Selforganizology

Vol. 3, No. 1, 1 March 2016

International Academy of Ecology and Environmental Sciences

Selforganizology ISSN 2410-0080

Volume 3, Number 1, 1 March 2016 Editor-in-Chief WenJun Zhang Sun Yat-sen University, China International Academy of Ecology and Environmental Sciences, Hong Kong E-mail: zhwj@mail.sysu.edu.cn, wjzhang@iaees.org Editorial Board Awf Al-Kassir (University of Extremadura, Spain) Ramiz M. Aliguliyev (National Academy of Sciences, Azerbaijan) Andre Bianconi (Sao Paulo State University (Unesp), Brazil) Chris Cannings (University of Sheffield, UK) Manuel De la Sen (University of Basque Country, Spain) Alessandro Ferrarini (University of Parma, Italy) Zeljko Kanovic (University of Novi Sad, Serbia) Xin Li (Northwest A&F University, China) Abdul Qadeer Khan (University of Azad Jammu & Kashmir, Pakistan) Zdzislaw Kowalczuk (Gdansk University of Technology, Poland) Muhammad Naeem (Abbottabad University of Science and Technology, Pakistan) Lev V. Nedorezov (University of Nova Gorica, Slovenia) Quanke Pan (Northeastern University, China) Sergio Valero Verdu (Universidad Miguel Hernandez de Elche, Spain) Hafiz Abdul Wahab (Hazara University, Pakistan) ZhiGuo Zhang (Sun Yat-sen University, China) Editorial Office: selforganizology@iaees.org

Publisher: International Academy of Ecology and Environmental Sciences

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Tel: 00852-2138 6086 Fax: 00852-3069 1955 Website: http://www.iaees.org/ E-mail: office@iaees.org

Selforganizology, 2016, 3(1): 1-9

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Article

A random network based, node attraction facilitated network

evolution method

WenJun Zhang

School of Life Sciences, Sun Yat-sen University, Guangzhou 510275, China; International Academy of Ecology and Environmental Sciences, Hong Kong E-mail: zhwj@mail.sysu.edu.cn, wjzhang@iaees.org

Received 6 August 2015; Accepted 28 September 2015; Published online 1 March 2016

Abstract

In present study, I present a method of network evolution that based on random network, and facilitated by

node attraction. In this method, I assume that the initial network is a random network, or a given initial

network. When a node is ready to connect, it tends to link to the node already owning the most connections,

which coincides with the general rule (Barabasi and Albert, 1999) of node connecting. In addition, a node may

randomly disconnect a connection i.e., the addition of connections in the network is accompanied by the

pruning of some connections. The dynamics of network evolution is determined of the attraction factor of

nodes, the probability of node connection, the probability of node disconnection, and the expected initial

connectance. The attraction factor of nodes, the probability of node connection, and the probability of node

disconnection are time and node varying. Various dynamics can be achieved by adjusting these parameters.

Effects of simplified parameters on network evolution are analyzed. The changes of attraction factor can

reflect various effects of the node degree on connection mechanism. Even the changes of only will generate

various networks from the random to the complex. Therefore, the present algorithm can be treated as a general

model for network evolution. Modeling results show that to generate a power-law type of network, the

likelihood of a node attracting connections is dependent upon the power function of the node’s degree with a

higher-order power. Matlab codes for simplified version of the method are provided. Keywords network evolution; node attraction; connection probability; disconnection.

1 Introduction

In 1998, Watts and Strogatz presented a method for generating random graphs. Thereafter, Barabasi and Albert

(1999) proposed a general and known mechanism for network evolution. The algorithm developed by Cancho

and Sole (2001) can generate a variety of complex networks with diverse degree distributions. Zhang (2012a,

2012b, 2015, 2016) proposed a series of methods for network generation and evolution. In present study, I will

propose method of network evolution that based on random network, and facilitated by node attraction. Deep

analyses will be implemented to understand the properties of the method.

Selforganizology   ISSN 2410­0080   URL: http://www.iaees.org/publications/journals/selforganizology/online­version.asp RSS: http://www.iaees.org/publications/journals/selforganizology/rss.xml E­mail: selforganizology@iaees.org Editor­in­Chief: WenJun Zhang Publisher: International Academy of Ecology and Environmental Sciences 

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2 Algorithm

I assume that the initial network is a random network (this is popular in nature. For example, the distribution

of particles with different sizes with which the water vapor attaches to generate droplets; the random

distribution of matter/nucleus of crystallization for the generation of stars/crystals, etc.), or a given initial

network. When a node is ready to connect, it tends to link to the node already owning the most connections

(the largest node), which coincides with the general rule of node connecting (Barabasi and Albert, 1999). In

addition, a node may randomly disconnect a connection, i.e., the addition of connections in the network is

accompanied by the pruning of some connections.

Assume there are totally v nodes in the network. Expected initial connectance (connectance=practical

connections/potential maximum connections) is c (initial condition) if the initial network is a random network

generated by the algorithm, expected final connectance is ce (termination condition), the attraction factor of

nodes is (t,a) (driving variable; (t,a)>0, where a is the node degree), the probability of node connection is

p(t,a) (driving variable), the probability of node disconnection is q(t,a,b) (driving variable, where b is the

connected node’s degree), maximum number of iterations is iter (termination condition), and the confidence

degree for detecting the statistic significance of network type is (auxiliary constant). (t,a), p(t,a), and

q(t,a,b) are time and node (in particular node degree) varying. The procedures are as follows

(1) Generate the initial network. In the situation of random initial network, assume the adjacency matrix

of the random network is d=(dij), i, j=1,2,…,v, where dij=dji, dii=0, and if dij=1 or dji=1, there is a connection

between nodes i and j. For each pair of i, j (i=1,2,…,v-1; j>i), generate a random value r, if r<c, dij=1 and

dji=1. Otherwise, the initial network is a given network.

