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Potential Interaction between predation risk, food limitation and
disease
Wigganson Matandiko, Montana State University
Supervisor: Prof. Scott Creel, Senior Lecturer, Department of Ecology
Co-Supervisor: Dr Matthew Becker
Project Duration: August 2012 – July 2015;
Budget: U$ 252, 070
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Potential Interaction between predation risk, food limitation and
disease
Project Summary
Predators influence prey in both direct and indirect way resulting in an effect on their population
dynamics. The direct influence is observed through prey kills. The indirect effects on pray can either be
physiological and / or behavioral responses due to the risk of predation. Both the physiological and
behavioral responses are an attempt to counteract predation. The mere risk of predation causes some
prey species to alter their group and foraging patterns. Experiments carried out in aquatic and avian
species do show remarkable changes in reproduction which include reduced number of eggs laid,
reduced offspring per year, and poor hatchability in eggs. These costs some authors argue that they may
even be far more detrimental compared to direct effects on prey. The challenge then is how to measure
and quantify the effects of risk predation alone being the indirect influence on prey species dynamics.
In this this proposal we seek to investigate the distribution of prey in predator home ranges and compare
to outside ranges. The home ranges will be determined by radio collared predators of the lion, African
wild dog and hyenas. The prey species density will be determined from transects from past aerial surveys
to current. We will elect to undertake either air or ground transect in the two ranges to estimate prey
density comparable to the census surveys. We also wish to determine the predator home ranges in three
seasons (cold, dry and wet) with their associated densities. We are hypothesizing that predator density is
more or less equal in the cold and dry but lesser in the wet season.
We also seek to determine group size changes and contact rates on two prey species (wildebeest and
zebra) in predator and outside predator home range using proximity collars. Approximate position of
predators will be determined relative to the group of prey at each observation. The contact rates will be
correlated to the proximity distances of predator. The idea here is to correlate high intra-species contacts
to higher titers of disease antibodies to foot and mouth disease (FMD), malignant catarrhal fever (MCF)
and bovine tuberculosis (BTB). The high contact rates will be interpreted in the context of grazing
preference and nearness of the predator. The same analysis will be followed for the zebras except the
disease entity chosen will be different. In the case of zebras we will investigate the prevalence of two
helminthes common in equine species namely, strongylus and parascaris worms. This later and the
earlier we hope will help answer the question of disease transmission driven by the risk of predation
through group and foraging pattern alteration (aggregation [high contact rates] and disaggregation[ low
contact rates]).
The research will also follow dietary changes of prey through examination of the fecal and grass
chlorophyll concentrations. Low chlorophyll has to do with a poor diet; this then will have to be correlated
with place, contact rates and nearness or absence of predator to come up with analysis as to whether
predation risk could be contributing to food limitation of prey species.
Ancillary study on metabolite of fecal glucocorticoids hormone variation in game ranches and park
animals will be investigated in different environment mimicking diverse stressors. Areas will be classified
as high or low in perceived stress and the differences between these analyzed to see if they can be
significant level differences that can be warranted to particular stressors.
We plan to analyze the data with t-tools, regression analysis and confidence intervals of associated
parameters established. Data collection is supposed to span a period of three years beginning July 2012
to June 2015. The project is estimated to cost two hundred and fifty two thousand and seventy United
States dollars (U$ 252, 070).
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Introduction
Recent studies and publications show that predation risk can play significantly negative
impact on prey species such as elk in the Greater Yellowstone Ecosystem. A
conservative view has been that predators limit prey through direct killing. Research
finding has however shown that it is not the only factor at play, but those anti-predator
responses mounted by prey have costs such as lowered survival, growth and
reproduction. Creel (2011) advocates that stronger tests of these hypotheses will
require continued development of methods to identify and quantify the fitness costs of
anti-predator responses in wild animals2,6,7. That potential interaction between predation
risk, food limitation and disease may come about due to altering foraging pattern and
group aggregation versus disaggregation is the focus of the proposed study. In an
attempt to test the hypothesis of the risks of predation, we seek to quantify the
magnitude of disease transmission and food limitation arising from the perceived risk
effects of predation. The predators to be considered in the study as a source of risk to
prey species are lions (panthera leo), hyenas (crocuta crocuta) and African wild dogs
(lycaon pictus) in Liuwa Plain National Park (LPNP) of Western Zambia. The
measurements of interest are the average predator home range and predator density (in
the cold, dry and wet seasons), prey density (with estimates of age structure) within and
outside predator home range, prey fecal glucocorticoid metabolites 7, vegetation and
prey fecal chlorophyll trends8 in droppings (to detect alteration in foraging patterns and /
or seasonal forage quality), contact rates using proximity collars among prey species
[prey species will be limited to Wildebeest and Zebra only for the purpose of this study].
The rational is to establish contact rates that are related to host density due to risk of
predation. An estimate of the distance between prey and predator will be established in
the vicinity of the prey herds that will be observed at set times and intervals to
determine behavioral responses to presence of predator. The serological prevalence of
three disease entities will be investigated in wildebeest, these being foot and mouth
disease (FMD), malignant catarrhal fever (MCF), bovine tuberculosis (BTB) and fecal
parascaris and strongylus helminthes in zebras. The idea is to investigate the
correlation of disease exposure or transmission dynamics in various groupings that will
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be observed, the hypothesis being that the higher the contact rates, the higher the
disease pathogen transmission (this is density – mediated transmission [DMT].
Predator – prey interaction with the result of limiting prey by direct killing is well
documented in both terrestrial and aquatic animals. Of equal importance in current
literature is the fact that the risk of predation may have effects of equal magnitude if not
greater than direct observable killings.9
The preoccupation in current research on this
subject is to find some measure that will quantify the effect of predation risk alone.
