Population Survey of Tettigoniidae within Tambopata National Park
Connor Pierson and Francisco Martinez
Introduction:
One of the most widely dispersed families of insects in the world, the katydid is no
stranger to the Peruvian Amazon where a single study outside of Iquitos identified nearly 380
different species. The Katydid’s general lack of chemical defenses make it an extremely
important source of protein for leaf-gleaning secondary and tertiary consumers including many
iconic species associated with the ecotourism industry. The intense evolutionary pressure driven
by the insect’s wide variety of predators has led it to develop impressive array of cryptic
defenses that have themselves, peaked the interest of tourists and are therefore a potential source
of human-nature interaction that supports the growth of the industry.
This study is the first of its kind carried out in southern Peru and was conducted in the
area surrounding the Tambopata Research Center outside of Puerto Maldonado. While
orthopterists such as David Nickle and James Castner (Nickle and Castner 1995, Nickle 2003,
Nickle 2006 etc.) have done much to expand our knowledge of neotropical katydids by
conducting studies near eco-lodges in the Loreto Province of northeastern Peru, limited attention
has been paid to other areas of the world’s largest rainforest. Despite having a large variety of
leaf-gleaning predators, the ecologically diverse area outside of Puerto Maldonado has been
generally ignored in this respect. Therefore, this preliminary analysis of tettigoniidae population
densities, defensive strategies, and roost fidelity is the first of its kind conducted in the tropical
floodplain of southern Peru.
This paper seeks to outline the basic population dynamics of tettigoniidae in southern
Peru in the hopes that it might inspire further analyses of neotropical katydid behavior and their
ecological significance in the region. In a twelve-week period, data on general population
1
densities, defensive strategies, and roost selection patterns was collected and logged. Although
the authors are not experienced entomologists, this basic data is provided in the hopes if aiding in
the formulation of more specialized investigation.
Another goal is to promote interest in an interesting animal that the author’s believe could
have a positive association with ecotourism much like that which already exists between the
industry and the Amazons’ charismatic mega fauna. The authors owe much to the incredible
generosity of Rainforest Expeditions and its employees for not only providing room and board
but also often directly aiding in data collection. During our time in Tambopata, we were struck
with the interest our investigation inspired in the tourists we interacted with and the enthusiasm
inspired by the touristic accessibility of the insect. Over time, it became clear that the general
frequency with which Katydids are encountered and the physical diversity of the family render it
particularly easy to package within a larger discussion of ecology, forest preservation, and
sustainability. We hope this data might be of use in inspiring a belief in the importance of
preserving even the rainforest’s oft-overlooked species.
Methods:
Nocturnal Transects. Because the vast majority of the regions katydids are nocturnal, these
transects were the largest component of data collection in this project. Transects were conducted
exclusively along trails surrounding the Tambopata Research Center (GPS: 13.08.049 69.36.632). These transects were conducted in areas classified as “Old”, “Upper”, and “Middle”
Floodplain forest types by previous microgeographic analyses of the region (Phillips 1993, Doan
2002). Transect walks were completed nightly between the hours of 9:00 pm and 1:00 Am. This
period, rather than that immediately after sundown was chosen in the hopes of increasing sample
size as many leaf-gleaning diurnal predators and bat species were extremely plentiful during
2
dusk and early evening and some studies suggest that the insects remain in their roosts until later
accordingly (Nickle 2006). Transects were conducted by at least a pair of individuals whom were
often accompanied by one to four volunteers. When more than two individuals were involved in
data collection, a proportionally larger geographic area was selected to ensure that the number of
katydids encountered was not skewed by the increased number of data collectors. Transects were
continuous point transects, speed of travel was less than .03 kilometers per minute, and highpowered torches and flashlights with a minimum of 50 lumens were used. However, the vast
majority of Katydids encountered did not appear to be actively attracted to light emanating from
headlamps.
When a katydid was encountered, GPS coordinates, distance from the trail, and a
description were recorded. This description consisted of a basic physical report (including
measurements); a characterization of the defensive strategy employed by the insect, and included
a high-resolution photo evidence for reference. Although on the spot identification of species and
genera was impossible due to a lack of published reference materials and inability to take
samples, these descriptions were taken in the hopes of identifying common species in the future
for guide use, and studies of katydid predation by larger mammalian, reptilian, and other
predators. Over time the database of descriptions allowed the authors to group assumed members
of the same genera together.