(2) Let t=1. Calculate the degree of node, ai(t), i=1,2,…,v. The cumulative attraction strength of node 1 to

node i is

v

j

atj

i

j

atji

jj tatatp1

),(

1

),( )(/)()(

(3) Generate/disconnect connections. For the node i, i=1,2,…,v, generate a random value s, if s<p(t,ai),

the node i is ready to connect to one of the remaining nodes. Let p0(t)=0. For the node j, j=1, 2,…,v, ji,

generate a random value w. dij=1 and dji=1, if pi-1(t)w<pi(t). In the practical uses, the interval [pi-1(t), pi(t))

represents the mass or volume of the particle i, the gravity of the celestial body i, the personality charm of the

person i, the academic impact of the scientist i, etc.

For the node i, i=1,2,…,v, generate a random value g; if g<q(t,ai,b), one of the connections of the node i,

e.g., dij, is randomly disconnected, and let dij=0 and dji=0.

By doing so, a network at time t is generated. Various indices and methods, e.g., coefficient of variation

(CV), aggregation index (AI), and entropy (Zhang and Zhan, 2011; Zhang, 2012a) can be used to detect the

types and properties of the network.

(4) Calculate the connectance C of the network. Let t=t+1 and return (2), if C is greater than the expected

final connectance ce; otherwise, the algorithm terminates, if C is less than ce, or the maximum iterations iter

are achieved.

For convenience and simplicity, assume (t,a)=, p(t,a)=p, q(t,a,b)=q, i.e., the attraction factor of nodes,

the probability of node connection, and the probability of node disconnection are constants for any degree of

nodes at any time. Thus we obtain a simplified version of the algorithm.

The following are Matlab codes for simplified version of the algorithm (netEvolution.m)

2

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%Reference: Zhang WJ. 2016. A random network based, node attraction facilitated network evolution method.

Selforganizology, 3(1): 1-9

v=input('Total number of nodes in the network= ');

choice=input('Input the type (1: a random network generated by the algorithm; 2: a given network) of generating initial network:

');

if (choice==1) ci=input('Expected initial connectance (=practical connections/potential maximum connections; e.g., 0.05, etc)= ');

end

if (choice==2) adjstr=input('Input the file name of adjacency matrix of the given initial network (e.g., raw.txt, raw.xls, etc.

Adjacency matrix is d=(dij)v*v, where v is the number of nodes in the network. dij=1, if vi and vj are adjacent, and dij=0, if vi

and vj are not adjacent; i, j=1,2,…, v: ','s'); end

ce=input('Expected final connectance (=practical connections/potential maximum connections; e.g., 0.1, 0.15, etc)= ');

lamda=input('Attraction factor of nodes (lamda; e.g., 2, 4, etc. lamda>0)= ');

p=input('Probability of node connection (e.g., 0.1, 0.2)= ');

q=input('Probability of node disconnection (e.g., 0, 0.01)= ');

alpha=input('Confidential degree for detecting network type (e.g., 0.05, 0.01)= ');

iter=input('Permitted maximum iterations (e.g., 5000)= ');

adj=zeros(v);

degr=zeros(1,v);

prop=zeros(1,v);

z=zeros(v);

if (choice==1)

for i=1:v-1

for j=i+1:v

if (rand()<ci) adj(i,j)=1; adj(j,i)=1; end

end; end; end

if (choice==2) adj=load(adjstr); end;

degr=sum(adj);

fprintf('Initial adjacency matrix\n')

disp([adj])

fprintf('Initial degree distribution\n')

disp([degr])

t=1;

while (v>0)

propdegr=degr.^lamda;

prop(1)=propdegr(1)/sum(propdegr);

for i=2:v;

prop(i)=prop(i-1)+propdegr(i)/sum(propdegr);

end

node=zeros(1,v);

nu=0;

for i=1:v

if (rand()<p) nu=nu+1; node(nu)=i; end

end

for k=1:nu;

for i=1:v

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if (node(k)~=i) continue; end

lab=0;

ran=rand();

for j=1:v

if (j==i) continue; end

if (j==1) st=0; end

if (j>=2) st=prop(j-1); end

if ((ran>=st) & (ran<prop(j))) lab=1; adj(i,j)=1; adj(j,i)=1; break; end

end

if (lab==1) break; end

end; end

nodes=zeros(1,v);

for i=1:v

if (rand()<q) nodes(i)=1; end

end

for i=1:v-1

if (nodes(i)~=1) break; end

nuu=0;

for j=i+1:v

if (adj(i,j)==1) nuu=nuu+1; z(i,j)=nuu; end

end

np=round(rand()*nuu+0.5);

for j=i+1:v

if (z(i,j)==np) adj(i,j)=0; adj(j,i)=0; end

end; end

fprintf(['\n\nTime ' num2str(t)])

fprintf(['\n\nAdjacency matrix\n'])

disp([adj])

degr=sum(adj);

fprintf('\nDegree distribution\n')

disp([degr])

cnow=(sum(degr)/2)/((v^2-v)/2);

fprintf(['\nConnectance=' num2str(cnow) '\n'])

meann=mean(degr);

varr=(std(degr))^2;

fprintf(['\nEntropy=' num2str(varr-meann) '\n'])

num=0;

cv=varr/meann;

fprintf(['\nCoefficient of variation (CV)=' num2str(cv) '. '])

x2=cv*(v-1);

sig=chi2cdf(x2,v-1);

if (sig<=alpha) fprintf('The network is a random network according to CV.\n'); end

if ((sig>alpha) & (cv>1)) fprintf('The network is a complex network according to CV.\n'); num=num+1; end;

summ=sum(degr);

summa=sum(degr.*(degr-1));

