data analysis ss15 (18790)

1

Hochschule Rhein-Waal

Rhine-Waal University of Applied Sciences

Faculty of Communication and Environment

Prof Dr Ralf Darius

REPORT

ON

Reproductive life histories

Of

Thousands of female killer whales

A Report Submitted in

Partial Fulfillment of the

Requirements of the Degree of

Masters

In

Information Engineering & Computer Science

By,

Muhammad Ahsan Nawaz

Matriculation Number:

18790

Submission Date: 19/07/2015

2

Statement of Authorship

This report is the result of my own work. Material from the published or unpublished

work of others, which is referred to in the report, is credited to the author in the text.

Name: Muhammmad Ahsan Nawaz

Signature:

Date: 19.07.2015

Mian Ahsan

Typewritten Text

Ahsan

3

Table of Contents

1. Introduction ------------------------------------------------------------------------------------------------------------------------------ 5

1.1. Problem Statement-------------------------------------------------------------------------------------------------------------- 6

2. Methods ------------------------------------------------------------------------------------------------------------------------------------ 6

2.1. Probability ------------------------------------------------------------------------------------------------------------------------- 6

2.2. Probability Distribution------------------------------------------------------------------------------------------------------- 6

2.3. Normal Distribution ------------------------------------------------------------------------------------------------------------ 6

2.4. Binomial distribution ---------------------------------------------------------------------------------------------------------- 7

2.5. Conditional Statement --------------------------------------------------------------------------------------------------------- 7

2.6. Iteration & Loop ----------------------------------------------------------------------------------------------------------------- 7

2.7. Initial & Final Parameters --------------------------------------------------------------------------------------------------- 8

3. Results -------------------------------------------------------------------------------------------------------------------------------------- 8

3.1. Scenario 1: Rich & Stable Environment -------------------------------------------------------------------------------- 9

3.1.1. Histogram of Ages -------------------------------------------------------------------------------------------------------- 9

3.1.2. Histogram of Inclusive Fitness (Recruits) --------------------------------------------------------------------- 10

3.2. Scenario 2: Poor & Stable Environment ------------------------------------------------------------------------------ 10

3.2.1. Histogram of Ages ------------------------------------------------------------------------------------------------------ 11


3.3. Scenario 3: Rich & Variable Environment -------------------------------------------------------------------------- 12



3.4. Scenario 4: Poor & Variable Environment -------------------------------------------------------------------------- 13


3.4.2. Histogram og Inclusive Fitness (Recruits) --------------------------------------------------------------------- 14

4. Discussion of Results ---------------------------------------------------------------------------------------------------------------- 15

References ------------------------------------------------------------------------------------------------------------------------------------- 16

Appendix --------------------------------------------------------------------------------------------------------------------------------------- 17

4

List of Figures

Figure 1: Histogram of Ages in Rich & stable Environment --------------------------------------------------------- 9

Figure 2: Histogram of Inclusive Fitness in Rich & Stable Environment--------------------------------------- 10

Figure 3: Histogram of ages in Poor & Stable Environment ------------------------------------------------------- 11

Figure 4: Histogram of Inclusive Fitness in poor & Stable Environment --------------------------------------- 11

Figure 5: Histogram of Ages in Rich & Variable Environment --------------------------------------------------- 12

Figure 6: Histogram of Inclusive Fitness in Rich & Variable Environment ----------------------------------- 13

Figure 7: Histogram of ages in Poor & Variable Environment ---------------------------------------------------- 14

Figure 8: Histogram of Inclusive Fitness in Poor & Variable Environment ----------------------------------- 14

5

1. Introduction

The following paper is concerned with the analytical assessment of reproductive life

histories of thousands of female killer whales. Here is a brief introduction related to

killer whale.

The killer whale is the most cosmopolitan of all cetaceans and may be the second-most

widely-ranging mammal species on the planet, after humans. Their scientific name is

Orcinus orca, from it, the word Orcinus means “from the realm of the dead,” relating to

the Roman god Orcus master of the underworld. Killer whales are marine mammals

belonging to the family Delphinidae, formed by several species of dolphins, false killer

whales and pilot whales.

There are up to five distinct killer whale types distinguished by geographical range,

preferred prey items and physical appearance. Some of these may be separate races,

subspecies or even species. Their social structures are complex, and most are organized

in matriarchal societies. There are several pods within a sub-population that exchange

members for breeding purposes. Maintaining a strong group cohesion and

communication is essential for the pod.

Males reach sexual maturity at around 13 years of age or 5.2-6.4 meters in length,

depending on the ecotype, while females reach it between six and ten years or when they

are 4.6 to 5.4 meters long. However, females mate until they are 14 or 15 years old. The

links between a female and her calf are the strongest within a social group of orcas, but

once they grow up they leave the mother to travel either alone or with another pod.

The average life expectancy of killer whales is 35 years, but in exceptional cases they

can reach up to 50 years. Female killer whale that live in the wild for example have been

known to live for up to 70 – 80 years, although the average is about 50 years. And male

killer whales can live to be 50 – 60 years old, but usually live until around their 30’s.

6

In this report, we are going to provide you methods, results and discussion of the result.