Behavioral responses observed due to predation risk are reported on altered foraging
pattern (e.g. less time spent on grazing and much time spent in hiding from predator),
mating and even suppression of conception or laying of eggs in aquatic fishes. 4
Creel, S.,2 has identified and listed the following mounted response to predation risk:i). change of group size in order to dilute direct predation risk. He affirms “the risk that
at least one herd member will be killed, increases as herd size increases and that
individual risk, decreases as herd size increases”. However it is also important to note
that the risk factor for disease transmission also increases as animals congregate. The
animals will tend to share common grazing ranges and watering points. So while
combating risks of predation, a subtle spread of disease may be enhanced. This is one
level where disease can interact with predation risk. At the same time, if this is
happening in the dry season when forage is scarce, the herd usually depletes the
immediate available resource and then move on in search for better pastures or “sweet
spots”. This tends to lead them further away from watering points. It is often the case
that the very young and old succumb due to exhaustion and lack of water. Such effects
resulting in mortalities are often reported in the drier months of the year (August to
November).
ii).The degree of forage specialization as a strategy against predation can be seen in
some bulk grazers that target the grass plains to improve their visual acuity in detecting
predators but others do the opposite by going in the underbrush and forested area
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where they cannot easily be noticed. The strategy is least effective in the dry season
when most deciduous shrubs and trees shed their foliage. In Liuwa Plains National
Park, our proposed sight for the research, it is observed that wildebeest and zebra
graze mostly in the plain grasslands. Sometimes they venture into the woodlands but
sparingly.
iii). Increased serum glucocorticoid that can be detected in fecal matter as indicator of
stress (fecal glucocorticoid [fGC]). This however was found with limitation due to
progesterone (pregnancy hormone) that equally yield metabolites resembling fGC and
extruded in fecal droppings.7 If GC concentrations increase due to stress; it follows that
any stressor outside risk of predation may increase the serum level. In view of the
difficulty of measuring fGC in relation to predation risk it is here proposed to investigate
the hormonal variation in game ranches (where risk due to predation is absent) to a
range of stressors such as hunting, fencing and disturbance due to tourist movements.
A comparison with Game ranches where these activities are not taking place will be
included to aid in detecting the difference and then followed by comparison with
wildebeest and zebra in the wild. The question of interest is whether the changes in
concentration are significantly different in game ranch animals with disturbances
compared to those without and the wild stock. This investigation will target ranches that
have been in establishment for a period of two years and above with the same species
being studied in the wild (wildebeest and zebra). This will be a baseline survey to
establish how GC hormone varies with factors mentioned in play above.
iv). Vigilance - there is a cost that comes with vigilance such as reduction in feeding
time as a trade off in trying to minimize chances of being preyed upon.
I wish to quantify to some degree the effect of such responses (either directly or
indirectly) by investigating firstly the prey density estimates in predator home range
versus outside home range. The hypothesis1 to be tested here is that the density of
prey in predator home range is lower than outside the predator home range. In other
ways the presence of predator will tend to drive the prey away as far as possible to safe
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refuges. The process of animals leaving may be slow but ultimately only few will remain
in the predator’s home range. Secondly, we will establish predator home range
estimates in the cold, dry and wet season and seek to establish hypothesis2 that the
density of predators is less in the wet and cold season than the dry season. Thus seek
to establish when risk of predation is more predominant in the three seasons.
Monitoring of the collared predator and collared prey movement will aid to estimate the
proximity of the predators to prey. While proximity collars will aid in establishing group
contacts to be used as follow up on prevalence of disease. Theoretically, in the
presence of a transmissible circulating pathogen among herds, the higher the contact
rates the more probable the chances of contracting the disease. The season most
predominant with high predation risk will impact group size changes and foraging
pattern. The comparison then for serological analysis for disease will be carried out
between animals exhibiting high contact rates versus those with low contact rates. The
hypothesis3a being that antibody titers due to a circulating antigen will tend to be higher
in animals with high contact rates than those with low contact rates. Funds allowing,
repeated aerial surveys or fixed transect counts in predator home range versus non
predator home range will confirm the abundance or scarcity of prey in the two ranges. It
is suspected that predation risk is capable of triggering a cascade that can lead to
disease and food limitation. It also holds that food limitation can also trigger disease and
predation risk, leading to the weaker being hunted first. The challenge stands at
isolating predation as a sole factor leading to food limitation or disease because the
factors sometimes do interact synergistically.
Absence of predators may have a desirable effect in a short to medium terms in that
prey abundance may increase. However, over a long period this tends to have
deleterious effect as a result of unchecked increase of prey density that results in over
foraging (thus leading to food limitation). If the pasture range being foraged is seeded
with such organisms as anthrax spores, overgrazing could result in ingestion of the
spores from the soil and that could trigger anthrax outbreaks or clostridia disease. For
reproductive diseases such as brucellosis, fetal fluids and membranes extruded in the
environment increases the oral route transmission to other members of the herd. The
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same can be said of helminthes that are predominantly transmitted via fecal oral route.
This will be the focus for strongylus and parascaris worm examination in zebra herds
exhibiting high contact rates versus those with low contact. Worm counts and egg load
per gram will be measured in fecal matter collected at the time of collaring the zebras
followed by a dose of dewormer (subcutaneous administration of ivomectin injection).
The zebras will then be followed through the seasons to see how the worm load will fare
between the high and the low contact rates (sub-hypothesis3b – average egg count
and worm load will be higher in high contact rated zebra than in low contacts). We will
apply the ideal situation of selecting a herd of between ten and fifteen and deworm all
members of this herd). Then another herd with the same number collared but left
without deworming to act as a source of contaminating the pastures with helminthes
egg.
The overarching hypothesis4a we seek to test is the fact that the disease antibody titers
and worm load will be highest in the season when predation risk is higher in animals
rated with high contact rates than when predation risk is low. It is hoped that this will
bring about the element of risk predation in disease transmission dynamics. We are also
going to assume that high predator density in the dry season is synonymous with high
predation risk, and hence in the last Sub-hypothesis4b, we want to test the fact that
prey fecal chlorophyll will tend to be lower in prey than the vegetation chlorophyll in the
“sweet spots”. And that this may be attributed to the disturbance from predators when
the prey is driven from the “sweet spots” for fear of being preyed upon (in the dry
season).
The “sweet spots” being referred to here are those that retain moisture and therefore
relatively fresh grazing throughout the dry season and consequently attracting prey to
the area. Practically, the predators have to have more than one such spots in their
home range if they are to survive from starvation.
The specific research objectives are to24:
1. Assess how wildebeest and zebra contact rates relate to group size, disease
status, age, and environmental conditions.
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2. Determine relationships between contact rates and measures of population
density at several spatial scales, from highly local (group size) to very broad (e.g.
mean density for an entire national park).
3. Test for effects of predation risk on patterns of aggregation.
4. Examine relationships of the above variables to the incidence of FMD, MCF,
BTB, strongylus and parascaris helminthes.
The expected development outcomes are24:
1. Estimation of contact –group size relationships using proximity collars and
determination of predator –prey interactions that influence zebra-wildebeest
grouping patterns with potential for risk of disease transmission.
2. Determination of group size and prevalence of BTB, FMD, MCF, and some
helminthes in zebras (parascaris and strongylus), and thereby justify disease
management policy changes where needed.
3. Disease mitigation strategy from the resulting ecological and epidemiological
survey.