4

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h=v*summ

fprintf(['\n

x2=h*(sum

sig=chi2cd

if (sig<=al

if ((sig>alp

if (num>=

if (cnow>=

if (t>=iter)

t=t+1;

end

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3.3 Model’s universality

As mentioned above, the changes of attraction factor can reflect various effects of the node degree on

connection mechanism (Table 1, Fig. 2). The larger will lead to generate complex networks, e.g., exponential

law, power law networks, etc. 0 means a trend to generate the random network. Even the changes of only

will generate various networks from the random to the complex (Table 1). Therefore, the present algorithm can

be treated as a general model for network evolution.

Modeling results (Table 1) show that to generate power-law distributed node degrees (i.e., to generate a

power-law type of network), the likelihood of a node attracting connections is dependent upon the power

function of the node’s degree with a higher-order power.

4 Discussion

In present method, the dynamics of network evolution is determined of (t,a), p(t,a), q(t,a,b), and c. I

simplify all parameters as constants. However, more complex mechanism for network evolution can be

achieved by setting reasonable forms of (t,a), p(t,a), q(t,a,b), depending on the networks being studied. In

present study, I use a small range of parametrical values for parametrical analysis. More properties may be

found by broadening the range of parametrical values. In present algorithm, the addition of connections

coincides with the general rule of node connecting (Barabasi and Albert, 1999). However, the mechanism for

pruning of connections is still unknown (unknown q(t,a,b)), thus in the simplified version of the algorithm,

q=0 is a better choice.

Acknowledgment

I am thankful to the support of High-Quality Textbook Network Biology Project for Engineering of Teaching

Quality and Teaching Reform of Undergraduate Universities of Guangdong Province (2015.6-2018.6), from

Department of Education of Guangdong Province, Discovery and Crucial Node Analysis of Important

Biological and Social Networks (2015.6-2020.6), from Yangling Institute of Modern Agricultural

Standardization, and Project on Undergraduate Teaching Reform (2015.7-2017.7), from Sun Yat-sen

University, China.

References

Barabasi AL, Albert R. 1999. Emergence of scaling in random networks. Science, 286(5439): 509

Cancho RF, Sole RV. 2001. Optimization in Complex Networks. Santafe Institute, USA

Watts D, Strogatz S. 1998. Collective dynamics of ‘small world’ networks. Nature, 393:440-442

Zhang WJ, Zhan CY. 2011. An algorithm for calculation of degree distribution and detection of network type:

with application in food webs. Network Biology, 1(3-4):159-170

Zhang WJ. 2012a. Computational Ecology: Graphs, Networks and Agent-based Modeling. World Scientific,

Singapore

Zhang WJ. 2012b. Modeling community succession and assembly: A novel method for network evolution.

Network Biology, 2(2): 69-78

Zhang WJ, 2015. A generalized network evolution model and self-organization theory on community

assembly. Selforganizology, 2(3): 55-64

Zhang WJ. 2016. Selforganizology: The Science of Self-Organization. World Scientific, Singapore

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Article

A review on research of the predator-prey interactions

H. A. Wahab1, Hazrat Ali1, Muhammad Naeem2, Sarfraz Ahmad3, Saira Bhatti4, Muhammad Shahzad1,

Khalid Usman1 1Department of Mathematics, Hazara University, Manshera, Pakistan 2Department of IT, Abbottabad University of Science and Technology, Havelian, Abbottabad, Pakistan 3Department of Mathematics, Abbottabad University of Science and Technology, Havelian, Abbottabad, Pakistan 4Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

E-mail: wahabmaths@yahoo.com,wahab@hu.edu.pk

Received 13 July 2015; Accepted 20 August 2015; Published online 1 March 2016

Abstract

In this review article, we aim to study predator-prey interactions and their historical development from time to

time. A general overview of the predator-prey model, its evolution, and the physical meanings of this model

has been discussed here. A brief discussion on the classification of predators and process of predation it its

effect on the environment is presented in this review article. One important characteristic of the predation

process is that predators co-operate with each other against preys which becomes more visible when the prey

are strong enough to be over-powered easily.

Keywords predator-prey interactions; classification of predators; predators’ co-operation; research

developments.

1 Introduction to Predator Prey Interactions

The predator-prey models are the basis which helps to see the life and ecosystems in which the predator and

prey have certain role. This model explains how the predators interact with its prey. It explains the sustenance,

evaluation and alternative dispersion of some species in the case of failure to complete in the life in which the

stronger has advantage of dominate role. The predator-prey model is like the survival of the fittest-theory

(Zhang and Liu, 2015). The fittest are the stronger species targeting the weaker species and win life for

themselves and this evaluation of life for one species results in the numerical and sometime general extinction

of other weaker species. The weaker species remain in constraint struggle to achieve their security in the

diaspora where general fear of life remains ever present. The weaker species which become prey adopt many

measures to trick the predator to avoid being hunted.

