions on the path; it’s
not like the particle will start from an erroneous position. Put
another way, the true position will be corrupted by errors.
v. ***
vi.
f. ***
19. Can the operator/analyzer get an estimate of the error from changes in position over very
short time scales, which presumably would be due to error?
20. Maybe a running average could be used to partition the apparent changes in position into
real changes and detector error.
21. ***
22. Time to go Bayesian? http://en.wikipedia.org/wiki/Bayesian_inference
a. ***READ THE Hanson et al. 1990 PAPER***
b. How would this go? Bayesian inference gives a conditional probability or
likelihood that some hypothesis is true (or false) given some observations.
c. Bayes Theorem: relates the conditional and marginal probabilities of events A
and B, where B has a non-vanishing probability:
Pr(B|A)Pr(A)
Pr(A|B) =
Pr(B)
Each term in Bayes' theorem has a conventional name:
 P(A) is the prior probability or marginal probability of A. It is "prior" in the
sense that it does not take into account any information about B.
 P(A|B) is the conditional probability of A, given B. It is also called the
posterior probability because it is derived from or depends upon the
specified value of B.
 P(B|A) is the conditional probability of B given A.
 P(B) is the prior or marginal probability of B, and acts as a normalizing
constant.
Intuitively, Bayes' theorem in this form describes the way in which one's beliefs
about observing 'A' are updated by having observed 'B'.
d. Applied to spam filtering:
Mathematical foundation
Bayesian email filters take advantage of Bayes' theorem. Bayes' theorem, in the
context of spam, says that the probability that an email is spam, given that it has
certain words in it, is equal to the probability of finding those certain words in
spam email, times the probability that any email is spam, divided by the
probability of finding those words in any email:
Pr(words|spam)Pr(spam)
Pr(spam|words) =
Pr(words)
e. I would want the posterior probability that a bogy was a bad guy given some
observation(s). 
Pr(Data|Bad Guy)Pr(Bad Guy)
Pr(Bad Guy|Data) =
Pr(Data)
***So, what are the data?***
i. One possibility: assume the distribution of velocities is as I stated in the
feasibility study proposal – Gaussian when foraging, negative exponential
(Poisson?) when ‘migrating’.
ii. Another possibility: Say we know that there’s a probability that an animal
will stop every T minutes, meaning it would disappear at least every T
minutes. Let’s say that
f.
23. Need to look at this: http://en.wikipedia.org/wiki/Empirical_Bayes_method ***
24.
Position new particle
at start, (x_path,
y_path) = (−2000, )
Pick duration of the
next bout of movement
along the path.
t_res
bout_dur
While t_res < t_per, occupy patch
Move one step along
the path.
time = bout_dur?
?
> t_per
1. Move to patch
2. Choose persistence
time, t_per
3. Track residence
time, t_res.
NO
YES
YES
YES
End of path?
NO
Stay on path?
NO
time < step_dur
?
YES
***end of page***
Notes, thoughts, etc.
1. ***IMPORTANT – what the radar operator will see – and what the decision algorithm
will have as data – is the radar echo. Nothing else.
2. Superdiffusion is exactly the way to go for the non-human animal movement.
3. Animal moves a long distance along the path, then finds something interesting, leaves the
path, wanders around a bit, then returns to path, takes another long jaunt, repeats.
4. During field evaluations, take along a dog or two, to simulate a non-human moving along
a path.
a. ***
5. Does the accuracy of positioning depend on the radial velocity?
a. I’ll let them worry about that…I’ll just create the models.
6. Many animals in forested areas are crepuscular, relatively few are diurnal, many
predators will be active all night (until they catch prey).***
a. Local knowledge will be important here.
7. Need to scale things to realistic values:
a. Velocities/step lengths appropriate for humans and other animals.
b. Minimum detection velocity 1 m s1 (2.2 mile h1)
i. Heavily-laden humans would barely be detectable
c. Radar-target distance = 10,000 m
d.