Diurnal Roost Studies. In order to gauge roost fidelity, the authors conducted diurnal transects
along the same trails used in nocturnal studies. Initially, the authors mapped 2x2 meter quadrats
on and off-trail and thoroughly searched the flora and debris within these regions for
tettigoniidae. However, extremely low numbers of katydids were found and this method was
abandoned early in the program. Instead, diurnal transects were conducted along existing trails
3
and plants were visually scanned and physically inspected from ground level up to 2 meters for
signs of the insects. While this second approach was much more successfully than the utilization
of quadrats, the total number of katydids found remained low (similar findings were made by
Nickle et al. 2006) and tree dwelling katydids were not accounted for.
Once katydids were encountered, the methodology utilized during nighttime transects
was used in order to describe each specimen. In addition to these details a written description of
the location as well as a photograph of each roost was logged. Finally, a piece of neon tape was
placed as close to the roost as possible without disturbing it so that the insect could be located in
following visits to the site. Transects on which these roosts were identified were checked daily.
Careful care was taken not to disturb the animals from their roosts so that an accurate measure of
roost fidelity could be taken. A record was taken of each day an insect remained in the same
roost and only after a roost was found empty for more than two days was it considered
abandoned. Photo evidence and careful descriptions of each insect were used to ensure that
multiple individuals were not registered as the same resident. In the few instances in which
evidence proved an insect had been predated within the roost, or the roost had been destroyed by
animal activity, the data was not counted.
Baseline Data. Katydid data were also compared with baseline temperature and precipitation
figures recorded every day. Minimum and maximum temperature was recorded daily using
thermometers in an open box with a roof, to protect it from water, located 300m from lodge in
the jungle. Rainfall was also recorded daily at the same location. The number of Katydids
encountered each day was superimposed over these figures to determine whether any apparent
short-term correlation existed between these figures and katydid foraging activity.
4
DISTANCE. Data was then compiled using the density modeling software DISTANCE and
Excel. Data in Distance was then used to calculate: a summary containing area, covered area,
abundance and associated CV and confidence limits, density and associated CV, and confidence
limits. To calculate the probability density function at any distance. This formula was used:
Where, n is the number of observations, and w is the truncation distance. (Assuming no left
truncation). F(x) has to be 0<x<w< infinity and is the probability density function of observed
perpendicular distances. Xi and j refer to the physical location of each observation. W refers to
the truncation distance.
To expand our results past our transects and for the larger designated area we use this formula, in
conjunction with Chi Square tests: Where c refers to confidence interval.
Further Statistical test such a goodness model test, Cramer-von Mises family tests or
Kolmogorov-Smirnov test can be used to further ascertain the accuracy of projections.
Results:
Defensive Strategies.
Cryptic defenses: True to the family’s reputation, an impressive diversity of
tettigoniidae defensive adaptations was witnessed. Most of these strategies fell under one of the
5
following categories: green generalists (43.9% of total), brown generalists (25.9%), bark mimics
(3.9%), twig mimics (2.4%), leaf mimics (6.6 %), and lichen mimics (4.5%). Because not all
individuals were observed in their roosting positions, potential instances of mimicry were only
categorized as such if morphological adaptations and behavior were sufficient to allow the
authors to infer this assumption.
Generalists: Generalists lack intricate morphological adaptations and instead rely only
upon a basic level of cryptic coloration in order to avoid predation. They make up, by far the
largest number of species of tettigoniidae that have been identified in the Peruvian amazon.
David Nickle claims that over 71% of Amazonian species are generalists (Nickle 1995). In this
study, generalists represented fewer than 70% of individual organisms encountered. Overall,
individuals of the genus copiphora were the most frequently encountered genera in this category
during both diurnal and nocturnal searches. The iconic insects were generally encountered
exposed on the underside of green leaves on low shrubs as well as larger palms and heliconia
species. Katydids in the subfamily phaneropterinae were also commonly encountered at night.
Because many species spend daylight hours in arboreal roosts, they were not well represented in
diurnal studies. However, they demonstrated a strong attraction to light and were frequently
identified during nocturnal transects. These individuals generally exhibit rapid saltation but the
subfamily itself is extremely diverse (Nickle 1995). The morphological adaptations of some
members of this subfamily were detailed enough that they were categorized as leaf mimics.