4. Facilitation to build the tourism potential of the region by taking proactive safety
measures in diseases affecting humans, domestic stock and wildlife thereby
earn benefit to the local communities in LPNP.
5. Training and advanced education of Zambia’s wildlife professionals.
Literature Review
“Predation is defined as interactions in which one organism consumes all or part of
another organism. This includes predator-prey, herbivore-plant, and parasite-host
interactions. These linkages are the prime movers of energy through food chains.”1
Predator-prey interaction also plays a role in natural selection in the sense that the
stronger are get favored. To illustrate this point, it is perceived that the better the
predators are at hunting the better the chance of passing their fitness trait to succeeding
generation through reproduction. The converse is also true that the weak get eliminated
through starvation or through becoming easy targets by other predators. The prey in
order to survive have to have better anti-predator defense mechanisms such as seeking
the safety in big herds thereby diluting the risk of lethal predation on themselves even
though the risk is not completely removed. They may also alter their foraging pattern
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due to presence of predators in their habitat. 2,
3
Other anti-predator responses have
been documented even in aquatic species, such as altering mating behavior in the
presence of predators without the predators necessarily mounting lethal attacks. 4 These
observation have led to the theory of costs associated with the risk of predation. That is,
the cost arising from the risk of predation and not the actual demise of prey from being
hunted. Traditionally, “Predator effects on prey demography have been ascribed solely
to direct killing by population ecologists and wildlife managers because the effect of
killing is directly observable.”
5, 6
However, “indirect effect resulting from the anti-
predator behavior” have been reported to have produced “trophic-level effects similar in
form and strength to those generated by direct predation events”10. The same author
categorizes the predator effect on prey populations as lethal direct effect, lethal indirect
effect (such as risk starvation when foraging pattern is altered due to potential of
predation risk) and nonlethal indirect effect. The last one may be seen through such
effect as altered reproduction behavior due to predation risk 11,
12.
The evidence that
predators have an influence on population communities besides direct killing is
undeniably being proven with each passing moment in literature publications. This even
goes to the level of affecting the demography of communities due to delayed
recruitment of young for instance when reproduction pattern is altered due to risk of
predation.
“The relationship between host density and parasite transmission is fundamental to
understanding disease dynamics and implementing effective control strategies
13,14.
Models predict that when transmission is correlated with host density the parasite will be
unable to persist when the host density is reduced below some threshold
15,16.
This
forms the basis for using social distancing (e.g. school closures) to control pandemics 17,
18, 19.
In natural populations, the distribution and abundance of a host species can be
affected by manipulating hunting pressure
20,
artificial food sources
21, 22, 23,
and
predator distributions” 24. The effect of predator distribution on prey grouping patterns to
mitigate against predation is one of the main focus for the research proposed. Whether
the result of this anti-predator response can be quantified in terms of high prevalence of
specific disease entities in high contact rated animals is another focus that is being
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investigated towards the theory of disease transmission dynamics due to risk of
predation. The strength of this finding will depend on the frequency of detecting
predators within the vicinity of prey groups at any given time.
Approach:
The interaction between predator and prey may have impacts that are yet to be
discovered and explained beyond mere killing of prey. The difficulty comes in when
considering methods of detecting and quantifying the cost of the risk due to predation.
The investigation proposed supposes that we can quantify the response to predation
risk either directly or indirectly. To address the questions the research is designed to
take inventory of wildlife numbers in perceived large carnivore ranges by taking
transects from previous animal census counts. This is in a bid to establish abundance or
absence of prey species. Upon confirmation of their presence, home ranges for three
carnivore species (Lion, hyena and African wild dog) will be determined from the
collared carnivores that are a source of risk predation. The information of aerial surveys
from the past to current record will be a used to asses density of prey in both predator
home range and outside the predator home range. The density of predators will also be
determined with the changing seasons from the approximated home ranges. In view of
the challenge that exists in census counts of large carnivores that are nocturnal, we are
going to apply the number of predators in our study to compute density that will be
assumed to be proportionately to the estimates of the actual density.
“In this study, we will deploy 30 contact collars on wildebeest and 30 on zebra,
distributing the collars in clusters of 5 sampling both large and small herds. What
defines a contact depends upon the transmission mode of the parasite. As in prior work
by Creel et al, we will define contact as being within 2m (approximately one body
length) of another individual. The 2m radius is a compromise between providing an
adequate number of contacts and decreasing the number of false-positives (i.e.
contacts that are too distant to result in transmission). We recognize that this is only an
index of the contacts that can cause transmission, but this index is probably not biased
by age, serostatus or group size (i.e. those individuals that have more 2m contacts are
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also likely to have more 1m contacts). We will set 3 collars to a critical distance of 10m
and 20m (6 total) to assess the importance of contact distance. In addition, we will
investigate several different contact metrics (probability of contact per day, number of
unique individuals contacted, and cumulative time in contact per dyad per day), as in
the current work on brucellosis in elk. The proximity collar data will allow us to assess
which variables affect contact (e.g. group size, habitat, predation risk, age, sex)”24.
The second aspect of the research study is to assess the response to predation by the
frequency with which prey is found within the home ranges of the selected carnivores
comparatively to outside predator home range. “We will conduct ground line transect
surveys (but preferably funds allowing by airplane transects) to determine the
distribution of group sizes across LPNP and the underlying factors associated with large
groups. Sampling will be stratified by season, topography and habitat type, intensity of
use by lions and spotted hyenas, human activity and livestock density”
24.
The analysis
will narrow down to compare predator home range versus outside. The information will
also be correlated to previous transect counts for rough comparison of the distribution
prey in past record.
Observing fecal glucocorticoid metabolites in some studies have not yielded results to
warrant stress levels due to predation. Moreover as already mentioned it has been
noted that pregnant females tend to have high yields of the metabolite due to
progesterone whose metabolites resemble that of glucocorticoids and have an affinity
for serum binding globulins. None the less the metabolites will still be investigated after
careful consideration of the likely calving seasons and avoid fecal sample collection in
the months of suspected pregnancy. Reproducing the findings reported by other
researchers in a different environmental setting will augment the conclusion of the
results from other researchers. The addition here is that we will collect fresh fecal
droppings in control groups of the same species found in game ranches so as to
provide a comparison platform of how serum glucocorticoids vary in a range of stressing
disturbances in the game ranches versus the wild species. The disturbances in
consideration are those arising from hunter and tourist activities and seasonal changes.