8. #6 (need for scaling) means I need to consider
a. tortuousness of the path, since that will determine what proportion of the time the
particle is moving radially or tangentially with respect to the radar unit.
b. length of path  number of data points
9. Where should the radar be positioned relative to the path?
a. Perpendicular to path: humans rarely visible because almost all movement would
be point-to-point, animals visible when they interrupt point-to-point movement to
forage.
b. In line with path: humans almost always visible because almost all movement
would be point-to-point, animals would tend to disappear when they interrupt
point-to-point movement to forage.
10. ******
11.
12. WHAT IS THE QUESTION/PROBLEM?
a. Only detect if moving 1 m/sec
b. Identify the paths.
c. Send a CV, flesh out e-mail,  seed funding $5K 
d. Range to meters; azimuth to tens of meters; random noise; don’t see tangential
motion; ground clutter;
13. Supplement scientific data with local intelligence regarding species, their abundance,
behavior, etc.
14. This will be a somewhat involved exercise, perhaps more so than you were expecting.
a. The model may need to be terrain-specific.
i. In flat deserts, game trails seem to go straight from one water hole to
another. In mountainous terrain, seem to take path of least resistance,
energy minimization, time minimization, or??? Humans moving through
desert terrain might ignore the game trails, in order to get from one tactical
objective to another, rather than from one water whole to another, but
follow game trails more closely in mountainous terrain.
1. Or, they might be like the Apache, and not worry about little things
like mountains.
ii. Fractal dimension of a path could well differ in mountainous terrain if
humans tend to follow game paths.
iii. Also, there’s some evidence that size will affect the results – it’s relatively
cheaper for smaller animals to run up and down hills than it is for larger
ones. So, assuming that a range of animal sizes – dog-sized to elk-sized,
say – would produce the same radar footprint, one could imagine that
b. May need to take into account the age of animals, even their gender.
i. Take bears, leopards, lions, deer? – when they’re ‘kicked out of the nest’,
juvenile females often are allowed to remain relatively close to the
mother’s territory, meaning they already know their environment, while
juvenile males are often expelled – if not by the mother, by any resident
male(s) in the area – meaning they have to move to an unfamiliar habitat.
It’s easy to imagine that the foraging patterns of juvenile males might will
differ from those of juvenile females, and that both might differ from
adults with established territories, yet change as they learn their ‘new’
habitat. . ***
c. ***
15. levy_partition.m generates frequency distributions for Levy flight-based
movements, with
Questions for Allan
1. Will we know the paths? Will we be able to position the radar to maximize the
proportion of the path that’s pointing directly at or away from the radar?
Crossing a ridge model:
1. ***
a. ***
∫ √𝒂 − 𝒙( ) 𝒅𝒙 =
References
Ecological Modelling
Volume 132, Issues 1-2, 30 July 2000, Pages 115-124
Modelling animal movement as a persistent random walk in two dimensions: expected
magnitude of net displacement
Hsin-i Wua, Bai-Lian Li
,
, b,
Timothy A. Springerc and William H. Neilld
a
Department of Industrial Engineering, Center for Biosystems Modelling, Texas A&M
University, College Station, TX 77843-3131, USA b Department of Biology, University of New
Mexico, 167 Castetter Hall, Albuquerque, NM 87131-1091, USA c Wildlife International, 8598
Commerce Drive, Eastern, MD 21601, USA d Department of Wildlife and Fisheries Sciences,
Texas A&M University, College Station, TX 77843-2258, USA
Available online 18 August 2000.
Abstract
We present semi-empirical model of persistent random walk for studying animal movements in
two-dimensions. The model incorporates an arbitrary distribution for the angles between
successive steps in the tracks. Inclusion of a turning angle distribution enables explicit
computation of the effect of persistence in the direction of travel on the expected magnitude of
net displacement of the animal over time. We employed a form-analogous approach to obtain
expressions for the expected net displacement and derived root mean square of the expected
displacement of an animal at the end of a multi-step random walk in which turning angles were
drawn from the Lemicon of Pascal, the elliptical, the von Mises, and the wrapped Cauchy
distributions. The accuracy of these expressions for the expected magnitude of net displacement
was tested by comparison with simulated results of persistent random walks where turning
angles were drawn form the wrapped Cauchy distribution. Our results should be useful in
predicting two-dimensional distribution of moving animals for which frequency distributions of
the turning angles can be measured.