Mimicry: While intricate morphological coloration and structure were far less common
than general cryptic coloration, cryptic mimicry did take a variety of forms. Bark and twig
mimics demonstrated a strong resemblance to the woody stems and bark to which they clung.
Bark mimics generally pressed themselves close to the exterior of larger plants whereas twig
6
mimics roosted in notches on small branches. Past research suggests that twig mimics chew these
notches themselves (Nickel 1995). While the specificity of the notches supports this claim, this
behavior was not observed directly. Most of the encountered species were members of the
subfamily pseudophyllinae. The most frequently encountered twig mimics were most likely
members of the tribe Pleminiini but the young age of many nymphs rendered more specific
identification difficult.
A variety of leaf mimics were also identified both in diurnal and nocturnal studies.
Individuals mimicked both live and decaying flora and some species have been proven to
demonstrate morphological characteristics of both types (Castner 1995). Live leaf mimics were
often represented by the subfamily phaneropterinae. However, dead leaf mimics demonstrating
an intense level of morphological adaptation were encountered far more often than equivalently
sophisticated mimics of live flora. The genera Typophyllum, Mimetica, and Cycloptera were
represented in this category. These insects demonstrated a high degree of physical specialization
that included mimicry of leaves affected by herbivores and avian excrement. They were most
often encountered nocturnally as their intricate defense rendered them nearly impossible to
encounter during the day. Despite this fact, the author’s experience encountering what appeared
to be the exact same individual in a particular region in sequential nights supports assertions by
entomologists such as James Castner that some species may move as little as only a few
centimeters in an evening (Castner 2009).
Other previously documented forms of mimicry by Peruvian katydids include cryptic
lichen mimics and forms of Batesian mimicry. Lichen mimics encountered in this study had
developed sophisticated coloration that highly resembled lichen but did not have the intricate
structural adaptations witnessed in some documented Peruvian species such as members of the
7
tribe Dysonini. Other forms of mimicry were not encountered in this study. However, Batesian
mimicry, especially of wasp species, is relatively well documented in the northern Peruvian
Amazon and it is likely that similar species also exist in the Tambopata area.
Other Defenses:
While care was taken not to disturb roosting katydids discovered during the day,
individuals encountered at night were lightly aggravated in order to record the range of
behavioral and physical adaptations (excluding crypsis) that these organisms rely on to avoid
predation. As a general trend, highly cryptic species were much slower to resort to saltation and
flight when approached. The following are a few examples of notable defensive action:
Release of odor and warning coloration: The bright colors of a number of a number of
species seemed exemplify aposematic warning coloration exhibited by other toxic and distasteful
insects. Among these, members of the genus Vestria within Copiphora were relatively common.
Previous studies suggest that these odor-emitting Vestria species are, in fact, distasteful to large
predators (Nickle 1995). One unidentified twig-like orthopteran also emitted bursts of an
odorous substance whose particles were visible to the naked eye.
Biting: Although many species pursued defensive strategies other than biting, this
retaliatory action proved to be by far the most common of those witnessed with as many as 20%
of individuals encountered attempting to bite when captured. Members of the genera
Conecephalus and, especially, Copiphora, proved especially willing to engage their powerful
jaws to deliver a painful bite before quickly letting go in order to flee.
“Nutcracker” defense and Foreleg batting: The so-called “nutcracker” defense is
described by David Nickle and James Caster as “a strong, rapid, flexing of the mid- and hind
legs on some aspect of the attacker's anatomy, e.g., a finger, beak, or tongue” (Nickle 85, 1995).
8
This reaction was frequently utilized by some Copiphora and was particularly effective in those
species with sharp spines on their hind legs. Foreleg batting occurs when the insect raises its
body up using its hind legs and abdomen in order to lash out at the potential predator using its
forelegs. This proved to be a less common phenomenon but was utilized by some unidentified
species bearing sharp spines on these limbs.
Autotomy and Regurgitation: In handling katydids, care was taken to avoid permanently
injuring individual insects. However, when handled improperly, a variety of species
demonstrated the ability to quickly cast off a limb. Individuals already missing limbs were
frequently encountered and it seems likely that this trait is nearly universal among Amazonian
Orthoptera. Another common reaction was the regurgitation of a viscous brown or yellow liquid.
