Measuring animal
activity from signal strength recordings
William W.
Cochran, Sparrow Systems, Fisher IL
Contents
Background and Quick Primer
Introduction
Methods, theory
Radio Equipment
Animal movement and signal change (Ds)
Visually derived estimates of activity
Reducing sequences of
signals (S) to digitized states via DS.
Converting state data to quantitative
activity indices (A%)
Accuracy of A% estimates
Interference, false or
fragmented data
Site selection
Relations among Dt, SI,
the number of animals (N), and transmitter specifications
Getting A% while direction finding
Comparison with activity switch methods
Glossary of terms
Literature & Bibliography
Bibliography
Appendix I: ARU technical
Appendix II: Worklists, Number of Channels
Appendix III: Additional figures
Appendix IV: Viewing and analysis tools
Appendix V: Review of methods literature
If you don’t have time for details,
jump over Background to Quick Primer and stop at its end..
Development of the method to be
described began in earnest about 1990 although I developed equipment for the
application much earlier, ie., the Falcon Five tracking receiver and
accessories in 1977-1982, marketed by Wildlife Materials,
Arlo Raim, from 1992 to present, often as a volunteer and
variously employed by the UI ECE dept, and INHS, is and has been a key participant in
operating the equipment and gathering much of the data presented. Thanks are
due and here given to the National Audubon Society, the INHS, and the UI ECE
department for their support, interest, or benign consent during the early
development period. Special thanks are due Dr. Larry Pater
and CERL; Pater’s vision, enthusiasm, and drive and the
contracts from CERL made possible the conversion of ad-hoc prototypes into a commercially
available product (ARU) that we hope will find use in the wildlife ecology
field. Feedback from Larry Pater, George Swenson,
Dave Delaney, and Andrew Walde (CERL project) and
Martin Wikelski, Roland Kays, and Franz Kuemmeth (STRI project) is
appreciated; it has helped reveal bugs in and fine tune the various programs
used in running the ARUs. It should be noted that the
CERL and STRI projects employ the equipment for direction finding and
radiolocation by triangulation as well as for generating activity data; only
the latter is the subject matter here.
Quick Primer
Aural or visual
detection of signal change has been used in a number of studies (
3,
4,
6,
8,
10,
11,
15,
17,
19,
23,
26,
34,
36,
43,
44,
47,
52
) and in the era of paper and tape
recorders, it was the only method available. These approaches adequately
revealed the presence of or times of onset and cessation of activity in
relation to environmental factors such as change in food supply, ambient light
level, temperature, etc. Such timing may be all that is asked of data, with no
attempt at a quantitative estimate of the level of activity in the intervals
between activity onset and cessation.
A quantitative employment of the
amplitude change method is based on body movements and posture changes that
cause a change in received signal. Animal posture
changes cause variations of proximity of an attached transmitter and its
antenna to the animal, causing the radiated power to vary due to resultant
changes in antenna efficiency and impedance. Also, because the signal radiated
in different directions varies with the transmitter antenna orientation,
movements of an animal as it turns or raises or lowers its head cause the power radiated toward the receiver to vary. The
combination of varying degrees of change of posture and orientation result in a
chaotic relationship between signal change (DS) and movement; small body movements sometimes causing large change
and vice versa. Change, therefore, is not a valid measure of the movement that
caused it. It is most important, however, that there is virtually no change
when there is no movement, permitting
successive pairs of signal measurements to be categorized either as no change =
no movement or some change = some unknown amount of movement.
It is the percent change in signal
that needs to be recorded, not the absolute change. Typical wildlife receivers
provide the latter, which has led users to believe that change is not a
reliable indicator of movement (trace this false rumor back from ref 25). A
receiver with output (S) proportional to the logarithm of input automatically
provides the needed percentage signal changes that are here called DS. In addition, it does not saturate at high
signal levels (animal nearby) or lose resolution at low levels (animal
distant). The Automatic Receiving Units (ARU) that we used record S values for
many animals at set time intervals (Dt, seconds).
The signal change
DS between
successive S measurements S1 and S2 spaced by time interval Dt was tested against a change
threshold T1 (Figure 3). Two states may result, active (A) when DS => T1 and inactive (I) when DS < T1. As noted above, DS is not a measure of the amount
of movement during Dt, instead, it
is an indicator of whether some unknown amount of movement has (DS => T1) or has not (DS < T1) occurred during Dt. Thus, a count of A states over a sampled interval
(SI) is not a count of
movements and, as we show later, derivation of a quantitative index of activity
(A%) must derive from a substantial collection of
state data (an SI much much greater than Dt).
A minimum signal
threshold T2 is necessary to account for periods when the signal is very weak
or absent, such as when the transmitter is distant or underground. Signal
cancellation from multipath propagation or signal
nulls due to transmitter antenna orientation can also cause very weak or
undetectable signals, even when the average received signal is strong.
Occasional and extended periods of very weak or absent signals are handled by
application of T2 as follows. If S1 < T2 and DS => T1 an A state results. If S2 < T2 and DS < T1 an
I state results. If S1 and S2
are both < T2, then a third weak-signal (W) state results.
In summary, DS measurements are evaluated as
above to create a temporal data set of A,
I, and W states. We refer to temporal plots of state data as
actograms (14. Georgii
1981, Figure 4). Actograms provide an excellent overview of the temporal
distribution of activity but differences in the intensity of activity, say for
whole days from one day to another or one animal to another, are not visually
apparent unless they are large (Figure
5).
Quantified differences in intensity of
activity for different weather, seasons, climates, habitats, individuals,
sexes, ages, etc. could, it seems, enhance understanding of the general ecology
of animals. Actograms provide an excellent visual impression of differences,
but impressions are subjective; a quantitative measure is preferable, such as
that shown in Figure 6.