Full Text:
Abstract:
S0218348X07003460.pdf
The origin of fractal patterns is a fundamental problem in many areas of science. In ecological systems,
fractal patterns show up in many subtle ways and have been interpreted as emergent phenomena related to
some universal principles of complex systems. Recently, Lévy-type processes have been pointed out as
relevant in large-scale animal movements. The existence of Lévy probability distributions in the behavior of
relevant variables of movement, introduces new potential diffusive properties and optimization mechanisms
in animal foraging processes. In particular, it has been shown that Lévy processes can optimize the success of
random encounters in a wide range of search scenarios, representing robust solutions to the general search
problem. These results set the scene for an evolutionary explanation for the widespread observed scaleinvariant properties of animal movements. Here, it is suggested that scale-free reorientations of the movement
could be the basis for a stochastic organization of the search whenever strongly reduced perceptual capacities
come into play. Such a proposal represents two new evolutionary insights. First, adaptive mechanisms are
explicitly proposed to work on the basis of stochastic laws. And second, though acting at the individual-level,
these adaptive mechanisms could have straightforward effects at higher levels of ecosystem organization and
dynamics (e.g. macroscopic diffusive properties of motion, population-level encounter rates). Thus, I suggest
that for the case of animal movement, fractality may not be representing an emergent property but instead
adaptive random search strategies. So far, in the context of animal movement, scale-invariance, intermittence,
and chance have been studied in isolation but not synthesized into a coherent ecological and evolutionary
framework. Further research is needed to track the possible evolutionary footprint of Lévy processes in
animal movement.
1: Nature. 2007 Oct 25;449(7165):1044-8.
Links
Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees
and deer.
Edwards AM, Phillips RA, Watkins NW, Freeman MP, Murphy EJ, Afanasyev V,
Buldyrev SV, da Luz MG, Raposo EP, Stanley HE, Viswanathan GM.
British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK.
EdwardsAnd@pac.dfo-mpo.gc.ca
The study of animal foraging behaviour is of practical ecological importance, and
exemplifies the wider scientific problem of optimizing search strategies. Lévy flights are
random walks, the step lengths of which come from probability distributions with heavy
power-law tails, such that clusters of short steps are connected by rare long steps. Lévy
flights display fractal properties, have no typical scale, and occur in physical and
chemical systems. An attempt to demonstrate their existence in a natural biological
system presented evidence that wandering albatrosses perform Lévy flights when
searching for prey on the ocean surface. This well known finding was followed by similar
inferences about the search strategies of deer and bumblebees. These pioneering studies
have triggered much theoretical work in physics (for example, refs 11, 12), as well as
empirical ecological analyses regarding reindeer, microzooplankton, grey seals, spider
monkeys and fishing boats. Here we analyse a new, high-resolution data set of wandering
albatross flights, and find no evidence for Lévy flight behaviour. Instead we find that
flight times are gamma distributed, with an exponential decay for the longest flights. We
re-analyse the original albatross data using additional information, and conclude that the
extremely long flights, essential for demonstrating Lévy flight behaviour, were spurious.
Furthermore, we propose a widely applicable method to test for power-law distributions
using likelihood and Akaike weights. We apply this to the four original deer and
bumblebee data sets, finding that none exhibits evidence of Lévy flights, and that the
original graphical approach is insufficient. Such a graphical approach has been adopted to
conclude Lévy flight movement for other organisms, and to propose Lévy flight analysis
as a potential real-time ecosystem monitoring tool. Our results question the strength of
the empirical evidence for biological Lévy flights.
1: J Anim Ecol. 2007 Mar;76(2):222-9.
Links
Minimizing errors in identifying Lévy flight behaviour of organisms.
Sims DW, Righton D, Pitchford JW.