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Briefly predator prey interaction is like a win-loss interaction (Zhang, 2012), it is the victory for one and

loss for the other; and life for one and elimination of the other.

2 A General Predator-Prey Model

Let us consider two kinds of populations, that have sizes at a reference time t and shown by ( ),X t and ( ),Y t

respectively. Where X and Y might show population number or the size of the respective population. Any

change in the size of population with reference to time or based is described by the time derivatives;

dtdXX /

and dtdYY /

respectively. The general model of interacting populations is usually put in

terms of independent differential equations presented by

),,( yxXgX

(1)

).,( yxYhY

(2)

For instance, the time ' 't does not seem clearly in the functions of ( , ),Xg x y and ( , )Yh x y and the

functions of g and h show the respective per capita growth rate of the two species. One assumption that

comes to us about this is as follows:

( , )dg x y

dy

and

( , )dh x y

dx

The general name for this model is the predator-prey model of Kolmogorov (Freedman, 1980).

3 The Historical Model of Lotke-Volterra

This model was presented by Vito-Volterra and Alfred J. Lotka. Vito, who studied the population of different

species of fish in the Adriatic sea (Voltera, 1926). He saw increasing number of predators and decreasing

number of prey in the Adriatic fauna. Thus, he observed on the three fishing markets. He gave his assessment

that reducing number of fish (prey) was due to the hostile interaction between predators and prey. Alfred J.

Lotka and Volterra presented many mathematical formulae in order to explain the Vito’s observation in the

form of mathematics (Kingsland, 1985). Lotka in his book provided predator-prey systems which consisted of

a plane population and herbivorous animals which dependent on the plants for food (Lotka, 1958).

4 Lotka-Volterra Model

This model is also called the predator prey equations, which is the non-linear, pair of first order differential

equations, given as

XYaXaX 21

(3)

21 YbXYbY

(4)

where 1 2 1 2, , ,a a b b are parameters representing the interaction of the two species.

This model was the first ever mathematical model on the population which achieved a balanced in a

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population in a very cyclical way. This model shows the eco-logical systems in which the predator and prey

interact resulting in the competition between the two (Hoppensteadt, 1977). This model has following

important variables;

X : The prey-population

Y : The predators-population

1a : The natural growth rate of prey in the predation absence

2a : The predator’s effect on the prey-population

1b : The prey’s effect on the predator-population

2b : The natural predator’s death rate in the absence of prey to eat.

The following are the important Assumptions:

1) If a predator is absent, the population of the prey will increase at the rate proportional to the

current population.

Therefore, 1

dXa X

dt , when 0Y .

2) If the prey is absent, then there are no chances for predator to live.

Thus 2

dYb Y

dt , where 2 0b

when 0X .

3) The number of encounters between a predator and the prey is proportional to the product of

their populations. Every encounter will increase the population of the predator and reduce the

population of the prey.

Thus the growth rate of predator increases in the form of XY , if the growth rate of prey decreases in the form

of 2a XY , where 2a is positive constant, and 1 1 2, ,a b b all are positive constants. 1a

and 2b show the

growth rate of prey and the death rate of predator, respectively. 2a

and 1b measure the level of effect of

interaction between the prey and predator.

5 The Model Equations and Their Physical Meanings

This model presents some assumptions as to how predator and prey populations operate/interact, and evolve or

disappear.

1) The prey population has always more than required food.

2) Food supply for predator depends on how much size the prey population has.

3) The rate of change of population remains proportional to its size, in this process environment becomes

unhelpful for any species.

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4) The predators have un-limited appetite and this process is cyclical. The generation of both species continues

to interact this way (Cooke et al., 1981).

6 The Predator and Prey Interaction

The earth inhabits millions of such species that assume the role of predators. They kill other herbivores or even

the carnivore predators in order to achieve the survival for them. The predator prey interaction results in the

continuation of life for some and elimination for the others (Begon et al., 1996). Charles Darwin’s theory of

survival of the fittest appears to be very relevant in the life and elimination of different species. The predators

may have herbivores as their target, or may be, have even small predators as targets, thus giving us the

glimpses of an ever insecure world for smaller species. This piece of work will focus on following important

points:

7 Defining a Predator

A predator is one which kills and eats other living beings in order to live. It happens through the physical

outburst of predators that aggressively attack the prey and win life for themselves. In fact, the predators are

said to be killing which is an effort to guarantee life for them (Begon et al., 1996).

8 Classification

Predators have a variety of types, and some of them are;

i. Some predators may target large-size preys and may not directly eat them but they dismember or chew them

before eating them.

ii. Some predators may eat their prey directly as a whole not in parts. Some examples of this include dolphin

which swallows a fish or a snake that devours a frog.

iii. Some predator animals may swallow prey in a whole or in parts depending on the situation.

iv. Some predators kill some other animals or insects but may not eat them. This way, classification goes a

long way in which different predators may choose to target or kill the preys differently.

9 The Process of Predation

The process of killing preys may take great deal of caution and careful step-wise planning by predator in order

to ensure that prey does not escape. The predators may hunt preys actively in which preys may be chased. The

chasing of prey by predator is a race for life for both in which the prey fears life and predators does not want to

let the target escape in order to win security against hunger.