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The third aspect of this research will look at changes in the diet of prey species to be
investigated through assessment of fecal and grass chlorophyll concentration using the
technique applied by Christiansen et al (2009)8. The question of interest is whether food
limitation can be detected at differing predator density in prey species in the three
seasons. The currency used in this question is chlorophyll measurement because it is
the bulk constituent in the diet of herbivores. In the study random browse and grass
samples will be collected within predator ranges and outside to be used in assessing
months of scarcity in contrast to the months of abundance grazing. The landscapes in
Zambia have a typical three season phase categorized as the rain, dry and cold. By
experience, we know the months when browse and grazing grass is scarce. In such
months prey tend to travel longer distances in search of forage or keep to some soil
patches with high ground water table that retain moisture and hence maintain fresh
grazing. Such patches can maintain fresh grazing well into the dry season and
sometimes up to the following rain season. In the rain season the weather is favorable
to an abundance of plant regrowth and hence acts to limit the long distance movements
between grazing grounds and water (natural water catchment areas tend to be full in the
rain season). As a result of abundance in vegetation prey species tend to spread over a
wider area. Of interest is how ‘elastic’ the carnivore home range will be in response to
availability of food resource, will it remain static or is there periodic oscillation between
expansion and shrinkage? What does it mean when there is expansion; can it be
interpreted in terms of expanding carnivore population or a sign of food scarcity such
that carnivores have to spread in search of prey? What is the effect on such survival
instincts on both predator and prey? In the unlikely hood of shrinkage of home ranges,
what would the carnivores be subsisting on? This might lead to a theory of survival on
scavenging or targeting one or more patches that still attracts prey. Scavenging may be
a function of inability to hunt in some predators due to a variety of reasons one of which
is lack of readily available prey for hunting. The implication of scavenging on carcasses
whose cause of death is unknown is in itself a risk that might lead to the demise of
carnivores. The research will broadly attempt to answer the following pertinent
questions:
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i) When prey is most abundant within the carnivore home range and why.
ii) When prey have to balance between risk of predation and survival (food and
water availability).
iii) Whether prey herd pattern changes in the face of predation risk can lead to
disease transmission dynamics that can significantly be quantified.
iv) Synchrony variation in carnivore home range size with the seasonal change.
v) Evaluation of fGC as stress indicator from diverse disturbance regimes (human
and non-human induced.
vi) Factors affecting carnivore home range.
vii) Differences among prey within and outside carnivore home ranges.
viii) Anti-predator responses to predation risk.
Two sources of retrospective data will be sort to arrive at species density estimates. The
anti-poaching patrol teams keep records of animals encountered and mortalities seen in
the area of patrol. This will be useful information pertaining to the area where research
is to be conducted. Other sources through interviews and questionnaire surveys to be
considered are the tour operators, non-governmental organizations actively engaged in
conservation activities and hunting safari operators. Secondly records from aerial
surveys will be used to guide in determining prey species abundance in assumed
carnivore home ranges. Random transect counts, (preferably by airplane, financial
resources allowing) will be undertaken in the areas to see how the figures correlate with
aerial surveys on record. This will be followed by selection of an area (transects most
consistent with aerial surveys) in the park where two to three predator (lion, hyena and
wild dogs) species are frequently located in proximity to the prey species from the aerial
survey records. To the existing collared predators additional representative predator
species will be fitted with VHF collars that will be used to monitor movement and
subsequent home range size. It is anticipated that at least two lions per pride will be
collared (minimum of two prides to be monitored), two hyenas per clan (minimum of
three clans) and three wild dogs per park (minimum of two parks). Chemical
immobilization will be done by use of Dan inject darting gun. A cocktail immobilizing
drug of MZT (Medetomidine hydrochloride – 8mg [Zalopine] and Zolazepam-Tiletamine
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– 125mg [Zoletil]) is here proposed for use because of the advantage of reversal with
antidote (Atipamezole [antisedan 5mg/ml]). This will minimize mortality risk due to
anesthesia by reducing wake up time.
As home ranges of the predators become more and more pronounced, the transects will
narrow down to the home ranges of the predators. This will give a good comparison of
the transect densities within predator home range versus outside. A foot and vehicle
patrol team will undertake quarterly visits to assess vegetation biomass, mortality and
frequency of prey presence / absence in the predator ranges. Prior information of any
recorded mortalities in the area will also be used as baseline data for investigating
pathogens endemic to the area in prey species.
Selection of game ranches to be used as control will be subjected to random sampling
after looking at those ranches with most representative prey species. It is targeted to at
least have a minimum of three to four game ranches where fecal and vegetation
biomass will be obtained to tally with samples from the National Parks.
Data to be collected and measurement method
i.
Predator and prey density – for monitoring changes in group size of the quarterly
transects in predator ranges compared with transects outside the predator
range (Ground or aero transects depending on availability of resources)
ii. Predator home range size fluctuation determined by VHF collared representative
species – mean areas for different seasons to be compared for analysis of
statistical variation within and between seasons.
iii. Frequency of prey species presence within predator range in comparison with
outside predator range (Ground or aero transects depending on availability of
resources).
iv. Prey fecal Glucocorticoids in park animals versus game ranch species (from
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fresh dropping to be preserved in liquid nitrogen tanks upon collection) to be
submitted to specialized laboratory for hormone assay reading.
v. Fecal and grass chlorophyll concentration trends in the park versus control group
of game ranches randomly selected (Laboratory spectrophotometry of forage
and fecal extract is used to read chlorophyll concentration)8. Environmental
conditions through fecal and chlorophyll concentration analysis are to be used
as a guide in following the nutritional curve and hence the body condition
estimates of the prey and predator (pictures and video recording to be taken).
vi. Alterations in foraging pattern – Where are the prey species found foraging
when transects are taken? Is it in the savannah grasslands, miombo
woodlands, plains, riparian forests? It is generally hoped that a species
without threat or risk of predation will tend to inhabit areas of high nutritional
gain most of the time intermittent with breaks for watering (Proximity collars
will aid in determination of herd pattern changes).