1.1. Problem Statement

In developing this simulation, there is a problem that can be solved, as follows:

• How to simulate the prediction of killer whales lifecycle?

• What is the role of environment in killer whales lifecycle?

2. Methods

There are different types of method we used in our Assignment. Here is a brief

introduction about these methods.

2.1. Probability

The notion of "the probability of something" is one of those ideas, like "point"

and "time," that we can't define exactly, but that are useful nonetheless. Four

perspectives on probability are commanly used:

Classical

Empirical

Subjective

Axiomatic

2.2. Probability Distribution

A statistical function that describes all the possible values and likelihoods that

a random variable can take within a given range. This range will be between

the minimum and maximum statistically possible values, but where the

possible value is likely to be plotted on the probability distribution depends on

a number of factors, including the distributions mean and standard deviation.

2.3. Normal Distribution

The normal distribution is the most important and most widely used

distribution in statistics. It is sometimes called the "bell curve," although the

tonal qualities of such a bell would be less than pleasing. To speak specifically

7

of any normal distribution, two quantities have to be specified: the mean ,

where the peak of the density occurs, and the standard deviation , which

indicates the spread or girth of the bell curve.

2.4. Binomial distribution

When you flip a coin, there are two possible outcomes: heads and tails. Each

outcome has a fixed probability, the same from trial to trial. In the case of

coins, heads and tails each have the same probability of 1/2. More generally,

there are situations in which the coin is biased, so that heads and tails have

different probabilities. Binomial distribution have several properties such as:

The experiment consists of n repeated trials.

Each trial can result in just two possible outcomes. These outcomes are

classified as success and failure

The probability of success is the same on every trial.

The trials are independent; that is, the outcome on one trial does not

affect the outcome on other trials.

2.5. Conditional Statement

Conditional statements are useful when you want to execute a set of

commands, but only when a certain set of conditions hold. So, the sort of thing

you might like to say in plain language is "If a set of conditions is satisfied

then do something ". There are many of conditional statement we used in this

report such as; If, else.

2.6. Iteration & Loop

Iteration is the repeated application of a set of commands. In most occasions

we can perform tasks iteratively by using the vectorisation capabilities of R.

Sometimes, iterative tasks require a different programming device, called a

loop, which comprises of 1) a loop declaration and 2) the main body of the

loop. Here, we will introduce two types of loops, the for loop, performs a set of

8

tasks for a predefined number of iterations. The while loop performs a set of

tasks while a set of conditions hold.

2.7. Initial & Final Parameters

It is generally good practice to represent parameters by symbols whose

numerical assignments are collected together at the beginning of the code,

separately from its main body. This is for three reasons: 1) it gives an overview

of the kind of numerical information required for the model, 2) the statement

of the model in the main body of the code is more reminiscent of its

mathematical description which makes it easier to find mistakes and 3) in

many models the same parameter is repeated several times. Rather than having

to trawl through the entire code and change the parameter’s numerical value in

all these instances, it is only necessary to change its numerical assignment at

the beginning.

3. Results Well, after modelling the probablity of Killer whales, 2 types of vectors is

assigned in R Software. Which are ages vector & Recruits vector. These

vectors are applied in order to record age and recruit data from 1000 female

model. Making scenario is done in order to simulate the model. Our simulation

is divided into four different scenario’s, Scenario 1 is related to Rich & Stable

Environment, Scenario 2 is related to poor and stable environment, Scenario 3

is related to Rich and stable environment and Scenario 4 is related to poor and

variable environment. The aim of this simulation is to find differences killer

whales lifecycle influenced by environments by changing mean and standard

deviation of annual condition improvement.

9

3.1. Scenario 1: Rich & Stable Environment

Rich and stable environment have a mean value 20 and standard deviation

value 1. Changing the value of Mean and Standard Deviation has to be done in

order to getting data of age and data of recruit. After all of the data is known,

visualize each data by using hist command in R. the histogram of ages data in

reach and stable environment can be seen in Figure 1. and histogram of

Inclusive Fitness can be seen in Figure 2.

3.1.1. Histogram of Ages

Figure 1: Histogram of Ages in Rich & stable Environment

In above mentioned figure the X-axis shows the Number of ages and Y-Axis

shows Frequency.

10

3.1.2. Histogram of Inclusive Fitness (Recruits)

Figure 2: Histogram of Inclusive Fitness in Rich & Stable Environment

In above mentioned figure the X-axis shows the Number of inclusive

fitness and Y-Axis shows Frequency.

3.2. Scenario 2: Poor & Stable Environment

Poor and stable environment have a mean value 2 and standard deviation value

1. Changing the value of enMu and enSD has to be done in order to getting

data of age and data of recruit. After all of the data is known, visualize each

data by using hist() command in R. the histogram of ages data in reach and

stable environment can be seen in figure 3 and histogram of recruit can be seen

in figure 4.

11


Figure 3: Histogram of ages in Poor & Stable Environment

In above mentioned figure the X-axis shows the ages fitness and Y-Axis

shows Frequency.