Some predators may sit inactive, waiting for the prey to come close to them. They may act in such a way

that preys are led to believe that the predator is uninterested in them. This caution plan by predator may be a

great success; however, some preys may hesitate to come near to the predator as they are more cautions and

have less trust in the apparently good intentions of predators. This hack of trust by prey may save its life and

may shatter the confidence of predator in its tricky plans forcing active chasing (Alcock, 1998).

10 Why Predation?

Why animals so for predation? It is a very important question. The answer to that is present in the heart of the

argument; is the survival of these animals. The carnivorous animals, faced by ever-increasing hunger, have

found a natural principle for their survival in the middle of rich wildlife that serves as the tasty food for them.

The other besides life is the increasing competition between different species. Some species, although with

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greatest influence in the wildlife, may confront a threat to them should their population shrink. To this effect,

they embark on ruthless killings to make sure that other species have got small number around them. This

small number of other species may be considered synonymous with security of these predator species.

11 What Happens When Predator Does Not Take Place

If the predation does not take place, there may be two serious consequences;

1) Absence of predation would mean massive increase in the population of these species.

2) The second important consequence is that if predation does not take place, the herbivores increase in

population and finally, it affects the grass and green plants which will have more pressure on it.

12 Different Predators in Co-operation

One important characteristic of the predation process is that predators co-operate with each other against preys.

The co-operation becomes more visible when the prey species are strong enough to be over-powered easily

(Lloyd, 1965).

Moreover, the predators may confront two problems. The first problem may about the large size of prey.

The large size may undermine predator’s ability to successfully target the prey (Molles, 2002). The second

issue facing predators is about the tough terrain. The tough terrain may be the movement of predators and

preys affect understanding of location may benefit it. The speed of predator may be affected. They may also

get injured while chasing the prey (Ripple and Robert, 2004).

13 Recent Developments

We have introduced the quasi chemical approach to represent the different types of mechanisms between the

predator and its prey by taking a case study of foxes and rabbits and determined the modeled equations for

these mechanisms including the mechanism of circulation, mechanisms of attraction and repulsion and

mechanism of sharing place (Shakil et al., 2014)

In our second serried of papers, we developed the modeled equations for different types of mechanism of

the predator-prey interactions with the help of a quasi chemical approach while taking a special study case of

foxes and rabbits, these mechanisms include autocatalysis mechanism, pair wise interactions and the

mechanism of their movements to some free places (Shakil et al., 2015). The chemical reactions representing

the interactions obey the mass action law. The territorial animal like fox is assigned a simple cell as its territory.

Under the proper relations between coefficients, this system may demonstrate globally stable dynamics.

14 Future Plan

We aim to build up a concise study of complex biological systems and to tackle some key research questions

concerning our study case by proposing some new techniques and algorithms that are inspired by those complex

biological systems. After the developments of the models with the help of our quasi-chemical approach, we aim

to check the stability of all the mechanisms discussed in our study case (Shakil et al., 2015). We will then find

the solution of the mechanism in relation to the existence and uniqueness of those solutions.

References

Alcock J. 1998. Animal Behavior: An Evolutionary Approach. Sunderland, Sinauer Associates, Mass, USA

Begon MC, Townsend, Harper J. 1996. Ecology: Individuals, populations and communities. Blackwell

Science. London, UK

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Selforganizology, 2016, 3(1): 10-15

IAEES www.iaees.org

Cooke D, Hiorns RW. 1981. The Mathematical Theory of the Dynamics of Biological Populations II.

Academic Press Inc, USA

Freedman HI. 1980. Deterministic Mathematical Models in Population Ecology. Monographs and Textbooks

in Pure and Applied Mathematics Vol 57. Marcel Dekker Inc, New York, USA

Hoppensteadt FC. 1977. Mathematical Methods of Population Biology. Courant Institute of Mathematical

Sciences New York University, New York, USA

Kingsland SE. 1985. Modeling Nature, Science and Its Conceptual Foundations. University of Chicago Press,

Chicago, USA

Lotka J. 1958. Elements of Mathematical Biology (Formerly published under the title Elements of Physical

Biology), Dover Publications Inc. New York, USA

Lloyd JE. 1965. Aggressive mimicry in Photuris: Firefly Femmes Fatales. Science, 149(3684): 653-654

Molles Manuel C. Jr. 2002. Ecology: Concepts and Applications. The McGraw-Hill Companies, New York,

USA

Shakil M Wahab HA, Naeem M, Bhatti S. 2014. A quasi chemical approach for the modeling predator-prey

interactions. Network Biology, 4(3): 130-150

Shakil M, Wahab HA, Naeem M, Bhatti S, Shahzad M. 2015. Modeling of the predator-prey interactions.

Network Biology, 5(2): 71-81

Shakil M, Wahab HA, Naeem M, Bhatti S, Shahzad M. 2015. The predator-prey models for the mechanism

of autocatalysis, pair wise interactions and movements to free places. Network Biology, 5(4): 169-179

Voltera V. 1926. Variations and Fluctuations of the Number of the Individuals in Animal Species Living

Together. In: Animal Ecology. McGraw-Hill, New York, USA

Wahab HA, Shakil M, Khan T, Bhatti S, Naeem M. 2013. A comparative study of a system of Lotka-Voltera

type of PDEs through perturbation methods. Computational Ecology and Software. 3(4): 110-125

Zhang WJ. 2012. Computational Ecology: Graphs, Networks and Agent-based Modeling. World Scientific,

Singapore

Zhang WJ, Liu GH. 2015. Coevolution: A synergy in biology and ecology. Selforganizology, 2(2): 35-38

15

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Selforganizology, 2016, 3(1): 16-24

IAEES www.iaees.org 

2 Back Ground

Jane Hillston (September 19, 2003) define validation as: “Validation is the task of demonstrating that the

model is a reasonable representation of the actual system”. Validation concerned with building the right model.