Statistical methods
This far we have identified two statistical methods that will be used to analyze the
results as follows:
Prey Density Estimates in Predator home range Versus Outside predator home
range
step1: Repeated prey counts up to 100000 trials in predator home range (set the
average of the counts = lamda = 5 in Poisson random generator)
10000
0
5000
Frequency
15000
Distribution of Counts of Prey within predator home range
0
5
10
15
Counts of Prey
Step 2: Repeated prey counts up to 100000 trials outside predator home range (set the
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average of the counts = lamda = 20 in Poisson random generator)
4000
0
2000
Frequency
6000
8000
Distribution of Counts of Prey outside predator home range
10
20
30
40
Counts of Prey
Prey density for each of the 100000 trials in predator home range and outside
predator home range (Area set at 200km²)
Step 3 – Prey density in predator Home range versus outside predator home range
Density of Counts
4000
Frequency
10000
0
0
2000
5000
Frequency
6000
15000
8000
Density of Counts
0.00
0.04
0.08
Counts of Prey
Within Home Range of Predator
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0.05
0.15
Counts of Prey
Outside Home Range of Predator
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Step 4: Difference: Prey density outside – prey density in predator home range
Density of Counts
Difference in densities
0.04
0.08
Counts of Prey
Within Home Range of Predator
2000
0
2000
0
0
0.00
4000
Frequency
4000
Frequency
10000
5000
Frequency
6000
6000
15000
8000
8000
Density of Counts
0.05
0.15
Counts of Prey
Outside Home Range of Predator
0.00
0.10
0.20
Counts of Prey
Outside - Home Range of Predator
Step 5: Comparison of the Range of prey densities – within, outside & difference
•
Within home range of predator
0.0
to 0.08 prey / km²
•
Outside predator home range
0.04 to 0.2 prey / km²
•
Difference of the densities
0.00 to 0.2 prey / km²
Step 6: Conclusion – 1st part
•
The hypothesis is that density of prey in predator home range is lower than
outside predator home range.
-
Calculate the mean density for within & out
Calculate standard error of the mean density
Proceed with a paired sample t test for the difference in the mean
Null Hypothesis: Mean density difference = 0
Alternative Hypothesis: Mean density difference ≠ 0
17
18
Step 7: Predator Home range estimates in the cold season (cs), dry season (ds), wet
season(ws)
• Number of trials 10,000 (cold, dry & wet)
Cold Season Predator Home range
Mean home range 250km²
Standard Deviation 30km²
Predator density = 0.06 lions / km²
Dry Season Predator Home range
mean home range 190km²
standard deviation 25km²
Predator Density = 0.079 lions /km²
Wet Season Predator Home range
Mean home range 300km²
Standard deviation 35km²
Predator density = 0.05 lions / km²
Step 8: Comparison of seasonal Predator Home Ranges
Distribution of area estimates (cold season)
Distribution of area estimates (dry season)
250
200
150
Frequency
100
200
50
100
200
250
300
Area estimates of Predator cs
350
0
0
50
50
0
150
18
150
Frequency
150
100
Frequency
200
250
250
300
300
350
Distribution of area estimates(wet season)
100
150
200
Area estimates of Predator ds
250
200
250
300
350
Area estimates of Predator ws
400
450
19
Step 9: Conclusion – Second Part
•
-
The Hypothesis is that density of Predator:
Wet Season ≤ Cold Season < Dry Season
0.05 < 0.06 < 0.079
Regression of Seasonal Prey density vs Predator density (wet, cold, dry) =
Separate line model
-
Compare the intercepts (β₀) for the three regression lions (Parameter relates to
zero predator)
-
Compare the slope (β₁) for the three regression lines (Parameter relates to rate
of prey decrease per unit increase in predator)
We will subject the parameters to power analysis by calculating the 95% confidence
intervals and compare as to whether there is an overlap in the intervals for each
season. Absence of overlap will be indicative of significant difference in prey and
predator densities in the seasons whereas overlaps will cast doubt on plausibility of the
research findings.
Adequacy of design (Appendix V refers)
19
20
APPENDIX I
References
1. www.global
change.umich.edu/globalchange1/current/lectures/predation/predation.html
2. Creel, S. (2011): Toward a predictive theory of risk effects: hypothesis for prey
attributes and compensatory mortality. Ecology 110726112314008
(2011).doi.1890/11-0327.1
3. Christianson D. and Creel S. (2008): Risk effects in elk: Sex-specific responses
in grazing and browsing due to predation risk from wolves. Behavioral Ecology
doi.10.1093/beheco /arn 079. Pp 1258 - 1265
4. Fraser, D. F and Gilliam, J.F. (1992): None-lethal impacts of predator invasion:
facultative suppression of growth and reproduction. Ecology 73, pp 959 – 970
5. Lima S.L.(1998): Nonlethal Effects in the Ecology of predator prey interactions.
BioScience Vol. 48, pp 25 – 34
6. Scott Creel and David Christianson (2008): Relationship between direct
Predation and Risk Effects. Trends in Ecology and Evolution, Vol 23, pp 194 –
201.
7. Creel, S., Winnie, J. A., Christianson, D. (2009): Glucocorticoid Stress Hormones
and the effects of Predation Risk on Elk. PNAS –
WWW.pnas.org/cgi/doi/10.1073/pnas.0902235106
8. Christianson, D. and Creel, S. (2009): Fecal chlorophyll describes the link
between primary production and consumption in a terrestrial herbivore.
Ecological Applications, 19(5), pp. 1323 – 1335
9. Smith, M. T and Smith, L. R (200): elements of Ecology- 7th Edition Published by
Benjamin Cummings pp. 304 - 306
10. Schmitz, O. J., et al (1977): Behaviorally mediated trophic cascades: Effects of
predation risk on food web interactions. Ecology, 78(5), 1997, pp 1388 – 1399
11. Berglund, A. (1993): Risky sex: Male pipe fishes mate at random in the presence
of a predator. Animal Behavior, 46, pp 169 – 175
12. Forsgreen, E.(1992): Predation risk affects mate choice in a Gobbid fish.
American Naturalist 140 pp 1041 – 1049.
13. Anderson R.M. & May R.M. (1991) Infectious Diseases
Dynamics and Control. Oxford University Press, Oxford.
of
Humans:
14. McCallum H., Barlow N. & Hone J. (2001) How should pathogen transmission be
20
21
modelled? Trends in
Ecology and Evolution, 16, 295-300.
15. Kermack W.O. & McKendrick A.G. (1927) Contributions to the
mathematical theory of epidemics. Proceedings of the Royal Society of
Edinburgh, 115, 700-721.
16. Getz W.M. & Pickering J. (1983) Epidemic models:
population regulation. American Naturalist, 121, 892-898.
thresholds
and
17. 5. Halloran M.E., Ferguson N.M., Eubank S., Longini I.M., Cummings D.A., Lewis
B., Xu S., Fraser C.,
Vullikanti A., Germann T.C., Wagener D., Beckman
R., Kadau K., Barrett C., Macken C.A., Burke D.S. & Cooley P. (2008) Modeling
targeted layered containment of an influenza pandemic in the United States.
Proceedings of the Academy of Natural Sciences of Philadelphia, 105, 46394644.
18. Glass K. & Barnes B. (2007) How much would closing schools reduce
transmission during an influenza
pandemic? Epidemiology, 18, 623-628.