Marine Biological Association of the United Kingdom, The Laboratory, Citadel Hill,
Plymouth, UK. dws@mba.ac.uk
1. Lévy flights are specialized random walks with fundamental properties such as
superdiffusivity and scale invariance that have recently been applied in optimal foraging
theory. Lévy flights have movement lengths chosen from a probability distribution with a
power-law tail, which theoretically increases the chances of a forager encountering new
prey patches and may represent an optimal solution for foraging across complex, natural
habitats. 2. An increasing number of studies are detecting Lévy behaviour in diverse
organisms such as microbes, insects, birds, and mammals including humans. A principal
method for detecting Lévy flight is whether the exponent (micro) of the power-law
distribution of movement lengths falls within the range 1 < micro < or = 3. The exponent
can be determined from the histogram of frequency vs. movement (step) lengths, but
different plotting methods have been used to derive the Lévy exponent across different
studies. 3. Here we investigate using simulations how different plotting methods
influence the micro-value and show that the power-law plotting method based on 2(k)
(logarithmic) binning with normalization prior to log transformation of both axes yields
low error (1.4%) in identifying Lévy flights. Furthermore, increasing sample size reduced
variation about the recovered values of micro, for example by 83% as sample number
increased from n = 50 up to 5000. 4. Simple log transformation of the axes of the
histogram of frequency vs. step length underestimated micro by c.40%, whereas two
other methods, 2(k) (logarithmic) binning without normalization and calculation of a
cumulative distribution function for the data, both estimate the regression slope as 1micro. Correction of the slope therefore yields an accurate Lévy exponent with estimation
errors of 1.4 and 4.5%, respectively. 5. Empirical reanalysis of data in published studies
indicates that simple log transformation results in significant errors in estimating micro,
which in turn affects reliability of the biological interpretation. The potential for detecting
Lévy flight motion when it is not present is minimized by the approach described. We
also show that using a large number of steps in movement analysis such as this will also
increase the accuracy with which optimal Lévy flight behaviour can be detected.
1: J Anim Ecol. 2008 Jul 9. [Epub ahead of print]
Links
Using likelihood to test for Lévy flight search patterns and for general powerlaw distributions in nature.
Edwards AM.
Pacific Biological Station, Fisheries and Oceans Canada, 3190 Hammond Bay Road,
Nanaimo, British Columbia, Canada V9T 6N7, and British Antarctic Survey, High Cross,
Madingley Road, Cambridge CB3 0ET, UK.
1. Ecologists are obtaining ever-increasing amounts of data concerning animal
movement. A movement strategy that has been concluded for a broad variety of animals
is that of Lévy flights, which are random walks whose step lengths come from probability
distributions with heavy power-law tails. 2. The exponent that parameterizes the powerlaw tail, denoted micro, has repeatedly been found to be within the Lévy range of 1 <
micro </= 3. Here, we use Monte Carlo simulations to show that the methods used to
infer the value of micro are inaccurate. 3. The widely used method of simply
logarithmically transforming a standard histogram of movement lengths has been shown
elsewhere to be problematic. Here, we further demonstrate how poor it is, and show that
it actually biases estimates of micro towards the Lévy range of 1 < micro </= 3, and can
bias estimates towards the value of micro = 2. Thus, previous reports of animals
undergoing Lévy flights, or of micro being close to the reported optimal value of micro =
2, may simply be a consequence of the bias generated by this method. 4. A technique that
has been recently recommended is to logarithmically bin the data and then normalize the
resulting histogram. We show that this technique also produces biased results, and suffers
from similar problems as those just outlined, although to a lesser extent. 5. The proposed
solution is to use likelihood. We find that calculating the maximum likelihood estimate of
micro gives the most accurate results (having also tested the rank/frequency method).
Likelihood has the further advantages of being the easiest method to implement, and of
yielding accurate confidence intervals. Results are applicable to power-law distributions
in general, and so are not restricted to inference of Lévy flights. 6. We also re-analyse a
data set of grey seal movements that was originally reported to demonstrate Lévy flight
behaviour. Using Akaike weights, we test four models, and find no evidence for Lévy
flights. Overall, our results suggest that Lévy flights might not be as common as
previously thought.