This trait did not appear to be limited to individual subfamilies but was widely encountered,
especially in species that did not resort to biting. It has been suggested that such regurgitation
among Orthopterans is successfully employed to deter small predators.1
Remaining Prone: One of the most striking reactions to physical stimulus was the ability
to remain completely still. This reaction was usually encountered in highly cryptic genera such
as Typophyllum, Mimetica, and Cycloptera as well as in twig mimics in the tribe Pleminiini.
When prodded or picked up, these individuals quickly snapped all appendages closely against
their bodies and remained in an immobile, rigor mortis-like state for extended periods of time. In
one instance, an individual Typophyllum dead-leaf mimic initially encountered while foraging
remained in this state in excess of ten minutes. The individuals first assumed the position when
handled and remained as such for a period of five minutes while in a researchers hand. When
placed in leaf litter, the individual remained prone while under observation for another five
1
http://onlinelibrary.wiley.com/doi/10.1111/j.1440-6055.1980.tb00973.x/pdf (cite within text)
9
minutes. Observers (fearing it dead) then left the area for two minutes and found it foraging upon
their return. Interestingly, this behavior was not universal within these genera, and some
individuals attempted to flee after only minor prodding.
Other defense mechanisms: Other mechanisms previously noted in the Peruvian Amazon
were not chronicled in this study but are likely practiced by species in the region. These include
association with other species (notably wasps), the use of stridulation in order to alarm predators,
and a variety of wing adaptations. Adaptations such as eyespots, wing pigmentation, and wing
flaring are well documented in many species including the iconic “peacock katydid”
(Pterochroza ocellata) but were surprisingly absent from these observations.
Density analysis in DISTANCE:
Model number 5 of DISTANCE was chosen as the most accurate projection out of 5
models of density due to its low parameter values2. Our data yielded the following results:
Model 5
Average Density Per Meter squared: 0.01214
Average Density per hectare is 121.47
Point
Standard Percent
Coef.
95%
Percent
Parameter Estimate
Error of Variation
Confidence
Interval
------------------- ----------- --------------------------------D
23426.
425.3
18.25
15860-34602.
The low density suggested by the data is affected by the fact that the sample size only included
individuals identified between 0 and 2 meters in height and the general territorial nature of many
species (Castner 1995). The difficulty of detection from longer distances also influenced these
2
The 5 models and their calculations can be seen in the appendix.
10
findings. Detection probability decreased rapidly with distance from the transect. Due to the
small size of most individuals and cryptic camouflage, this result is not surprising. The following
chart demonstrates this trend:
Detection Probability V. Distance
Roosting:
The actual identification of roosts proved to be extremely time consuming and achieving
numbers that merited statistical significance proved impossible for many identifiable genera.
However, an analysis of the roosts tracked shows distinctly different roost periods that those
found in the only similar existing study carried out in northeaster Peru. The following table
compares the roost periods found by our study and that conducted by David Nickle and James
Castner in 1995:
Pierson &
Martinez
Nickle and
Castner
Sample size
(insects)
52
179
Roost Comparison (All Katydids)
Mean (Days)
Mode (Days)
3.621
2.12
Range
4
37.5% of Sample
1
81% of Sample
11
Despite the relatively small sample sizes of both studies, the authors were able to conduct
a comparison of insects identified as members of the subfamily Copiphorinae in both studies as
demonstrated by the following table:
Roost Comparison (Copiphorinae)
Pierson &
Martinez
Nickle and
Castner
Percentage of
Sample
18.6%
Mean (Days)
Mode (Days)
Range (Days)
4
1-10
20.7%
1.51
3
33.3% of Sample
1
72.9% of Sample
1-4
Although statistically significant numbers of species from other subfamilies and genera
were not found, this study did compare the two largest subcategories of insects in the roosts
inspected, brown generalists and green generalists (utilizing brown and green foliage
respectively). Within the sample, Brown generalists tended toward a longer mean roosting time
of 5.29 days while green generalists were found to have a mean roosting period of 3.57 days.
While these results are not definitive, they lead the authors to question whether roost fidelity is
shortened in cryptic green katydids due to the lifespan of living foliage or roost predation by
herbivores.