19. Cauchemez S., Valleron A., Boëlle P., Flahault A. & Ferguson N.M. (2008)
Estimating the impact of
school closure on influenza transmission from
Sentinel data. Nature, 452, 750-754.
20. Conner M.M., Miller M.W., Ebinger M.R. & Burnham K.P. (2007) A
meta-BACI
approach
for evaluating
management
intervention on
chronic wasting disease in mule deer. Ecological Applications, 17, 140153.
21. Miller R.E., Kaneene J.B., Fitzgerald S.D. & Schmitt S.M. (2003)
Evaluation of the influence of supplemental feeding of white-tailed deer
(Odocoileus virginianus) on the prevalence of bovine tuberculosis in the Michigan
wild deer population. Journal of Wildlife Diseases, 39, 84-95.
22. Cross P.C., Edwards W.H., Scurlock B.M., Maichak E.J. & Rogerson
J.D. (2007) Effects of management and climate on elk brucellosis in
the Greater Yellowstone Ecosystem. Ecological Applications, 17, 957-964.
23. Rudolph
B.A., Riley S.J., Hickling G.J., Frawley B.J., Garner M.S. &
Winterstein
S.R. (2006) Regulating hunter baiting for white-tailed deer in
Michigan: Biological and social considerations.
Wildlife Society Bulletin, 34,
314-321.
24. Creel, S. and Matandiko, W.(2011) – Proposal for grant application submitted to
National Science Foundation – 30th November, 2011
21
22
APPENDIX II
Travel Details
10th June 2012 – Travel from Bozeman, Montana State, to Lusaka Zambia, via
Republic of South Africa by air.
12thJune, 2012 – Travel to Liuwa Plains National Park by road from Lusaka via Mongu
and Kalabo districts of Western Zambia
14th June – 30th July, 2012 – one and half month at the research site in LPNP
5th August, 2012 – Travel from LPNP to Lusaka by road
15th August, 2012 – Travel back to Bozeman, Montana State (in readiness for fall
semester) by air
1st August, 2013 – Travel from Bozeman, Montana State, to Lusaka Zambia, via
Republic of South Africa by air.
5th August, 2013 - Travel to Liuwa Plains National Park by road from Lusaka via Mongu
and Kalabo districts of Western Zambia to commence research for two more years.
8th August, 2015 - Travel from LPNP to Lusaka by road
10th August, 2015 – Travel back to the Bozeman, Montana State by air and commence
data analysis, write up on research findings and compilation of PhD dissertation
22
23
APPENDIX III PROJECT BUDGET
TABLE 1. SUMMARIZED BUDGET (SEE TABLE 2 FOR DETAILS)
Note: List all amounts in U.S. dollars
only
Travel
Year 1
Year Two
(if requested)
Year Three
(if requested)
Project Total
1. Domestic Travel
2. Per Diem, Domestic
2,800
2,800
2,800
8,400
Travel Costs Total (A)
2,800
2,800
2,800
8,400
Equipment
1. Instruments
35,815
2. Materials and Supplies
2,475
1,350
1,350
5,175
Equipment Costs Total (B)
38,290
1,350
1,350
40,990
Other
Direct
Costs
770
3 International Travel
4. Per Diem, International
1. Computer Services
35,815
770
2. Publication Costs
1,500
1,500
3. Workshops and
conferences
4. Other (describe, add
additional lines if needed)
Helicopter Hire
5. Immobilizing / therapeutic
drugs
5,000
5,000
8,000
5,604
8,000
5,603
8,000
5,603
24,000
16,810
6. Transport running costs
9,533
9,533
9,534
28,600
7. Laboratory services
9,500
9,500
9,500
28,500
Other Direct Costs Total (C)
33,407
32,636
39,137
105,180
Salaries
and
Stipends
(list each
position on
separate
line and
indicate %
of time to be
spent – add
more lines if
needed)
Principal Researcher
5,000
30,000
30,000
65,000
Health Insurance
300
1,800
1,800
3,900
1,200
1,200
2,600
3, 600
3,600
10,800
36, 200
36,600
82,300
4,800
4,800
14,400
$78,186
$84,687
$251,270
Relocation Allowance
(Storage fees for
200
household goods)
Research Assistant x 2 @
300 / month x 26 (100%
3,600
Full time in shifts)
Labor Costs Total (D)
9,100
Institutional Indirect Costs (if
requested, full justification must
be provided) (E)
Grand Total Project Costs (F)
(A+B+C+D+E)
23
4,800
$ 88, 397
24
Table 2 – Detailed Budget
A
International Travel
Number
Unit price (U$)
Total Cost (U$)
required
1
2
June 2012 Round trip – Bozeman (USA) Lusaka (Zambia) – Air ticket & Excess lug
Aug 2013 Round trip – Bozeman(USA)Lusaka (Zambia) – Air ticket & Excess lug
1
2,800
2,800
1
2,800
2,800
Aug 2015 Round trip – Bozeman(USA) –
Lusaka(Zambia) – Air ticket & Excess lug
Subtotal 1
1
2,800
2800
3
4
B
Living Expenses
1
Living Allowance: June- Aug 2012
Aug 2013 – July 2014
Aug 2014 – July 2015
8,400
2 months
2,500
5,000
12 months
2,500
30,000
12 months
2,500
30,000
150U$ /month
3,900
400/month
10,400
2
Health Insurance
26 months
3
Institutional Allowance for camp utilities,
accommodation, electricity, internet
($400/month x 26 months)
Relocation Allowance (Storage fees:
$100/month x 26 months)
26 months
4
100/month
81,900
Subtotal 2
C
1
2
2,600
26 months
Labor / Service Higher
Research Assistants x 2 x 300 x 26 months
Helicopter higher (800 U$ / Hour x 10hrs /
year x 3 years
26 months
10 hours x
3yrs
600
15,600
800
24,000
39,600
Subtotal 3
D
Instruments required
1
Pole syringe (jab stick) with syringe
Spare Nylon syringe for Pole syringe
2
VHF Proximity collars for herbivores
3
GPS hand set
4
Batteries and miscellaneous supplies
($50/month x 26 months)
2
750
1500
10
13
130
60
200
12,000
2
220
440
50
1300
26 months
3
150
450
5
Flash lights
6
Night vision binoculars
3
700
2,100
7
Daylight binoculars
2
450
900
8
Trap cameras
25
300
7,500
24
25
9
10
11
12
13
Dan inject Darting Gun – 7 –JM- St 16mm bar 11
m smooth barrel