Activity indices (A%) were derived as follows. Over an SI >> Dt, a state ratio (the sum of A states divided by the sum of A and I states) can be expressed as an activity percentage for that SI (A% = 100 x the state ratio). A% is a quantitative index to an average of an animal’s movements during SI. It is an index because the amount of movement represented by each state is unknown. It is a quantitative index because details of the random and somewhat chaotic relationship between movement and individual DS tend to average out over SI. We emphasize that A% is an index derived from an average of many DS measurements that are randomly related to but on average positively correlated with the movements that cause them. As an average over SI, higher accuracy of A% would be expected for longer SI and shorter Dt, ie., for larger sample sizes (more states). We found this to be true (Figure 10); for typical values see Table 1.
Time plots of S show periods of inactivity interspersed with periods of activity (Figures 1, 2). The state data were processed to detect and measure intervals over which I states outnumber A states and vice versa. We call these intervals sessions, either inactive or active; a session is dominantly rather than exclusively one or the other state (see Figure 12a). Frequency distributions of the session durations (visible in the masked actograms Figure 11) can be extracted to obtain another perspective of animal activity behavior (Figure 12b). The intensity of individual sessions (Figure 12a) may also provide useful information.
Introduction
Early in
1962, shortly after animal telemetry appeared, Professor Dwain Warner (1963)
articulated his vision of a need for and value of motion studies.
“One of the most significant observations
of an animal is its motility. Since the environment apparently furnishes or
modifies the stimuli which trigger basic responses within an animal, the
ability to follow an animal’s movements continuously and to attempt to
correlate these movements with environmental factors seems essential to
advances in ecology. Nearly all animals are at some time motile; and, since the causal factors of this
motivation in the natural environment are not adequately understood, continuous
recording of animal movements correlated with other events in the environment
should be given major emphasis .... The need to know an animal’s diel (24 hr), seasonal, and annual movements and the
physical as well as biological stimuli responsible for these movements has
become paramount .... ”
Warner’s
reference to movements necessarily included locomotor activity as one of many kinds of
movement.
Subsequently, radio location became
a common method for tracking place to place movements of animals to determine
their home range or territorial behavior. In many of these tracking studies, it
was noted that bearing measurement was often difficult due to random short-term
signal pitch and/or amplitude changes caused by animal body movements,
including place to place flying, walking, and running. These signal changes
were sometimes recorded as indices of motility from which diel
and other patterns of activity were derived (
1-8,
10,
11,
13,
15,
17-19,
20,
23,
26-32,
34,
36,
40,
41,
43,
44,
46-50,
52,
53
). No standard activity
measurement methodology has emerged from these studies and virtually all used
linear or qualitative non-linear detection that precluded quantitative analyses
that would allow detailed comparison of results. However, these studies
adequately show transitions between periods of little or no activity and
periods of substantial activity, such as occur with the daily onset and
cessation of activity.
Limitations imposed by the
processing and storage capacity of strip-chart or tape recorders vanished with
the plethora of computers, making procurement and processing of large data sets
practical. Large data sets, coupled with standardized quantitative analyses,
provide an opportunity to evaluate overall animal activity to ascertain
differences influenced by climate, season, habitat, habitat manipulation, etc.
The simplest categorization of activity into 2 states (has moved or has not
moved) falls short of Warner’s ideal that would include the nature of these
movements and their function. Temporal patterns and prior knowledge of behavior
can sometimes enhance interpretation of results. References
1,
3,
9,
15,
18,
21,
33,
36,
43,
49
discuss some
aspects of 2-state activity analyses, similar to One-Zero state sampling used
in visual behavior studies of primates (
54. Altmann and Wagner, 1970).
In
this manual we describe an activity monitoring method that uses signal changes,
but is immune to signal strength bias and has accuracy equivalent to methods
using transmitters with motion sensitive switches. The method will work with
conventional wildlife transmitters, pulsed or continuous, and in addition, is
more flexible in application than motion switch methods and can be implemented
in an ongoing study with tagged animals already in the field. Data for several
different species are used to illustrate the method. We describe equipment for logarithmic detection of signals, algorithms for
standardized computer processing of signal strength data into activity indices,
methods for estimating the accuracy of the activity indices, and a method for
producing frequency distributions of the duration of activity sessions (bouts). A brief comparison with
switch sensor activity monitoring is given.
The data we present here were collected by automated
receivers operated by built-in microcontrollers. These automated receivers
(Model ARU, Sparrow Systems, Fisher, IL)
are portable (15 x 15 x 15 cm weighing 1000 g); a power consumption of 0.2 watts permits operation from an
automobile battery for 2 months, or indefinitely if charged from a 5 watt solar
panel. Receiver output is proportional to the logarithm of signal input over a
dynamic range of 75 dB (–140 to –65 dBm). Automation includes the agility to sequence
through a user selected list of up to hundreds of frequencies in the 148 to 170
MHz range. Pulse amplitude to the
nearest 0.3 dB, pulse width and interval
to the nearest 0.001 second, and date-time to the nearest second were recorded
on exchangeable memory modules with one month storage capacity. In some instances these data were transmitted
via a wireless serial link to a central location for display and analysis with
memory module storage used as a back up. For activity-only studies, a single
omni-directional antenna was used; for direction finding, we used circular
arrays of directional antennas (Larkin et al 1996, Cochran et al 2001).
The automated receivers briefly described above
(more details in Appendix
I) are convenient but not unique; any receiver that can be calibrated in
dB can be combined with a computer to provide equivalent signal processing,
frequency sequencing, antenna control, and data
storage. However, if portability and power consumption are important factors, they should not be
overlooked in the process of equipment selection.
Animal movement
and signal change (DS)
The amplitude change method is based on body
movements and posture changes that cause a change in received signal (Rin). As an animal moves from place to place, changed
distance to the receiver will cause large changes in the average Rin. This is important because received signal change for a
given body movement is greater for strong Rin from
nearby than for weak Rin from a distance. For
example, a head-down to head-up movement might cause Rin
to double, and if the animal was nearby, Rin would
double from say 100 to 200 mW (DRin = 100 mW), whereas if the animal was more distant, Rin could go from 0.01 mW to 0.02 mW (DRin = 0.01 mW). A linear receiver would
output these two Rin, one 10,000 times greater than
the other, both representing the same body movement and percentage change in Rin.