It is utilized to determine that a model is an accurate representation of the real system. Validation is usually

achieved through the calibration of the model, an iterative process of comparing the model to actual system

behavior and using the discrepancies between the two, and the insights gained, to improve the model. This

process is repeated until model accuracy is judged to be acceptable. A model is usually developed to analyze a

particular problem and may therefore represent different parts of the system at different levels of abstraction.

As a result, the model may have different levels of validity for different parts of the system across the full

spectrum of system behaviour For most models there are three separate aspects which should be considered

during model validation which are Assumptions, input parameter values and distributions and Output values

and conclusions.

There are three validation models or strategies for validating data:

- Rejecting bad data: creating a set of undesirable data and rejecting them. This model is also known as

“blacklist” approach.

- Accepting only known good data: data constrained by Five Primary Security Input Validation Attributes

which are: type, length, character set, format, reasonableness. Data is rejected unless it matches for known

good data. This model is also known as “white list” approach.

- Sanitizing data: sanitizing a defined set of dangerous data so that it does not pose a threat to the software

(PedramHayati 2008). It is important to know that how we can apply validation process to our model. Before

validation we will use metric to find different class and object number in model. Detail of metric use and

types are under:

Definition1: MetricModel

Model metrics are for estimating the size or the amount of information contained in a model.

We can use metrics according to pointed situation. Each different object and class relation has different metric,

as given below.

Table 1 Software metrics for UML models (Abbreviation UML Metric).

CBC Coupling between classes DIT Depth of inheritance tree NACM Number of actors in a model NACU Number of actors associated with a use case NAGM Number of the aggregations in a model NASC Number of the associations linked to a class NASM Number of the associations in a model NATC1 Number of the attributes in a class - unweight NATC2 Number of the attributes in a class - weighted NCM Number of the classes in a model NDM Number of the directly dispatched messages of a message NDM* Number of the elements in the transitive closure of the directly dispatched messages of a message NIM Number of the inheritance relations in a model NMM Number of the messages in a model NMRC Number of messages received by the instantiated objects of a class NMSC Number of messages sent by the instantiated objects of a class NMU Number of messages associated with a use case NOM Number of the objects in a model NOPC1 Number of the operations in a class - unweight NOPC2 Number of the operations in a class - weighted

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NPM Number of the packages in a model NSCU Number of system classes associated with a use case NSUBC Number of the subclasses of a class NSUBC* Number of the elements in the transitive closure of the subclasses of a class NSUPC Number of the super classes of a class NSUPC* Number of the elements in the transitive closure of the super classes of a class NUM Number of the use cases in a model

 

 

3 Model Metrics

1. Number of the packages in a model (NPM): This metric counts the number of packages in a model. Package

is a way of managing closely related modeling elements together. Also by using packages, naming conflicts

can be avoided.

2. Number of the classes in a model (NCM): A class in a model is an instance of the meta class “class”. This

metric counts the number of classes in a model. This metric is comparable to the traditional LOC (lines of code)

or a more advances McCabe’s cyclomatic complexity (MVG) metric for estimating the size of a system [7].

Thus, in OOP this metric can be used to compare sizes of systems.

3. Number of actors in a model (NAM): According to the UML specification [10], an actor is a special class

whose stereotype is “Actor”. This metric computes the number of actors in a model.

4. Number of the use cases in a model (NUM): The rationale behind the inclusion of this metric is that a use

case represents a coherent unit of functionality provided by a system, a subsystem, or a class.

5. Number of the objects in a model (NOM): In a similar manner that a class is an instance of the metaclass

“Class”, an object is an instance of a class.

6. Number of the messages in a model (NMM): A message is an instance of the metaclass “Message”.

Messages are exchanged between objects manifesting various interactions.

7. Number of the associations in a model (NASM): An association is a connection, or a link, between classes.

This metric is useful for estimating the scale of relationships between classes.

8. Number of the aggregations in a model (NAGM): An aggregation is a special form of association that

specifies a whole-part relationship between the aggregate (whole) and a component part.

9. Number of the inheritance relations in a model (NIM): This metric counts the number of generalization

relationships between classes existing in a model.

4 Related Work

Moha (2007) provided a systematic method to specify design defects accurately. Their approach is based on

detection and correction algorithms by using refactoring semi-automatically. To apply and validate these

algorithms on open-source object-oriented programs was used to show that method allows the systematic

description, detection, and correction of design defects with a reasonable precision.

Mekruksavanich (2011) proposed a methodology for detection of design flaws. Symbolic logic

representation and analytical learning technique are used to diagnose design flaws in simple way and to

extrapolate patterned rules for complex flaws. The methodology is validated by detecting design flaws in an

open-source system.

Saxena and Kuma (2012) helped to find the flaw in the design model and to remove it as early as possible.

They used the flaw pattern for finding the flaw. When design flaw is detected based in the design pattern, the

process exits after dispatching that flaw, the proposed approach was composed of model representation of

design model and flaws detection using flaw patterns. The design models of UML class and sequence

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diagrams were used as an input. It would be transformed to the proposed representation model. In detecting

flaws, flaw patterns are used in checking against the representation model. This study covered flaw patterns for

detecting Large Class, Refused Bequest, and Middle Man.