Temperature and Precipitation:
The sampling period featured an extreme range of temperature swings with a maximum
recorded daytime temperature of 28° Celsius and a minimum daytime temperature of 8° Celsius
during a particularly intense friaje. Although cold spells had marked effects on populations of
mammals and other large animals, no statistical correlation could be found between the number
of Katydids identified and the temperature. While it still expected that temperature no doubt
effects Tettigoniidae populations the correlation between temperature and katydid sightings
yielded a p value of over 60% suggesting that any connection could be due just to chance. This
12
statement was true even of regions that were checked multiple times during friajes and under
normal conditions.
Temperature V. Katydid Sightings
Infrequent precipitation similarly did not seem to have concrete effects on the number of
individuals spotted. However, one early storm was followed by a marked increase. It should be
noted that this research was conducted during the dry season and more reliable measures of the
effects of precipitation might be conducted during the wet season.
Rain V. Katydid Sightings
Acknowledgements:
This project could not have been undertaken without the help and guidance of our close
colleagues and mentors. In brief we would like to thank William Durham for his advice and
feedback of our project during its infancy as well as for facilitating our stay with Rainforest
Expeditions. As two young undergraduates we would have been lost without the orientation and
13
logistical support given to us by our fellow colleagues Katy Ashe and Claire Menke and we wish
them luck in their future ventures in the Tambopata area.
We are incredibly indebted to Rainforest Expeditions for providing food and lodging
while in the field. The entire staff demonstrated incredible hospitality and ensured that we did
not kill ourselves while conducting nocturnal studies. Special thanks are extended to Marco
Chalco and Julio Wayra who often accompanied us while conducting transects, Botanist Gustavo
Martinez who expanded our knowledge of local flora, and Rainforest Expedition managers Liz
de La Cruz and Liz Pai Pai who put up with a pair of crazy gringos for two months.
14
Works Cited
Castner, James. “Katydid Research by Stanford Students.” Email to Connor Pierson. 9 March,
2010.
Castner, James and Nickle, David. 1995.” Intraspecific color polymorphism in leaf-mimicking
katydids (Orthoptera:Tettigoniidae: Pseudophyllinae: Pterochrozini)”. Proc. 6thInternationa
lMeeting of the Orthopterists' Society. Hilo, Hawaii. August 2-6, 1993. J. Orth. Res. 4: 99-103.
Castner, James and Nikle, David. "Observations on the Behavior and Biology of LeafMimicking Katydids (Orthoptera: Tettigoniidae: Pseudophyllinae: Pterochrozini)." Journal of
Orthoptera Research 4 (995): 93-97. Print.
Doan, Tiffany, and Wilfredo Arriaga. "Microgeographic Variation in Species Composition of the
Herpetofaunal Communities of Tambopata Region, Peru." Biotropica 34.1 (2002): 101-17. Web.
Nikle, David and Castner, James. "Strategies Utilized by Katydids (Orthoptera: Tettigoniidae)
against Diurnal Predators in Rainforests of Northeastern Peru." Journal of Orthoptera Research
4 (1995): 75-88. Print.
Phillips, L. “Comparative evaluation of Tropical Forests in Amazonian Peru” Ph.D. Dissertation
Washington University, St. Louis, Missouri. 1993.
15
Appendix:
Model Selection and Criteria utilized for DISTANCE calculatios
Estimators:
----------Estimator 1
Key: Half-normal
Adjustments - Function
: Cosines
- Term selection mode
: Sequential
- Term selection criterion : Akaike Information Criterion (AIC)
- Distances scaled by : W (right truncation distance)
Estimator selection: Choose estimator with minimum AIC
Estimation functions: constrained to be nearly monotone non-increasing
Goodness of fit:
---------------Cut points chosen by program
Glossary of terms
----------------Data items:
n - number of observed objects (single or clusters of animals)
L - total length of transect line(s)
k - number of samples
K - point transect effort, typically K=k
T - length of time searched in cue counting
ER - encounter rate (n/L or n/K or n/T)
W - width of line transect or radius of point transect
x(i) - distance to i-th observation
s(i) - cluster size of i-th observation
r-p - probability for regression test
chi-p- probability for chi-square goodness-of-fit test
Parameters or functions of parameters:
m - number of parameters in the model
A(I) - i-th parameter in the estimated probability density function(pdf)
f(0) - 1/u = value of pdf at zero for line transects
u - W*p = ESW, effective detection area for line transects
h(0) - 2*PI/v
v - PI*W*W*p, is the effective detection area for point transects
p - probability of observing an object in defined area
ESW - for line transects, effective strip width = W*p
EDR - for point transects, effective detection radius = W*sqrt(p)
rho - for cue counts, the cue rate
DS - estimate of density of clusters
E(S) - estimate of expected value of cluster size
16
D - estimate of density of animals
N - estimate of number of animals in specified area
Effort
: 8.470999
# samples : 13
Width
: 4.000000
# observations: 260
Model 1
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Results:
Convergence was achieved with 5 function evaluations.