Logarithmic detection (Cochran, 1980), where
receiver output (S) is proportional to the logarithm of Rin,
eliminates the distance bias because changes of S (DS) are proportional to the ratio of the Rin that constitute the
change; i.e., the percent change in Rin
(Figure 1a). DS (S1 – S2) is conventionally expressed in dB
= 10 x log
(Rin1 / Rin2) where Rin1 / Rin2 is a power ratio. In addition to providing DS proportional to percent
change of Rin, a receiver with a logarithmic response
does not saturate at high Rin levels (animal nearby)
or lose resolution at low Rin levels (animal
distant), ie., over more than a million to one (60
dB) range of Rin, DS maintains a constant resolution for
percentage changes in Rin. Although a linear-to-log transformation
of the output of a linear receiver would remove a distance bias, linear
receivers are capable of handling an Rin range of only a few hundred to one (26 dB) before
saturation. 9 dB is a typical S change for doubling distance so 26 dB would represent
about a 1-to-8 distance ratio (say 100 to 800 meters) whereas 60 dB would
provide more than a 1-to-64 distance ratio (say 50 to 3200 meters). Moreover, since coverage area is proportional
to distance squared, the value of a high dynamic range is greater than these
distance figures suggest.
Animal posture changes cause variations of proximity of
an attached transmitter and its antenna to the animal, causing the radiated
power to vary due to resultant changes in antenna efficiency and impedance. Also,
because the signal radiated in different directions varies with the transmitter
antenna orientation, movements of an animal as it turns or raises or lowers its
head cause the power radiated toward the receiver to
vary. The combination of varying degrees of change of posture
and orientation result in a chaotic relationship between DS and movement; small body movements
sometimes causing large DS and vice
versa. Therefore, with one exception, the magnitude of DS is not a valid measure of
the movement that caused it. The exception, that a very small DS implies no movement, is an
important one because it permits each DS to be categorized either as some unknown
amount of movement or as no movement.
The times of onset or cessation of
activity in relation to environmental factors, such as change in ambient light
level or temperature, may be all that is asked of the data, with no interest in
levels of activity before or after the change. The times of changes may be taken
from the time axis of S plots, for instance the end activity of nine Quail in
Figure 1a
occurred within a minute or two of 1958 CST for all of
them. The timing of such transitions is usually clear in plots because S
changes (DS) for no movement are much smaller than
those produced by even moderate movement. Carried a step further, the start and
end times of any periods of activity may be read from S plots and the durations
of these periods used to estimate activity as, for instance, a percentage of a
day (
Figure 1b). Visual selection becomes difficult and more
subjective when S plots contain a many short periods of inactivity
(Figure 2a), but this
selection can to some extent be automated
(Figure 2b).
Visual analysis
has been used in a number of studies (
3,
4,
6,
8,
10,
11,
15,
17,
19,
23,
26,
34,
36,
43,
44,
47,
52
) and in the era
of paper chart recorders, it was the only method available. As many of the
figures presented here show, computer processing of ARU data can provide a
variety of useful visual presentations from which activity estimates and other
insights into animal behavior obtained. However, with data already filed in
digital form, exploitation of opportunities for more detailed analyses is
logical.
Reducing
sequences of signals (S) to digitized states
via DS.
The magnitude of
signal change DS between successive S measurements S1
and S2 spaced by time interval Dt was tested against a change threshold
T1 (Figure 3).
Two states may result, active (A) when DS => T1 and inactive (I)
when DS < T1. As noted
above, DS is not a measure of the amount of
movement during Dt, instead, it is an indicator of
whether some unknown amount of movement has (DS => T1) or
has not (DS < T1) occurred during Dt. Thus, a count of A
states over a sampled interval (SI)
is not a count of movements and, as we show later, derivation of a quantitative
index of activity must derive from a substantial collection of state data
(an SI much much greater than Dt).
A minimum signal threshold T2 is
necessary to account for periods when the signal is very weak or absent, such
as when the transmitter is distant or underground. Signal cancellation from
multipath propagation or signal nulls due to transmitter antenna orientation
can also cause very weak or undetectable signals, even when the average
received signal is strong. Occasional and extended periods of very weak or
absent signals are handled by application of T2 as follows. If S1 < T2 and DS => T1 an A state results. If S2 < T2 and DS < T1 an I state results. If S1 and S2 are both < T2, then a third
weak-signal (W) state
results. T2 may be set at any value, but high values will result in unnecessary
loss of data, ie., many W
states when A or I states could be confidently
assigned. Setting T2 low, however, will cause periods of very weak or absent
signals to produce A
and some I states as
variation in S measurements of the fluctuating noise floor randomly mimic
activity or inactivity. A practical value for T2 is -128 dBm, 4 dB
above the average S value caused by noise alone (about -132 dBm for a
receiver bandwidth of 2 KHz and a typical rural external noise environment). To
preserve temporal continuity in the data set, no-data (Z) states are inserted for periods when the equipment is not
operating.
In summary, DS measurements are evaluated as above to create a temporal data
set of A, I, and W states. We refer to temporal plots of state data as
actograms
(14. Georgii 1981,
Figure 4). Actograms
provide an excellent overview of the temporal distribution of activity but
differences in the intensity of activity, say for whole days from one day to
another or one animal to another, are not visually apparent unless they are
large (Figure 5).
State-derived
activity indices (A%)
Quantified differences in intensity of
activity for different weather, seasons, climates, habitats, individuals,
sexes, ages, etc. would enhance understanding of the general ecology of
animals. Actograms provide an excellent visual impression of differences, but
impressions are subjective; a quantitative measure is preferable, such as that
shown in Figure 6a 6b.
Over an SI >> Dt, a state ratio (the sum of A
states divided by the sum of A
and I states) can be expressed
as an activity percentage (A%) for that SI.