Carbon dioxide canisters 74g
Carbon dioxide canisters 45g
Darts for dispensing chemical immobilizer - 3ml
with already fitted barbed needles
Digital Camera – Canon EOS Rebel T 2i 18.0
megapixel, ISO 100 – 6400 (expandable to
12,800)
Portable 12v fridge
1
1,975
1,975
20
16.00
320
10
10.00
100
300
17.00
5,100
1
700
700
2
650
1300
Subtotal 4
E
Computer Services
1
Computer software for downloading data from
VHF collars
Internet Broad band adapter
2
35,815
1
650
650
1
100
120
Subtotal 5
F
Publication cost (Journal & Doctoral
thesis),
Subtotal 6
770
lump sum
1,500
1500
1,500
G
Laboratory Materials Required
1
6 x 100 pkt
40
240
3 x 100 pkt
40
120
3
Vacutainers (for serum) – red topped, green
topped
Vacutainers (for whole blood) – purple topped
with heparin or EDT
Vacutainer needle holder
10
20
200
4
Vacutainer needles
9 x 100 pkts
15
135
5
Probang cups
3 cups
120
360
6
Universal bottles
60
12.50
750
7
Phosphate buffer polypac
Phenol Red pH indicator
3 x 4 liters
140
420
3 x 500ml
15
45
5 x 100g pkt
55
275
1 x 10 lt
480
480
1x 20lt
720
720
3 x 40 lt
1.5 / lt
180
1 pack
1250
1250
2
8
citric acid crystals
9
Liquid Nitrogen tank (flask)
10
Liquid Nitrogen – 40 lts per year x 3 years
11
Cryogenic vials (3.6mls tubes)
Subtotal 7
H
Laboratory services
Laboratory tests – FMD, MCF, Parascaris, and
strongylus worm test
25
5,175
150x FMD
90
13,500
26
150x MCF
90
13,500
100x worm
15
1,500
Subtotal 8
28,500
I
Drugs for Chemical immobilization
1
Etorphine Hydrochloride (M99)
@ 8 animals / bottle [for 3 years] with
Dioprenorphine Hydrochloride (M5050 –
animal antidote)
NB:Naltrexone (Human antidote): 50mg / ml
35 bottles
420
14700
3 bottle
420
1,260
Azaperone @ 66 animals/bottle
[for 3
years]
Drug alternative (if the above is not available
– but not effective in equines)
Thianil (A3838) - Dose Range: 5 – 6 mg
Thianil for in combination with
(Antidote / Reversal: Trexnil @ 10mg/ mg of
Thianil used
Azaperon (Tranquillizer)
5 bottles
20
100
250
750
2
3
*
**
***
4
J
K
Miscellaneous drugs – e.g. penicillin LA
(10), phenylbutazone (5), dexamethasone,
ivermectin (10), wound spray (5), healing oil
(5 litres) – 250U$ per year x 3
Subtotal 9
Workshop & conference – to attend at
least 2
Subtotal 10
35 bottles
5 bottles
3 years
16,810
2
2500
5,000
5,000
Transport running cost at project site
Vehicle Fuel ($600/month x 26 months)
Vehicle Maintenance ($500/month x 26
months)
Subtotal 11
GRAND TOTAL (A – K)
26
35 bottles
26 months
600
15,600
500
13,000
26
28,600
252,070
27
Researcher’s Curriculum Vitae
APPENDIX IV
Wigganson Matandiko
Graduate Student
Department of Ecology
Montana State University
Bozeman MT 59717
Education:
MSc. in Wild Animal Health, 1998, Royal Veterinary College, University of London
Batchelor of Veterinary Medicine (BVM), 1990, University of Zambia
Current Position:
Graduate Student
Past Appointments:
2009 - 2011
2002 - 2008
Head of Veterinary, Zambia Wildlife Authority, Chilanga, Zambia.
State Veterinarian, Department of Animal Health & Production, Nata &
Lobatse, Botswana.
2000 – 2002 State Veterinarian in charge of the Wild Animal Health Unit, Lusaka, Zambia.
1999 – 2000 State Veterinarian in charge of Disease Control, Southern Province, Zambia.
1997 - 1997
1991 - 1996
Counterpart – Southern Africa Animal Disease Control project (SAADCP) –
Lusaka, Zambia.
State Veterinarian, Department of Animal Health & Production, Choma,
Zambia.
Most Closely Related Academic Publications:
1998
1998
1998
1997
Matandiko Wigganson - “Electrophoretic Analysis of Sera in Mycobacterium avium
infected wild waterfowls compared with the non-infected” Royal Veterinary College,
University of London – UK.
Matandiko Wigganson – “Food and Mouth Disease in Zambia”. Royal Veterinary
College – University of London – UK.
Matandiko Wigganson – “Lead poisoning in a Blue streaked Lory (Eos Reticulate)
without exhibition of clinical syndrome” Royal Veterinary College, University of London –
UK.
Matandiko Wigganson – “Rabies Country report for Zambia” Hokkaido University –
Sapporo, Japan.
Core – authored closely Related Publications
1.
27
Munang’andu, H.M., Victor. Siamudaala, Wigganson Matandiko, Mulumba Misheck,
Andrew Nambota, Musso Munyeme, Stephen Mutoloki and Hezron Nonga (2009).
Detection of Theileria parva Antibodies in the African Buffalo (Syncerus caffer) in the
Livestock-Wildlife Interface areas of Zambia. Veterinary Parasitology 166 (2009) pp.
163-166
28
2.
3.
4.
Munang'andu HM., Mweene AS, Syachaba MZ, Siamudaala VM, Muma JB ,
Matandiko W (2009). The rabies status in Zambia for the period 1994 – 2004.
Zoonoses and Public Health
Munang’andu H.M., Victor Siamudaala, Musso Munyeme, Andrew Nambota, and
Wigganson Matandiko (2009). Detection of Trypanosoma brucei in Asymptomatic
Greater Kudu (Tragelaphus strepsiceros) on a Game Ranch in Zambia. Vector borne
and zoonoses, VBZ-2009-0133
Munang'andu HM., Mweene AS, Siamudaala VM, Muma JB , Matandiko W (2011).
Review of rabies status in Zambia for the period 1985 – 2004. Zoonoses and Public
Health, Vol 58, pp. 21-27
Other Significant Document related to export trade:
2009
Matandiko Wigganson, Masterson Chap, Siamudaala Victor, Sinkala Yona , Sitima
Almond – “Proposed Protocol to Facilitate Export of Sable Antelope to the Republic of
South Africa.” – Submission to the Department Veterinary Services and Livestock
Development in Zambia and Republic of South Africa.