In Mohamed et al. (2011), authors used the approach of automatic flaw detection in design model. To find

the number of flaw number of classes and detection. Which was based on model qualities metrics and design

flaws, author suggest a new demarche allowing the mechanized finding of model refactoring opportunities and

the assisted model restructuration. Which focused on class and sequence diagrams. That developed a software

call’s M-Refactor for those works.

According to Trifu et al. (2004) authors used the flaw detection and correction. The process as problem

detected, developers obtain a list of design flaws together with their location in the system. The necessary

transformations that removed them were left to their own judgment and experience. The mapping between

specific design flaw and code transformations is removed.

In Kessentini (2011) authors used an approach to detect the flaw in design and correct the flaw in the

source code. Their approach support automatic generation of rules to detect defects by the help of genetic

programming. Using a genetic algorithm, adjustment solutions are found by combining refactoring operations

in such a way to reduce the number of detected defects. The detection system is physically specified. Projected

corrections fix, in standard, more than 74% of detected defects.

Alikacem and Sahraoui (2010) provide support for source code analysis. They proposed a rule-based

approach that allowed the specification and detection of flaws. The approach provided a new language to

describe flaws as sets of rules. The latter are translated into Jess’s rule format, and given as input to Jess

inference engine. The current work is an extension of our source code analysis platform and PatOIS, a metric

description language. A main advantage of his approach was its extensibility since the tool is not limited to a

set of predefined flaws. Existing flaws could be modified to a specific context and new ones could be added.

Budi et al. (2011) provided a framework that automatically labels classes as Boundary, Control, or Entity,

and detects design flaws of the rules associated with each stereotype. Their evaluation with programs

developed by both novice and expert developers show that his technique is able to detect many design flaws

accurately.

The main theme of authors in the paper is to find flaw through metric base and convert it into code may in

Java or C++. They defined such detection strategies for capturing around ten important flaws of object-

oriented design found in the literature and validated the approach experimentally on multiple large-scale case-

studies (Marinescu, 2004).

Marinescu (2003) focused on flaw detection through metric base and converted into object-oriented

system.

This paper presented a metrics-based approach for detecting design problems, which describes two

concrete techniques for the detection of two well-known design flaws found in the literature. By an experiment

it was showed that the proposed technique found indeed real flaws in the system and it suggests that, based on

the same approach.

Moha et al. (2008) used an approach propose a novel approach for defect removal in object-oriented

programs that combines the efficiency of metrics with the theoretical strength of formal concept analysis

Algorithm. They suggested a novel approach for defect deduction in object-oriented programs that combines

the usefulness of metrics with the hypothetical power of formal concept analysis, and case study of an exact

fault.

Simon et al. (2006) have worked for finding bad smells. With four typical refactoring’s and present both a

tool supporting the identification and case studies of its application. They showed that special kind of metrics

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can support these skewed perceptions and thus can be used as effective and efficient way to get support for the

decision where to apply which refactoring. They demonstrate this loom for four typical refactoring’s and

present both a tool supporting the classification and case studies of its function.

Syed et al. (2015) worked on Refactoring of non-dispatchable flaws in the design model based on

coupling. In this work he cover all the aspects which was blank in the above all works. But one thing which is

validation still remained in his work.

The entire above techniques draw backs have been covered by Syed el al. but, one thing still remains that

is: When the process has been done of dispatch and non-dispatchable flaw, how we will find that our model

has been in required position. For this we are going to use an approach to validate our model after passing

through the process as under.

5 Our Approach

The previous work was divided into six steps, now we are going to fix the previous error in approach. For this

we will add another one step in the existing approach. So the new step will be validation of model.

Step 1: Domain analysis and metrics identification

Step 2: Modeling and meta modeling

Step 3: Flaw detection and flaw pattern

Step 4: Option if flaw >=1 or no flaw found

Step 5: Condition check for dispatch and non-dispatchable flaw

Step 6: validation check

The systematic view of our approach is

Step 1 (Domain Analysis): We will do the analysis of the domain area, in this step we associate manually

with each design defect to detect them and set refactoring by using metric based identification to find class and

their association through coupling.

Step 2 (Modeling): In modeling, the Meta model for software modeling is important, because it forms the

basis for the UML definition. The UML specification document is indeed a Meta model for UML. That is, it

includes a set of statements that must not be false for any valid UML model. In the metric forms that shows

different sort of associations. 

Step 3: (Flaw Detection): In this step, we find the flaws by using flaw detection patterns. Basically, a pattern

is a format which will identify a flaw in the model. We use coupling for the detection of flaws. Coupling

measures the strength of all relationships between functional units.

Step 4: (Flaw does exist or not): Using the above formula, if flaw exists then to be refactored or dispatched, if

not then exit. When the flaw =0, it will exit else if flaw≥1then condition shall be checked. That either flaw is

dispatchable or non-dispatchable, if dispatchable go to dispatch-able module otherwise non-dispatchable and

go for refactoring to refactor module. 

Step 5: (Flaw checking of dispatch-able or non-dispatch-able): Condition checking whether the flaw is

dispatch able or non-dispatch able. The dispatch able flaw goes to dispatch able flaw module and the non-

dispatch able flaw goes to the non-dispatch able flaw module. First condition is to check that if flaw is dispatch

able, the flaw goes to the dispatch able module and removed there. The second condition, If flaw is non-

dispatch able and been removed through refactoring a tag Ref; attached to the refactored flaw as a comment for

the detected flaw module to understand that this flaw has refactored and didn’t need to catch it again. Both

from dispatch and non-dispatch able flaw modules the model goes again for rechecking flaws to the detection

flaw module. The cycle continues until all flaws are dispatched or refactored.