1: Ecol Appl. 2007 Mar;17(2):628-38.Links
Measurement error causes scale-dependent threshold erosion of biological
signals in animal movement data.
Bradshaw CJ, Sims DW, Hays GC.
School for Environmental Research, Institute of Advanced Studies, Charles Darwin
University, Darwin, Northern Territory, Australia. corey.bradshaw@cdu.edu.au
Recent advances in telemetry technology have created a wealth of tracking data available
for many animal species moving over spatial scales from tens of meters to tens of
thousands of kilometers. Increasingly, such data sets are being used for quantitative
movement analyses aimed at extracting fundamental biological signals such as optimal
searching behavior and scale-dependent foraging decisions. We show here that the
location error inherent in various tracking technologies reduces the ability to detect
patterns of behavior within movements. Our analyses endeavored to set out a series of
initial ground rules for ecologists to help ensure that sampling noise is not misinterpreted
as a real biological signal. We simulated animal movement tracks using specialized
random walks known as Lévy flights at three spatial scales of investigation: 100-km, 10km, and 1-km maximum daily step lengths. The locations generated in the simulations
were then blurred using known error distributions associated with commonly applied
tracking methods: the Global Positioning System (GPS), Argos polar-orbiting satellites,
and light-level geolocation. Deviations from the idealized Lévy flight pattern were
assessed for each track after incrementing levels of location error were applied at each
spatial scale, with additional assessments of the effect of error on scale-dependent
movement patterns measured using fractal mean dimension and first-passage time (FPT)
analyses. The accuracy of parameter estimation (Lévy mu, fractal mean D, and variance
in FPT) declined precipitously at threshold errors relative to each spatial scale. At 100km maximum daily step lengths, error standard deviations of > or = 10 km seriously
eroded the biological patterns evident in the simulated tracks, with analogous thresholds
at the 10-km and 1-km scales (error SD > or = 1.3 km and 0.07 km, respectively).
Temporal subsampling of the simulated tracks maintained some elements of the
biological signals depending on error level and spatial scale. Failure to account for large
errors relative to the scale of movement can produce substantial biases in the
interpretation of movement patterns. This study provides researchers with a framework
for understanding the limitations of their data and identifies how temporal subsampling
can help to reduce the influence of spatial error on their conclusions.
1: Anim Cogn. 2007 Jul;10(3):357-67.
Links
What wild primates know about resources: opening up the black box.
Janson CH, Byrne R.
Department of Ecology and Evolution, Stony Brook University, Stony Brook, NY 11794,
USA. janson@life.bio.sunysb.edu
We present the theoretical and practical difficulties of inferring the cognitive processes
involved in spatial movement decisions of primates and other animals based on studies of
their foraging behavior in the wild. Because the possible cognitive processes involved in
foraging are not known a priori for a given species, some observed spatial movements
could be consistent with a large number of processes ranging from simple undirected
search processes to strategic goal-oriented travel. Two basic approaches can help to
reveal the cognitive processes: (1) experiments designed to test specific mechanisms; (2)
comparison of observed movements with predicted ones based on models of
hypothesized foraging modes (ideally, quantitative ones). We describe how these two
approaches have been applied to evidence for spatial knowledge of resources in primates,
and for various hypothesized goals of spatial decisions in primates, reviewing what is
now established. We conclude with a synthesis emphasizing what kinds of spatial
movement data on unmanipulated primate populations in the wild are most useful in
deciphering goal-oriented processes from random processes. Basic to all of these is an
estimate of the animal's ability to detect resources during search. Given knowledge of the
animal's detection ability, there are several observable patterns of resource use
incompatible with a pure search process. These patterns include increasing movement
speed when approaching versus leaving a resource, increasingly directed movement
toward more valuable resources, and directed travel to distant resources from many
starting locations. Thus, it should be possible to assess and compare spatial cognition
across a variety of primate species and thus trace its ecological and evolutionary
correlates.
1: Anim Cogn. 2007 Jul;10(3):317-29.
Links
Route-based travel and shared routes in sympatric spider and woolly
monkeys: cognitive and evolutionary implications.