Synergistic Activities:
Coordinated and / or participated in the following (Botswana and Zambia): Disease outbreak
control & surveillance, drought mitigation, game capture and translocation, Probang sampling
for FMD virus isolation, Bovine TB testing in Dairy herds and Buffaloes, establishment of FMD
free Buffalo herd and VHF collaring of lions, spotted and brown hyenas.
Collaborators in the last 48 months:
Dr Scott Creel – Montana State University, US, Bozeman, MT.
Dr Mattew Becker – Zambia Carnivore Program, Mfuwe, Zambia.
Dr Hetrone Munan’gandu – Norwegian School of Veterinary Medicine, Oslo, Norway.
Dr Musso Munyeme – University of Zambia School of Veterinary Medicine, Lusaka, Zambia
.
Graduate Advisor:
Professor Scott Creel, Montana State University, Bozeman MT.
28
29
APPENDIX V
ADEQUACY OF DESIGN
Simulated data set, graphs and R-codes used
> #Generate data from a poisson distribution for the number of prey
> #in the home range of a predator
> #Use lambda = 5 (mean of prey) and for 100000 trials
> ####################################################
>
> set.seed(2000)
> L1 <- 5
> ntr <- 100000
> prey.vec <- numeric(0)
> for (i in 1:ntr)
+
prey.vec[i] <- rpois(1, L1)
> hist(prey.vec, xlab='Counts of Prey', main = 'Distribution of Counts of
Prey within predator home range', nclass=60)
10000
0
5000
Frequency
15000
Distribution of Counts of Prey within predator home range
0
5
10
15
Counts of Prey
>
>
>
#suppose area is 200 km2
area <- 200
home.dens <- prey.vec/area
#############################################
> #Generate data from poisson distn for the number of prey outside the home
range of the predator
> set.seed(3000)
> L2 <- 20 # mean of prey outside predator home range
> ntr <- 100000 # Number of trials
> prey.vec2 <- numeric(0) # let R choose the values for the prey count in
vector
> for (i in 1:ntr){
+
prey.vec2[i] <- rpois(1, L2)
+ prey.vec2}
>
> hist(prey.vec2, xlab='Counts of Prey', main = 'Distribution of Counts of
Prey outside predator home range', nclass=60)
29
30
4000
0
2000
Frequency
6000
8000
Distribution of Counts of Prey outside predator home range
10
20
30
40
Counts of Prey
>
>
>
>
#suppose area is 200 km2
area <- 200
outhom.dens <- prey.vec2/area
#look closely at the distribution of densities
> par(mfrow=c(1,3))
> hist(home.dens, xlab='Counts of Prey', main = 'Density of Counts',
nclass=60, col='blue')
> title(sub='Within Home Range of Predator')
> hist(outhom.dens, xlab='Counts of Prey', main = 'Density of Counts',
nclass=60, col='lightgray')
> title(sub='Outside Home Range of Predator')
Density of Counts
Frequency
4000
10000
0
0
2000
5000
Frequency
6000
15000
8000
Density of Counts
0.00
0.04
0.08
Counts of Prey
Within Home Range of Predator
0.05
0.15
Counts of Prey
Outside Home Range of Predator
diff <- outhom.dens - home.dens
> hist(diff, xlab='Counts of Prey', main = 'Difference in densities',
nclass=60, col='green')
> title(sub='Outside - Home Range of Predator')
>
30
31
Density of Counts
Difference in densities
0.04
0.08
2000
0
2000
0
0
0.00
Counts of Prey
Within Home Range of Predator
4000
Frequency
Frequency
4000
10000
5000
Frequency
6000
6000
15000
8000
8000
Density of Counts
0.05
0.15
Counts of Prey
Outside Home Range of Predator
0.00
0.10
0.20
Counts of Prey
Outside - Home Range of Predator
#############################################################################
########
> # Predator Home range estimates in the cold season (cs), dry season(ds),
wet season(ws)
> ########################COLD SEASON Predator Home
Range############################
# set.seed(350)
> #Use mean home range = 250 km2 for 10000 trials
> #standard deviation = 30 km2
> #number of predators = 15
> set.seed(350)
> A1.cs <- 250 # mean of home range in square kilometers
>
> ntr <- 10000 # number of trials or measurement of area for home range
> sd <- 30 # Standard deviation of home range
> pred <- 15 # Number of predators
> csPred.density <- A1.cs/pred # Cold season predator density in the home
range
> Area1.vec <- numeric(0)
>
> for (i in 1:ntr)
+
Area1.vec[i] <- rnorm(ntr,A1.cs,sd)
There were 50 or more warnings (use warnings() to see the first 50)
> hist(Area1.vec, xlab='Area estimates of Predator cs',
+ main = 'Distribution of area estimates (cold season)', nclass=100)
31
32
0
50
100
150
Frequency
200
250
300
Distribution of area estimates (cold season)
150
200
250
300
350
Area estimates of Predator cs
##########################DRY SEASON Predator Home Range
#############################
> set.seed(200)
> A2.ds <- 190 # mean of home range in ssquare kilometers
>
> ntr <- 10000 # number of trials or measurement of area for home range
> sd <- 25 # Standard deviation of home range
> pred <- 15
# Number of predators
> dsPred.density <- A2.ds/pred # Dry season predator density in the home
range
> Area2.vec <- numeric(0)
>
> for (i in 1:ntr)
+
Area2.vec[i] <- rnorm(ntr,A2.ds,sd)
There were 50 or more warnings (use warnings() to see the first 50)
> hist(Area2.vec, xlab='Area estimates of Predator ds',
+ main = 'Distribution of area estimates (dry season)', nclass=100)
200
150
0
50
100
Frequency
250
300
350
Distribution of area estimates (dry season)
100
>
32
150
200
Area estimates of Predator ds
250
33
##########################WET SEASON Predator Home Range
#########################
> set.seed(400)
> A3.ws <- 300 # mean of home range in square kilometers
>
> ntr <- 10000 # number of trials or measurement of area for home range
> sd <- 35 # Standard deviation of home range
> pred <- 15
# Number of predators
> wsPred.density <- A3.ws/pred # Wet season predator density in the home
range
> Area3.vec <- numeric(0)
> for (i in 1:ntr)
+
Area3.vec[i] <- rnorm(ntr,A3.ws,sd)
There were 50 or more warnings (use warnings() to see the first 50)
> hist(Area3.vec, xlab='Area estimates of Predator ws',
+ main = 'Distribution of area estimates(wet season)', nclass=100)
150
100
0
50
Frequency
200
250
Distribution of area estimates(wet season)
200
250
300
350
Area estimates of Predator ws
33
400
450