Figure 4: Histogram of Inclusive Fitness in poor & Stable Environment

12



3.3. Scenario 3: Rich & Variable Environment

Rich and variable environment have a mean value 20 and standard deviation

value 30. Changing the value of enMu and enSD has to be done in order to

getting data of age and data of recruit. After all of the data is known, visualize

each data by using hist() command in R. the histogram of ages data in reach

and stable environment can be seen in figure 5 and histogram of recruit can be

seen in figure 6.


Figure 5: Histogram of Ages in Rich & Variable Environment


shows Frequency.

13


Figure 6: Histogram of Inclusive Fitness in Rich & Variable Environment



3.4. Scenario 4: Poor & Variable Environment

Poor and variable environment have a mean value 2 and standard deviation

value 30. Changing the value of enMu and enSD has to be done in order to

getting data of age and data of recruit. After all of the data is known, visualize

each data by using hist() command in R. the histogram of ages data in reach

and stable environment can be seen in figure 7 and histogram of recruit can be

seen in figure 8.

14


Figure 7: Histogram of ages in Poor & Variable Environment


shows Frequency.

3.4.2. Histogram og Inclusive Fitness (Recruits)

Figure 8: Histogram of Inclusive Fitness in Poor & Variable Environment

15



4. Discussion of Results

The purpose of this case study was to observe the effects of quality and

environmental variability on reproductive capacity in female killer whales’

productivity based on age. Following conclusions can be drawn from the analysis:

In rich & stable environment killer-whales have age’s up to 80 years and they

produce offspring maximally up to 3. In poor & stable environment killer wales have

ages less than 20 and they produce offspring 0 out of roundabout 800 whales.

In rich & variable environment killer-whales have age’s more than 80 years and

mostly they produce offspring 0. In poor & variable environment most of the killer

whales have age’s less than 20 and mostly they produce offspring 0.

The maximum of female whales end their reproductively in 80-90 years of old in

rich environment. There is less effect for stable and variable environment on

productivity age. There are a linear decreasing number of whales among one to

three offspring’s they recruits in the age between 15 to 60 years of age.

In case of poor environment maximum number of whales between 14 and 19

years old lose their reproductiveness. Average variable stable environment and has

a certain effect on the poor environment. In stable environment there is an increase

in the number of whales between 20 and 24 who have lost their reproductive

capacity.

16

References

[1] Bradford,A. 2014. Orcas: Facts about Killer Whales. [ONLINE] Available at:

http://www.livescience.com/27431-orcas-killer-whales.html.

[2] http://www.killer-whale.org/killer-whale-information/

[3] http://www.stat.umn.edu/geyer/old/5101/rlook.html

[4] http://statweb.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html

[5]Assignment given to us (Engr. Ralf Darius)

http://www.livescience.com/27431-orcas-killer-whales.html

17

Appendix #Ralf Darius

#Course: Data Analysis #Final Assignment

#Muhammad Ahsan Nawaz #Matriculation Number: 18790

#MSc.Information Engineering & Computer Science

#---------------------------------------------------------------------- #Reset R's Brain

rm(list=ls())

#---------------------------------------------------------------------- #Starting the Assignment Code

recruits <- vector()

ages<- vector() # Apply "for" loop here (1 observations of 1000 Variables)

for (i in 1:1000){

co <- rnorm(1, 100, 10) age <- 15

alive <- 1

enMu <- 2 # We can change the mean value for different scenario's

enSD <- 30 # We cahnge the standard deviation value as well for different scenario's

s0 <- -2

s1 <- 0.05 calf <- 0

calfage <- 0

offspring <- 0

b0 <- -10 b1 <- 0.1

inv <- 10

recruit <- 0

childborn <- vector()

while (alive>0 && age<=88 ) {

sr <- exp(s0 + s1 * co)/(1 + exp(s0 + s1 * co)) if (rbinom(1, 1, sr) == 1) {

# alive doesn't have calf

18

if (calf == 0) {

b <- exp(b0 + b1 * co)/(1 + exp(b0 + b1 * co)) if ((rbinom(1, 1, b) == 1 )&&(age<=40)) {

# give birth

calf <- 1

} } else {

# have calf

co <- co - inv if (rbinom(1, 1, 0.8) == 1) {

# calf alive

calfage <- calfage + 1

if (calfage >= 4) { # independence

offspring <- offspring + 1

childborn <- cbind(childborn,age-5) calf <- 0

calfage <- 0

}

} else { # calf die

calf <- 0

calfage <- 0

} }

age <- age + 1

co <- co + rnorm(1, enMu, enSD) } else {

# female dead

alive <- 0

} }

if (length(childborn)>0){

for (j in 1:length(childborn)){ if ((age-childborn[[j]])>=15&&rbinom(1,1,0.98)==1){

recruit <- recruit + 1

}

}

}

ages <- cbind(ages,age)

19

recruits <- cbind(recruits,recruit)

} hist(ages, main="Histogram of Ages in Poor & Variable Environment",

xlab="Ages", ylab="Frequency" )

#Histograms

hist(recruits, main="Histogram of inclusive fitness in Poor & Variable Environment", xlab="Number of inclusive fitness", ylab="Frequency")

data analysis ss15 (18790)

Documents