A% is a quantitative index to an average of an animal’s movements during SI. It is an index because the
amount of movement represented by each state is unknown. It is a quantitative
index because details of the random and somewhat chaotic relationship between
movement and individual DS tend to average out over SI. Accuracy and temporal
resolution of A% compete via Dt and SI as will
be demonstrated later.
A% is influenced by the selected T1 and Dt. In the extreme, as T1 is
made large or Dt short, the probability of DS causing A states approaches zero, biasing results toward the I state and reducing A%.
Conversely, as Dt is made long or T1 small, the probability of I states is reduced, biasing results toward the A state and increasing A%
(Figure_7a_7b).
It is axiomatic that as Dt approaches zero, DS and A%
must also approach zero. The effect of
long Dt is
less clear. The proposition that it is more probable that an animal will have
moved at least once over a long time interval than over a short one is sound.
However, the signal may have changed many times during a long (or any) interval
and at the instant of measurement differ by less than T1 from the previous
measurement. In other words, a false I
state will sometimes be generated no matter how long the time interval and no
matter how much movement has occurred during the interval. These false I states prevent A% from
reaching 100%, even for a very active animal and a long Dt.
(Figure 7a 7b).
Of course three consecutive A states (or any small number of consecutive A states) make A% equal to100%,
but such small samples do not adhere to the rule that SI >> Dt.
Accuracy of
state-derived estimates of
activity ( A% )
We emphasize
that A% is an index derived from an average of many DS measurements that are randomly related to, but on average
positively correlated with, the movements that cause them. As an average over SI, higher accuracy of an A% index (100 * A / (A + I) )
would be expected for longer SI
and shorter Dt, ie., for
larger sample sizes (more states). We found this to be true with tests as
follows.
To test accuracy, S readings of a radio tagged Swainson’s Thrush were made at 0.5s intervals for 9 days
(Figure 8).
On each of
the days the bird was inactive from 2000 to 0500 the following morning. We
sampled from this 9-day data set with various Dt and SI, using multiple passes at identical Dt. For example, to estimate the
accuracy for Dt = 60s for a days activity (SI
= 15 hours from 0500 to 2000, 900 S reading), an A% was calculated from every
120th S reading, starting with the 1st reading. This was repeated starting with
the 2nd reading, then with the 3rd, and finally with the 120th. Thus A% was
calculated 120 times from the same data set with each pass through the data
starting a half second later than the previous. The
120 data sets covered virtually the same period of time: 0500:00 to 1959:00 for
the 1st and 0500:59 to 2000:00 for the 120th. The above procedure was repeated
for each of the nine days, providing nine SD estimates of the error for a Dt of 60s and an SI
of 15 hours of the bird’s active period; The 9 SD ranged from 1.18 to 1.49 (mean 1.38, SD 0.084)
(Figure 8bc). It was repeated again for an SI that included the inactive
period (24 hours); the 9 SD ranging from 0.74 to 0.93 (mean 0.85, SD 0.054).
The strong correlations of
Figure 9b evolve because the
added I states increase
sample size (SI) without adding variability; this holds regardless of SI or Dt (see discussion of
Figure 9
below). In other words, the ratios of A%
values without and with inactivity periods included, and their respective SD
values, are 1.6:1, which is the ratio (24:15) of SI with and SI
without the inactive periods
(Figure 9b).
If the method was perfect, each day’s
120 data sets would produce virtually the same A% for that day because they
sample almost identical time periods in the same data set. Not being a perfect
method, A% varies from pass to pass, and these A%
variations are a measure of error of the method. The frequency distributions of
A% (Figure 8b) are close to
normal, thus standard deviation (SD) is an appropriate error statistic.
The procedure in the above example was
repeated for other Dt (7.5, 15, 30, 120, and 240s) and other
SI (3 days = 45 hours and 9
days = 135 hours) producing the upper plots of
Figure 9a.
Similarly, the procedure was repeated with night
inactivity included (SI = 24, 72, and 216 hours) to produce the lower plots of
Figure 9a.
It was no surprise that including night
inactivity reduced SD. Intuitively, if A% = 0 (all I states) there should be no variability (zero SD and zero
error). It follows that data sets that include a large number of consecutive I states will produce a lower SD
than those that include them, as is shown in the upper and lower plots in
Figure 9a
also see
Fig 2b.
The only measure of inactivity is
duration, and if this alone is sought, it may be taken directly from S plots or
actograms (or see Processing
state data to quantify clumped activity section below). We here speak
of inactivity as it occurs over long intervals of say rest or sleep, not of
short bouts of less than 15 minutes or so.
Periods of substantial activity, easily
seen in S plots and actograms, have two measures, one of which is their
duration, as with inactivity. The other is the intensity of activity during the
periods, such activity consisting of a mixture of varying short periods of
activity and inactivity. The two measures combine as a series of products
(duration times intensity) which along with long periods of inactivity yield a
movement index to activity (A%) over a sampled
interval (SI) such as an
hour, day, week, or season. Thus, long periods of inactivity are reasonably included
in A% calculations. The accuracy of these A%
calculations that include all data, however, is erroneously high (SD low) as we
have shown.
Fortunately, inclusion of long periods
of inactivity reduces calculated SD in a simple way, ie., in proportion to the
ratio of their duration to SI.
For example, if SD is calculated for a day of data and the animal sleeps 11
hours at night and takes a 1-hour
The data from
Figure 9a,
along with additional data for SI = 3.75 and 7.5 hours (during the active period), were
combined to produce
Figure 10a
from which a desired accuracy (a user selected function of SD on the Y axis) can be related
to SI (temporal resolution,
on the X axis) and Dt (plotted curves). The equation SD = SI -0.513
(Figure 10a) illustrates
the classical relationship that accuracy (1 / SD) is proportional to the square
root of SI (sample size).
The discussion above, revolving around
Figures 8
9
10a,
is based on processing with T1 = 4 dB.