Di Fiore A, Suarez SA.
Center for the Study of Human Origins, Department of Anthropology, New York
University, 25 Waverly Place, New York, NY 10003, USA. anthony.difiore@nyu.edu
Many wild primates occupy large home ranges and travel long distances each day.
Navigating these ranges to find sufficient food presents a substantial cognitive challenge,
but we are still far from understanding either how primates represent spatial information
mentally or how they use this information to navigate under natural conditions. In the
course of a long-term socioecological study, we investigated and compared the travel
paths of sympatric spider monkeys (Ateles belzebuth) and woolly monkeys (Lagothrix
poeppigii) in Amazonian Ecuador. During several field seasons spanning an 8-year
period, we followed focal individuals or groups of both species continuously for periods
of multiple days and mapped their travel paths in detail. We found that both primates
typically traveled through their home ranges following repeatedly used paths, or "routes".
Many of these routes were common to both species and were stable across study years.
Several important routes appeared to be associated with distinct topographic features
(e.g., ridgetops), which may constitute easily recognized landmarks useful for spatial
navigation. The majority of all location records for both species fell along or near
identified routes, as did most of the trees used for fruit feeding. Our results provide strong
support for the idea that both woolly and spider monkey use route-based mental maps
similar to those proposed by Poucet (Psychol Rev 100:163-182, 1993). We suggest that
rather than remembering the specific locations of thousands of individual feeding trees
and their phenological schedules, spider and woolly monkeys could nonetheless forage
efficiently by committing to memory a series of route segments that, when followed,
bring them into contact with many potential feeding sources for monitoring or visitation.
Furthermore, because swallowed and defecated seeds are deposited in greater frequency
along routes, the repeated use of particular travel paths over generations could profoundly
influence the structure and composition of tropical forests, raising the intriguing
possibility that these and other primate frugivores are active participants in constructing
their own ecological niches. Building upon the insights of Byrne (Q J Exp Psychol
31:147-154, 1979, Normality and pathology in cognitive functions. Academic, London,
pp 239-264, 1982) and Milton (The foraging strategy of howler monkeys: a study in
primate economics. Columbia University Press, New York, 1980, On the move: how and
why animals travel in groups. University of Chicago Press, Chicago, pp 375-417, 2000),
our results highlight the likely general importance of route-based travel in the memory
and foraging strategies of nonhuman primates.
1: J Exp Biol. 2007 Mar;210(Pt 6):935-45.
Erratum in:
J Exp Biol. 2007 Apr;210(Pt 8):1489.
Links
Fractal landscape method: an alternative approach to measuring arearestricted searching behavior.
Tremblay Y, Roberts AJ, Costa DP.
University of California, Santa Cruz, Long Marine Laboratory, Center for Ocean Health,
100 Shaffer Road, Santa Cruz, CA 95060, USA. tremblay@biology.ucsc.edu
Quantifying spatial and temporal patterns of prey searching is of primary importance for
understanding animals' critical habitat and foraging specialization. In patchy
environments, animals forage by exhibiting movement patterns consisting of arearestricted searching (ARS) at various scales. Here, we present a new method, the fractal
landscape method, which describes the peaks and valleys of fractal dimension along the
animal path. We describe and test the method on simulated tracks, and quantify the effect
of track inaccuracies. We show that the ARS zones correspond to the peaks from this
fractal landscape and that the method is near error-free when analyzing high-resolution
tracks, such as those obtained using the Global Positioning System (GPS). When we used
tracks of lower resolution, such as those obtained with the Argos system, 9.6-16.3% of
ARS were not identified, and 1-25% of the ARS were found erroneously. The later type
of error can be partially flagged and corrected. In addition, track inaccuracies erroneously
increased the measured ARS size by a factor of 1.2 to 2.2. Regardless, the majority of the
times and locations were correctly flagged as being in or out of ARS (from 83.8 to 89.5%
depending on track quality). The method provides a significant new tool for studies of
animals' foraging behavior and habitat selection, because it provides a method to
precisely quantify each ARS separately, which is not possible with existing methods.