Final Ln(likelihood) value = -108.93445
Akaike information criterion = 219.86890
Bayesian information criterion = 223.42957
AICc = 219.88440
Final parameter values: 0.73578904
Model 2
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Cosine adjustments of order(s) : 2
Results:
Convergence was achieved with 29 function evaluations.
Final Ln(likelihood) value = -80.877473
Akaike information criterion = 165.75494
Bayesian information criterion = 172.87631
AICc = 165.80164
Likelihood ratio test between models 1 and 2
Likelihood ratio test value = 56.1139
Probability of a greater value = 0.000000
*** Model 2 selected over model 1 based on minimum AIC
Model 3
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Cosine adjustments of order(s) : 2, 3
Results:
Convergence was achieved with 37 function evaluations.
Final Ln(likelihood) value = -67.625880
Akaike information criterion = 141.25175
Bayesian information criterion = 151.93381
AICc = 141.34550
Final parameter values: 0.98456735 0.49533683 0.54415627
Likelihood ratio test between models 2 and 3
Likelihood ratio test value = 26.5032
Probability of a greater value = 0.000000
*** Model 3 selected over model 2 based on minimum AIC
17
Model 4
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Cosine adjustments of order(s) : 2, 3, 4
Results:
Convergence was achieved with 97 function evaluations.
Final Ln(likelihood) value = -59.575487
Akaike information criterion = 127.15097
Bayesian information criterion = 141.39369
AICc = 127.30783
Final parameter values: 1.1506476
1.1114469 0.49682608E-01 0.42661479
Likelihood ratio test between models 3 and 4
Likelihood ratio test value = 16.1008
Probability of a greater value = 0.000060
*** Model 4 selected over model 3 based on minimum AIC
Model 5
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Cosine adjustments of order(s) : 2, 3, 4, 5
Results:
Convergence was achieved with 100 function evaluations.
Final Ln(likelihood) value = -58.433825
Akaike information criterion = 126.86765
Bayesian information criterion = 144.67105
AICc = 127.10387
Final parameter values: 1.1679152
1.1249004 0.56698488E-01 0.41576497
0.105335
Likelihood ratio test between models 4 and 5
Likelihood ratio test value = 2.2833
Probability of a greater value = 0.130771
*** Model 5 selected over model 4 based on minimum AIC
Effort
: 8.470999
# samples : 13
Width
: 4.000000
# observations: 260
Model
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Cosine adjustments of order(s) : 2, 3, 4, 5
18
Point
Standard Percent
Coef.