It is evident from
Figures 7a 7b
that A%
increases substantially with decreasing T1. SD for a given Dt, however, is little affected by T1
(Figure 10b).
We have also focused explanations and examples around a particular Swainson’s thrush for which S readings were taken at 0.5s
intervals (this is Swainson’s thrush 2005 in Table
1). As is evident in Table 1, data taken at 10s or 15s intervals may be
adequate for estimating SD if SI
is long (many days); the SD shown in the Table are valid for Dt = 60s, ie., it would be reasonable to
consider these data as focal data that provide a Dt = 60s SD and
to plan to monitor many animals with S readings taken at 60s intervals (see the
section: Relations among Dt, SI,
the number of animals (N), and transmitter specifications for the
importance of this). If a short Dt (<< 60s)
is practicable in a study, processing for A% can be done with Dt = 60s by skip sampling while continual estimates of SD are made
from the 4 or more samples of A% calculated from multiple passes; in this case
note that the basis for estimated error is the calculated SD divided by the
square root of the number of passes, eg. for the data in the Table, divide the SD by the square root
of 4 (or for the Red Fox, the square root of 6). In all this discussion, we
focus on 60s or 15s only as a means of example, but there is nothing magic
about these intervals; other numbers may be plugged in and the principles still
apply (see
Fig 10).
We have also
provided SD numbers to 2 decimal places, which is almost silly. In practice,
selecting the SD used as basis for error estimation would require looking at
data from several animals, perhaps in each season or environmental situation or
behavioral state, and making a judgement. For instance the Quail in Table 1
were lone survivors (not in a covey) and it was summer; all their SD but one
were in the range 1.5 to 1.65.
Table 1.
Standard deviations (SD) of error of A% for
several species, calculated for active-only periods and for 24-hour periods.
For each day of the sample, four A% values were
calculated using S readings at 15s intervals and the SD of these four A% was
calculated. The SD (of A%) shown are for Dt = 60s; they are the means of N of these 4-pass SDs
(N = number of days); and variation around the means is
indicated by SD of SD. The Red Fox is an
exception; there were six A% values for each day taken
at 10s intervals (other plots of its data are in
figures 1a,
6b, and
11b.
Eastern bluebird
data appear in
figures 11a,
12, and
14, and data for
the Northern cardinal appear in
figure 11d.
Other data for these animals are in Appendix
III.
|
Animal |
Dates |
|
Days |
Active only for SI
hours |
For 24 hours |
|||
|
|
begin |
end |
|
SD |
SD of SD |
SI
hours |
SD |
SD of SD |
|
Rabbit 117 |
17-Nov |
9-Dec |
22 |
1.04 |
0.58 |
12.0 |
0.84 |
0.39 |
|
Rabbit 157 |
30-Jan |
2-Mar |
22 |
1.55 |
0.65 |
13.0 |
0.90 |
0.38 |
|
Rabbit 220 |
8-Dec |
31-Dec |
21 |
1.22 |
0.76 |
14 |
1.01 |
0.48 |
|
|
2-Jan |
24-Jan |
21 |
1.44 |
0.58 |
14 |
1.04 |
0.50 |
|
|
|
|
|
|
|
|
|
|
|
Red Fox adult |
31-Aug |
7-Sep |
8 |
|
|
|
1.04 |
0.51 |
|
|
17-Sep |
28-Sep |
12 |
|
|
|
1.02 |
0.50 |
|
|
10-Oct |
31-Oct |
15 |
|
|
|
0.95 |
0.54 |
|
|
|
|
|
|
|
|
|
|
|
Downy Woodpecker 1 |
29-Jun |
9-Jul |
10 |
1.50 |
0.62 |
10.0 |
1.02 |
0.48 |
|
Downy Woodpecker 5 |
30-May |
21-Jun |
23 |
1.53 |
0.72 |
12.0 |
0.75 |
0.35 |
|
|
|
|
|
|
|
|
|
|
|
Swainson's thrush 2005 |
1-Jun |
10-Jun |
9 |
1.39 |
0.74 |
15.0 |
0.86 |
0.47 |
|
Swainson's thrush 188 |
21-Sep |
1-Oct |
11 |
1.60 |
0.67 |
11.0 |
0.92 |
0.43 |
|
Fox sparrow |
17-Oct |
29-Oct |
8 |
2.20 |
1.40 |
11.0 |
1.22 |
0.72 |
|
|
|
|
|
|
|
|
|
|
|
Eastern bluebird |
9-Jul |
16-Jul |
7 |
1.21 |
0.52 |
15.5 |
0.83 |
0.38 |
|
|
17-Jul |
23-Jul |
7 |
1.48 |
0.67 |
15.5 |
1.02 |
0.44 |
|
|
|
|
|
|
|
|
|
|
|
Northern cardinal |
12-Aug |
12-Sep |
32
|
1.52 |
0.71 |
12.5 |
0.92 |
0.41 |
|
|
|
|
|
|
|
|
|
|
|
Brown-headed cowbird |
26-Jun |
4-Jul |
9 |
1.52 |
0.75 |
16.0 |
0.90 |
0.43 |
|
|
|
|
|
|
|
|
|
|
|
Bobwhite quail 328 |
5-Jun |
12-Jun |
8 |
1.10 |
0.54 |
15.0 |
0.78 |
0.36 |
|
Bobwhite quail 347 |
5-Jun |
12-Jun |
8 |
1.52 |
0.63 |
15.0 |
1.00 |
0.45 |
|
Bobwhite quail 399 |
5-Jun |
12-Jun |
8 |
1.45 |
0.58 |
15.0 |
0.98 |
0.40 |
|
Bobwhite quail 524 |
5-Jun |
12-Jun |
8 |
1.63 |
0.67 |
15.0 |
1.07 |
0.48 |
|
Bobwhite quail 555 |
5-Jun |
12-Jun |
8 |
1.61 |
0.77 |
15.0 |
1.11 |
0.51 |
|
|
|
|
|
|
|
|
|
|
In summary, SD can be calculated from a number of
A% values from multiple passes with different start times through the same
data. Frequency distributions of these A% were found to be approximately
normal, making their SD a good basis for calculating A% error probabilities.
Data sets with long periods (say >15 minutes) of inactivity removed provide
the best estimate of SD for A% of the same data sets with no data removed. SD
was found to be little affected by T1 over its typically useful range of
Visual identification of clumps (sustained periods)
of inactivity from S plots (Visually
derived estimates of activity section) is a simple way to estimate a day’s activity as
the ratio of the minutes in a day minus the sum of the clumps, all divided by
the number of minutes in a day and finally multiplying by 100 to convert to
percentage. In other words, having identified clumps of inactivity, the
remainder must be clumps of activity. The clumps of inactivity can be
identified quantitatively from state data as periods of consecutive I states longer than a user
selected number of minutes, say 15 minutes as in
Figure 2b where these clumps are
called I bouts. This method
is somewhat erratic because single A
states sometimes break a sequence that obviously qualifies as a sustained
period of inactivity, eg. from 0540 to 0600 in the upper S plot in
Figure 2b.
We here present a majority logic
method that is not erratic because instead of detecting unbroken sequences of I states, it detects intervals
over which I states outnumber
A
states and vice versa. We refer to these intervals as inactive (Si) and active (Sa) sessions where
a session is dominantly rather than exclusively one or the other state.
The process is one of filtering out the minority
states. Quantitative removal of minority states is low-pass filtering, a
process that creates from a sequence of state data a second sequence of
filtered state data for each time (t) in the data set. For instance, an 11-state data nibble could consist
of 9 A states, begin and end
with an A state and contain 2
I states. Majority thought
and logic would consider this 11-state nibble to represent primarily activity
rather than to consider it as say separate 4-state and 5-state nibbles plus two
1-state nibbles. Thus considered, the
mid point of the 11-state nibble (at time t) is set as A. Time t is then moved forward to t + Dt and the process repeated
with the oldest state (at t – 5 Dt) dropped from the nibble
and the new state (at t + Dt + 5 Dt) added to maintain an
11-state nibble from which the state to be assigned to t + Dt is determined. The
process, continued throughout the desired data set, produces a filtered set of
state data with majority states emphasized. In this example for time t, all states, regardless of
their time differences from t, were
implied to have equal weight (1 vote) in the majority decision, ie. a linear filter. In a
triangular filter, the state at time t would be given 6 times as much weight as the states at t + 5Dt and t - 5Dt, 5 times the weight of
those at t + 4Dt and t - 4Dt, etc.
The above digital low-pass filtering is
(mathematically) the passing of a symmetrical convolution mask over the state
data. The width of a mask is usually referred to as a (time) window (Wt) that
is an odd number of Dt's in length. In the preceding word example the time
window, called a nibble, was 11Dt (Wt = 11Dt). Each state datum in the window is assigned plus 1 for an A state,
minus 1 for an I
state, and zero for a W
state. At each time (t), the
products of the mask and window of state data centered on time t is summed and the t assigned as A or I when the sum was > 0 or < 0, respectively
(Figure 11,
12a).
We found triangular masks, (eg.,
123454321, Wt = 9) more effective than linear masks with equivalent high
frequency cut-off (eg.
1111111, Wt = 7) because the latter tend to create some detail where none
exists. Digital filtering and a variety of masks are well covered in the
literature (see 55. Chi-Tsong, 1979; chapter 7).
Ties (mask sum = 0) are infrequent but happen. A
simple tie breaker rule is to favor the sign of the preceding (t -1) sum or to
widen the mask symmetrically until the tie is broken in favor of the overall
context. A few W states
(assigned value 0) do not invalidate the process; too many weaken the decision.
When W states were in the
majority a W state was
assigned and plotted in the session actogram. Although plotted in
Figures 11
and 12b,
the durations of active and inactive sessions adjacent to a session of no-data
or weak signal was
not included in the file of session durations, ie.,
active and inactive sessions that began with or ended in a weak or no-data
session were discarded for purposes of plotting session frequency distributions
because their durations were unknown.
Summarizing, state sequences can be
low-pass filtered to visually reveal sessions (sometimes called clumps or
bouts) of activity (or inactivity), defined as periods of time dominated by
either activity (A states) or
inactivity (I states). Low
pass filtering may reveal patterns that might otherwise be lost in detail.
Frequency distributions of the session durations (visible in the masked
actograms
Figure 11)
can be extracted to obtain another perspective of animal activity
behavior (Figure
12b). The intensity of individual bouts
(Figure 12a) may also provide
useful information.
Practical
Matters
In
the preceding methods sections we have focused on principles illustrated with
examples. Here we show how these principles apply in planning a study (Relations among Dt SI
the number of animals (N) and transmitter specifications, Choosing transmitters, Getting A% while direction finding) and in addition cover
practical matters that can impact a study (Interference, Site
selection). A brief comparison is made
with switch sensor methods (Comparison with activity switch methods).
External factors
can affect accuracy and create data gaps. Nearby thunderstorms produce static that shows up on
records as varying signal. Power lines are also a source of noise, often
intermittent due to variable wind and humidity. Siting of ARUs
away from power lines usually helps. These noise sources are broadband, thus
appearing on all frequencies. Programming the ARUs to
receive signals on one or more non-animal frequencies facilitates cutting
(changing to Z states)
periods with interference; loss of data is unavoidable. See
(Figures 13,
14,
15).
False activity can also be produced when wind-swayed
vegetation causes variations in the received signal. This effect is somewhat
reduced by siting the receiving antenna away from trees, or if in a woods, then
above the canopy. A stationary reference transmitter in the study area will aid
in detecting periods of false activity
(Figure 16).
Sections of records thus identified may be Z-coded
as no-data in the data files. Use of a higher value for T1, say 5 or 6 dB, can
place most wind-caused DS values occurring during inactive periods to be correctly recorded as I states. If, for any reason,
most data are processed with T1 = 3 or 4 dB, the A% taken with the higher T1
must be adjusted upward from charts like those of
Figures 7a, 7b to prevent bias in comparisons.