95 Percent
Parameter Estimate
Error
of Variation Confidence Interval
------------------- --------------------------------------------A( 1)
1.168
0.6214E-01
A( 2)
1.125
0.1196
A( 3)
0.5670E-01 0.1361
A( 4)
0.4158
0.1391
A( 5)
0.1053
0.1175
f(0)
1.5265
0.63017E-01
4.13
1.4073-1.6557
p
0.16378
0.67611E-02
4.13
0.15099-0.17764
ESW
0.65510
0.27044E-01
4.13
0.60397-0.71056
--------- ----------- ----------- -------------- ---------------------Sampling Correlation of Estimated Parameters
A( 1)
A( 1) 1.000
A( 2) 0.316
A( 3) -0.019
A( 4) 0.025
A( 5) 0.079
A( 2)
0.316
1.000
-0.656
0.622
-0.440
A( 3)
-0.019
-0.656
1.000
-0.865
0.655
A( 4) A( 5)
0.025 0.079
0.622 -0.440
-0.865 0.655
1.000 -0.722
-0.722 1.000
Kolmogorov-Smirnov test
----------------------D_n
= 0.2144
p = 0.0000
Cramer-von Mises family tests
----------------------------W-sq (uniform weighting) = 2.2094
Relevant critical values:
W-sq crit(alpha=0.001) = 1.1754
C-sq (cosine weighting) = 1.6223
Relevant critical values:
C-sq crit(alpha=0.001) = 0.8135
0.000 < p <= 0.001
0.000 < p <= 0.001
Perpendicular distance in meters
Cell
Cut
Observed
Expected Chi-square
19
i
Points
Values
Values
Values
-------------------------------------------------------------------------------1 0.000
0.400
191
143.23
15.932
2 0.400
0.800
24
76.39
35.927
3 0.800
1.20
28
21.16
2.210
4
1.20
1.60
6
6.93
0.125
5
1.60
2.00
6
5.48
0.049
6
2.00
2.40
0
2.30
2.296
7
2.40
2.80
1
1.02
0.001
8
2.80
3.20
2
1.47
0.188
9
3.20
3.60
0
1.33
1.334
10
3.60
4.00
2
0.69
2.524
----------------------------------------------------------------Total Chi-square value = 60.5860 Degrees of Freedom = 4.00
Probability of a greater chi-square value, P = 0.00000
Goodness of Fit Testing with some Pooling
Cell
Cut
Observed Expected Chi-square
i
Points
Values
Values
Values
-------------------------------------------------------------------------------1 0.000
0.400
191
143.23
15.932
2 0.400
0.800
24
76.39
35.927
3 0.800
1.20
28
21.16
2.210
4
1.20
1.60
6
6.93
0.125
5
1.60
2.00
6
5.48
0.049
6
2.00
2.40
0
2.30
2.296
7
2.40
2.80
1
1.02
0.001
8
2.80
3.20
2
1.47
0.188
9
3.20
4.00
2
2.02
0.000
----------------------------------------------------------------Total Chi-square value = 56.7280 Degrees of Freedom = 3.00
Perpendicular distance in meters
Cell
Cut
Observed Expected Chi-square
i
Points
Values
Values
Values
------------------------------------------------------------------------------1 0.000
0.250
119
95.23 5.933
2 0.250
0.500
83
74.27 1.027
20
3 0.500
0.750
8
44.49
29.931
4 0.750
1.00
31
20.17
5.819
5
1.00
1.25
2
7.68
4.203
6
1.25
1.50
6
4.27
0.703
7
1.50
1.75
0
3.93
3.934
8
1.75
2.00
6
3.15
2.584
9
2.00
2.25
0
1.76
1.759
10
2.25
2.50
1
0.79
0.054
11
2.50
2.75
0
0.62
0.620
12
2.75
3.00
1
0.84
0.030
13
3.00
3.25
1
0.97
0.001
14
3.25
3.50
0
0.86
0.864
15
3.50
3.75
0
0.61
0.609
16
3.75
4.00
2
0.35
7.682
-------------------------------------------------------------------------------Total Chi-square value = 65.7533 Degrees of Freedom = 10.00
Probability of a greater chi-square value, P = 0.00000
Goodness of Fit Testing with some Pooling
Cell
Cut
Observed Expected Chi-square
i
Points
Values
Values
Values
------------------------------------------------------------------------------1 0.000
0.250
119
95.23
5.933
2 0.250
0.500
83
74.27
1.027
3 0.500
0.750
8
44.49
29.931
4 0.750
1.00
31
20.17
5.819
5
1.00
1.25
2
7.68
4.203
6
1.25
1.50
6
4.27
0.703
7
1.50
1.75
0
3.93
3.934
8
1.75
2.00
6
3.15
2.584
9
2.00
2.25
0
1.76
1.759
10
2.25
2.50
1
0.79
0.054
11
2.50
2.75
0
0.62
0.620
12
2.75
3.00
1
0.84
0.030
13
3.00
4.00
3
2.80
0.014
------------------------------------------------------------------------------------Total Chi-square value = 56.6123 Degrees of Freedom = 7.00
Probability of a greater chi-square value, P = 0.00000
One or more expected values is < 1.