Various frequency-discrete signals from 2-way communications, data transmissions, and spurious radiation from high power television and FM radio transmitters are more difficult to eliminate. These, except for the latter, are usually very intermittent; all are plentiful in urban areas. Where their frequencies can be determined, they can be avoided by not using these frequencies for animal transmitters. These signals are usually heavily modulated and of durations often different from the pulse widths of animal transmitters. ARU detection algorithms provided flagging most signals of this type by the detecting these differences.
Many garage door openers and other remote control
devices are a source of continuous broadband noise. Although radiation from
such devices has been illegal for many decades in the
A
decision that sometimes precedes a study is where to conduct it. Sometimes
there are good reasons to conduct it in a particular place. In the section on
interference, we describe four types of external interference that can affect
accuracy and create data gaps; we also mention ways to mitigate these effects.
Nothing is to be done about wind or lightning other than the procedures
mentioned. However, the effects of urban-related interference can be avoided or
minimized by choosing a site well away from towns, power lines, and TV-radio
station towers. Where convenience alone is the reason for using a particular
area that is also interference prone, the potential for data sets being
fragmented or rendered useless should be avoided by finding a better area.
Part-time tracking of animals by listening to signals from a radio is orders of
magnitude less susceptible to interference than continuous automatic monitoring
of signals for the purpose of obtaining the clean and unfragmented signal
records that simplify data processing and produce accurate results.
If study objectives are minimal, for
instance to measure the circadian pattern of activity without quantification of
activity intensity during active periods, then the above cautions are not so
important because accuracy issues are much more relaxed. Whatever the study
objectives, a survey of the RF environments in the planned area will be useful
in finding frequencies to be avoided. Such a survey is not very useful in
projecting power line interference because power lines are often quiet but
always give interference sooner or later.
Relations
among Dt, SI, the number of animals (N), and
transmitter specifications
In general,
design of a study will involve specifying 3 parameters: accuracy (1/SD),
temporal resolution (SI), and
a number of animals (N). These parameters are related: SD is approximately
proportional to Dt / SI
(Figure 10)
and N is inversely proportional to Dt. The latter stems from
the fact that measurements are made sequentially and the dwell time “listening”
for each transmitter must be at least as long as its pulse interval (Pint) to
assure that a pulse will be present for measurement. The time between
measurements for each transmitter (Dt) is thus at
least as long as the sum of Pint for N transmitters (Psum).
The effect of N on Dt can be controlled with Psum by
appropriately specifying transmitter Pint. With Dt controlled in
this way, SI can be specified. Thus, it appears that accuracy (1/SD), temporal
resolution (SI), and a number
of animals (N) can be set arbitrarily. But there are practical limits to the
specification of Pint.
A
typical wildlife transmitter has a pulse interval of 1s and a pulse width (Pw) of 16 milliseconds (ms). To maintain transmitter
longevity-to-weight ratio while decreasing Pint, Pw can be
shortened in the same proportion as Pint, maintaining the same duty cycle or,
alternatively, peak pulse power of the transmitter can be reduced in the same
proportion. There are practical limits. Pw may be
reduced to 4 or 5 ms and peak pulse power by a factor of 2 or 3. Thus, without
affecting the longevity or weight of transmitters, a Pw
of 4ms and halving power would relieve specification of the combination of SD,
SI, and N by a factor of 8 as compared with using typical wildlife
transmitters. For example, for a given accuracy and temporal resolution, 8
times as many animals could be monitored, or for a given number of animals,
better accuracy and temporal resolution could be obtained. It seems something
has been gained for nothing. But some reception range is lost when Pw or pulse power are reduced; for the factor of 8 above
perhaps to 0.85 that for the typical transmitter. Moreover, since area of
coverage goes as the square of range, coverage would be reduced to about 0.72.
Sometimes
transmitter longevity is twice (or more) than that really needed, the idea
being that more than enough is better than enough, insurance so to speak. But
halving longevity will allow halving Pint without any impact on range and this
alone will double N.
These deviations from “typical” may not be welcomed
by some transmitter suppliers because they may find it inconvenient to produce
them, or simply think they know better than you what you need. If so, find a
supplier that knows its business, one who is willing to let the dog wag its
tail.
In practice,
because of attrition and logistical factors, the number of animals being
monitored will vary. To maintain a minimum number of animals under observation
for statistical purposes, an N somewhat larger than the minimum number should
be used. Thus, as the number of animals waxes and
wanes below N, Dt could also be allowed to vary by
equating it to the Psum of the actual number of
transmitters being monitored. A varying Dt not only means
varying accuracy, but complicates analyses and data presentations as well. Keep
the N and Dt constant to avoid these complications.
A more detailed discussion of N, Dt,
and the programming of single and double work lists is given in Appendix II.
As
a final caution, loose transmitter attachment can cause signal changes from
movement to be different from changes with a firm attachment, also a concern
with switch type sensors. Consistency of attachment is thus important if comparisons of activity among individuals is desired.
In summary, one
need not be too concerned about choosing Dt or
transmitters unless high accuracy and temporal resolution are required for
large numbers of animals. It may be satisfactory that 30 typical wildlife
transmitters can be monitored at Dt of 30s for a
SD of error about 1% for A% summations of about 1 day (SI = 1440 min).
Comparison
with activity switch methods
Having to think about the several factors involved
with choosing Dt may seem an undesirable complication of the amplitude-change method.
The same complication exists for switch type sensors whose reset time and
angular and/or acceleration sensitivity are equivalent to Dt and T1, respectively. A
disadvantage of switch type sensors is that Dt and T1 are set by the radio package design
and the way it is mounted on an animal. Thus set in advance, no flexibility is
allowed during data collection and analysis, and if the parameters turn out to
be less than optimal, the researcher is faced with accepting this or redoing
the study. In contrast, the amplitude change method allows the user to optimize Dt from samples taken early
in a study and later select an optimum T1 during data analysis. Considerations
for SI and N are virtually the same for both methods. Simple switch-sensor
devices produce A and I state data similar to that
from the amplitude-change method making analyses similar. More complex
switch-sensor packages that store motion data or respond to specific motions
will serve objectives not accessible with the simper switch devices or the
amplitude change method. The ARUs we used are capable
of recording pulse interval and pulse width or even a pulse code, allowing
switch-sensor and signal-strength methods to be used simultaneously.
Getting A% while direction finding
The ARUs can
be used for direction finding (DF) by switching among directive antennas
(56. Larkin et al 1996,
57. Cochran et al 2001,
ARTS Website).
Between 2 and 6 pulses are required to determine a
direction (Sparrow DF Manual in prep). The S data
gathered in the DF process may be used directly to obtain A%
indices. The penalty for such dual use is less accuracy or smaller N due to the
longer Dt required while waiting for the
additional pulses. In some installations for direction finding, the cost of a
tower, weather enclosure, battery, and solar panel, in addition to the several
antennas and an ARU,
may be large enough that addition of a second ARU and single
antenna, specifically for activity, represents only a moderate percentage
increase in cost. If N is large and activity is an important objective, this
approach will avoid compromise.
Glossary of
terms
N Number of frequencies in a
list that an ARU sequences through.
All
frequencies need not be different, ie., the same frequency may
be in the list more than once, adding to N
each time it appears in
the list. May be thought of as the number of
animals monitored with
the understanding that animals monitored
more than once in the
sequence increase N
proportionally. For animals monitored once in
the sequence, the sequence repetition time (Dt)
becomes the Dt for
processing their DS
to obtain A%.
Pint Abbreviation for transmitter
Pulse Interval in seconds. Pulse (beep)
rate is the reciprocal of Pint (beeps per second).
Psum Sum of Pint for the various
transmitters in the sequence (see N).
Pw Abbreviation
for transmitter Pulse Width in milliseconds.
Session A
period of time dominated by a particular state.
An active Session
is defined as a period dominated by A states, inactive by I states,
weak signal by W states, no-data by Z
states. Clump and bout
may be used instead of session.
Clump see
Session
Bout see
Session
Session The
degree of dominance of a particular state
in a Session. The simple
intensity majority rule is all or nothing
(dominance); it ignores the popular vote,
which
may vary from 51% to 100%; we call it intensity (of dominance).
ms
abbreviation for
milliseconds (1 ms = 1/1000 sec)
RF Radio
frequency
Rin Signal power present at an
antenna input of an ARU, expressed
in milliwatts
unless otherwise stated.
Wt Width
of convolution mask in Dt units. To convert to seconds,
multiply Wt by Dt. It is a time
interval.
nibble A sequential set of states
contained in the interval Wt.
activity
index A% is an activity index, usually
from the ratio of A states to
the sum
of A
and I states but can be a
ratio derived from periods of activity and
inactivity determined visually
from S plots or Actograms. However A%
is derived, it is an index because it is
not a direct measure of movement.
activity Activity of an animal, moved
(active) or did not move (inactive)
actogram Digital (2-state) graphical
illustration of activity and inactivity,
first mentioned in lit by Georgii
ARU General
term for Activity Recording Unit
A% An index to the percent of a sampled interval (SI) an animal
was active
I% An index to the percent of a sampled interval (SI) an animal
was inactive
I%
is not actually used in the text because it is always 100 – A%, thus
stating A% determines I%
automatically.
Dt Interval
separating two S measurements from the same animal
dt Dt
as in calculus as t approaches 0, not used except
in a few figures where a font problem
prevented using D.
SI Sampled time interval
>> Dt over which A% or I% is calculated
dBm decibels relative to 1 milliwatt, a measure of power
dB 10
x log of a power ratio: 10 x log (s2 / s1) s unit watts
20
x log of a voltage ratio: 20 x log (s2 / s1) s unit volts
s,
s1, s2 etc Signal received in watts
or volts (must specify)
S plot Time
plot of S (signal) values
S A
signal value expressed in dBm
10
x log (s / 1mw) expressed as dBm
(dB relative to 1 mw)
where s is power in milliwatts
(mw)
S1, S2 ..Sn Sequential S
measurements separated by interval Dt
DS ABS(S2 - S1), both expressed in dB relative to the same
reference,
the
reference is not important.
10 x log ( s1 / s2 ), s1 / s2
is a power ratio
or 20 x log ( s1 / s2 ), s1 / s2 is a voltage ratio
In
all cases the sign is ignored and the function is made positive,
thus swapping s1 and s2, or S1 and S2, does
not change the value.
dS as in calculus, rate of
change of S as t approaches 0, not used except
in a few figures where a font problem prevented using D.
t General point in
continuous time.
t1, t2, ... tn Points in a sequence of times in Dt
increments.
T1 Threshold
one, units dB, deltaS => T1 define an active
datum,
DS < T1 an inactive datum.
T2 Threshold
two, units dBm, minimum S1
and S2 allowed in determining
a state as active A or inactive I.
Not allowed if both S1 and S2 < T2.
State A
A state: DS
=> T1 ,
active state.
State I
I state: DS
< T1, inactive
state.
State W
W state: Unknown
state, S1 AND S2 < T2.
State Z
Z state: No-data
state, no data gathered or invalid data edited out.
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southern
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6.
Clapp, D. F., R.
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Loughlin, T. R. 1980. Radio
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Lord, R.D., Bellrose, F. C., and W. W. Cochran, 1962.
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Marshall, W. H. and J. J. Kupa. 1965. Development of
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Maurel, D. 1980. Home range and
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Mohas,
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Palomares, F. and M. Delibes.
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Appendix I: ARU technical
Appendix II: Worklists, Number of Channels
Appendix III: Additional figures
Appendix IV: Viewing and analysis tools
Appendix V: Review of methods literature