21
Perpendicular distance in meters
Cell
Cut
Observed
Expected Chi-square
i
Points
Values
Values
Values
--------------------------------------------------------------------------------1 0.000
0.167
58
64.94
0.742
2 0.167
0.333
110
58.13
46.283
3 0.333
0.500
34
46.42
3.324
4 0.500
0.667
5
32.87
23.628
5 0.667
0.833
8
20.49
7.617
6 0.833
1.00
26
11.30
19.127
7
1.00
1.17
0
5.83
5.825
8
1.17
1.33
6
3.39
2.005
9
1.33
1.50
2
2.73
0.197
10
1.50
1.67
0
2.66
2.659
11
1.67
1.83
0
2.46
2.461
12
1.83
2.00
6
1.96
8.313
13
2.00
2.17
0
1.32
1.318
14
2.17
2.33
0
0.77
0.771
15
2.33
2.50
1
0.46
0.624
16
2.50
2.67
0
0.40
0.396
17
2.67
2.83
0
0.48
0.476
18
2.83
3.00
1
0.59
0.289
19
3.00
3.17
1
0.65
0.188
20
3.17
3.33
0
0.63
0.635
21
3.33
3.50
0
0.55
0.553
22
3.50
3.67
0
0.44
0.437
23
3.67
3.83
0
0.32
0.315
24
3.83
4.00
2
0.21
15.266
----------------------------------------------------------------Total Chi-square value = 143.4492 Degrees of Freedom = 18.00
Probability of a greater chi-square value, P = 0.00000
The program has limited capability for pooling. The user should
judge the necessity for pooling and if necessary, do pooling by hand.
Goodness of Fit Testing with some Pooling
Cell
Cut
Observed Expected Chi-square
i
Points
Values
Values
Values
-------------------------------------------------------------------------------1 0.000
0.167
58
64.94
0.742
2 0.167
0.333
110
58.13
46.283
3 0.333
0.500
34
46.42
3.324
22
4 0.500
0.667
5
32.87
23.628
5 0.667
0.833
8
20.49
7.617
6 0.833
1.00
26
11.30
19.127
7
1.00
1.17
0
5.83
5.825
8
1.17
1.33
6
3.39
2.005
9
1.33
1.50
2
2.73
0.197
10
1.50
1.67
0
2.66
2.659
11
1.67
1.83
0
2.46
2.461
12
1.83
2.00
6
1.96
8.313
13
2.00
2.17
0
1.32
1.318
14
2.17
2.33
0
0.77
0.771
15
2.33
2.50
1
0.46
0.624
16
2.50
2.67
0
0.40
0.396
17
2.67
2.83
0
0.48
0.476
18
2.83
3.00
1
0.59
0.289
19
3.00
3.17
1
0.65
0.188
20
3.17
4.00
2
2.15
0.010
---------------------------------------------------------------------------------------Total Chi-square value = 126.2534 Degrees of Freedom = 14.00
Probability of a greater chi-square value, P = 0.00000
One or more expected values is < 1.
Try pooling some some cells by hand to obtain a more reliable test.
Effort
: 8.470999
# samples : 13
Width
: 4.000000
# observations: 260
Model 5
Half-normal key, k(y) = Exp(-y**2/(2*A(1)**2))
Cosine adjustments of order(s) : 2, 3, 4, 5
Point
Parameter
--------D
N
---------
Standard Percent
Coef.
95% Percent
Estimate
Error of Variation Confidence Interval
--------------------- ----------------------------------23426.
425.3
18.25
15860-34602.
48656.
889.7
18.25
32941-71869.
--------------------- -----------------------------------
Measurement Units
--------------------------------Density: Numbers/Sq. kilometers
23
ESW: meters
Component Percentages of Var(D)
------------------------------Detection probability : 5.1
Encounter rate
: 94.9
Estimate %CV
df
95% Confidence Interval
--------------------------------------------------------------------------n
260.00
k
13.000
L
8.4710
n/L 30.693
17.78 12.00
20.899- 45.076
Left 0.0000
Width 4.0000
Estimate
%CV df
95% Confidence Interval
---------------------------------------------------------------------------Half-normal/Cosine
m
5.0000
LnL -58.434
AIC 126.87
AICc 127.10
BIC 144.67
Chi-p 0.0000
f(0) 1.5265
4.13 255.00
1.4073-1.6557
p
0.16378
4.13 255.00
0.1509-0.17764
ESW 0.65510
4.13 255.00
0.60397-0.71056
Estimate %CV
df
95% Confidence Interval
-------------------------------------------------------------------------Half-normal/Cosine
D
23426.
18.25 13.33
15860-34602.
24