20

IAEES

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22

Selforganizology, 2016, 3(1): 16-24

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7 Conclusion

As for performing this sort of process we will be able to refactor all the dispatch able and non-dispatchable

flaws, we will also be able to re-structure the model if the model has been misplaced. The model simply makes

meta models using metrics and the store that metric code. After performing all the operations for validation the

model again comes to modeling state. Here the previous and new model metric compared and find the

differences between them. If the model metrics same validate and exit, or else it restructure the model and go

to exit state.

References

Ahmad SU, Naeem M. 2015. Refactoring of non-dispatchable flaws in the design model based on coupling.

Selforganizology, 2015, 2(3): 46-54

Alikacem H, Sahraoui HA. 2010. Rule-Based System for Flaw Specification and Detection in Object-Oriented

Programs. 13th TOOLS Workshop on Quantitative Approaches in Object-Oriented Software Engineering.

1-11

Bacchelli, Lanza M. 2010. On the Impact of Design Flaws on Software Defects.IEEE 10th International

Conference on Quality Software (QSIC), 23-31 Budi A, Lucia, Lo D, Jiang L, Wang S. 2011. Automated

Detection of Likely Design Flaws in Layered Architectures, Research Collection School of Information

Systems, 1-6

Fowler M, Beck K. 1999. Refactoring: Improving the Design of Existing Code. Addison-Wesley Professional,

USA

Kessentini M, Kessentini W, Erradi A. 2011. Example-based Design Defects Detection and Correction.IEEE

19th International Conference Program Comprehension (ICPC). 81-90

Marinescu R. 2001. Detecting Design Flaws via Metrics in Object-Oriented Systems. 39th International

Conference and Exhibition on Technology of Object-Oriented Languages and Systems (TOOLS), 173-182

Marinescu R. 2004. Detection Strategies: Metrics-Based Rules for Detecting Design Flaws. International

IEEE20th Conference on Software Maintenance. 350-359

Mekruksavanich S. 2011. Design flaws detection in object-oriented software with analytical learning method.

International Journal of e-Education, e-Business, e-Management and e-Learning, 1(3): 210-216

Mens T, Tourw T. 2004. A survey of software refactoring. IEEE Transactions on Software Engineering, 30(2):

126-139

Moha N. 2007. Detection and Correction of Design Defects in Object-Oriented Architectures. Companion to

the 22nd ACM Special Interest Group ACM SIGPLAN Conference, 949-950

Moha N, Rezgui J, Gueheneuc Y, Valtchev P, Boussaidi G. 2008. Using FCA to Suggest Refactorings to

Correct Design Defects. 4th International Conference on Concept Lattices and Their Applications. LNCS

4923, 269-275

Mohamed M, Romdhani M, Ghedira K. 2011. M-REFACTOR: A new approach and tool for model refactoring.

American Resources Policy Network (ARPN). Journal of Systems and Software, 1(4): 1-6

Objecteeing. 2015. http://support.objecteering.com

Saxena V, Kumar S. 2012. Impact of coupling and cohesion in object-oriented technology. Journal of Software

Engineering and Applications, 671-676

Seidewitz E. 2003. What Models Mean. IEEE Software. IEEE Computer Society Press Los Alamitos, CA,

USA, 20(5): 26-32

23

Selforganizology, 2016, 3(1): 16-24

IAEES www.iaees.org 

Simon F, Steinbrückner F, Lewerentz C. 2001. Metrics Based Refactoring. IEEE 5th European Conference on

Software Maintenance and Reengineering. 30-38

Sunyé, Gerson, Pollet D, Traon Y, Jézéquel J. 2001. Refactoring UML Models. UML2001—TheUnified

Modeling Language. Modeling Languages, Concepts and Tools. 134-148, Springer, Berlin, Heidelberg,

Germany

Tahvildari L, Kontogiannis K. 2003. Metric-Based Approach to Enhance Design Quality ThroughMeta-Pattern

Transformations. Proceedings of 7th European Conference on Software Maintenance and Reengineering.

183-192

Trifu A, Seng O, Genssler T. 2004. Automating Design Flaw Correction in Object-Oriented Systems.

Proceedings of 8th European Conference on Software Maintenance and Reengineering (CSMR 2004).174-

183

Yaowarattanaprasert N, Muenchaisri P. 2013. Graphical pattern matching approach for detecting design flaw

in design model. International Journal of Advanced Research in Computer Science and Software, 2: 1-5

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Article

Non-traditional approach to fitting of time series of larch bud moth

dynamics: Application of Moran – Ricker model with time lags

L.V. Nedorezov Center of Interdisciplinary Investigations of Environmental Problems, Russian Academy of Sciences, nab. Kutuzova 14, Saint-Petersburg, 191187, Russia E-mail: l.v.nedorezov@gmail.com

Received 28 October 2015; Accepted 5 December 2015; Published online 1 March 2016

Abstract

In current publication analyses of time series of larch bud moth (Zeiraphera diniana Gn.) dynamics are

considered. For fitting of time series Moran - Ricker model with time lags was used. Estimations of model

parameters were provided with non-traditional approach: for every considered case feasible sets of points in

space of model parameters were determined where selected statistical criterions give required results for

deviations between theoretical (model) and empirical datasets. In all considered situations obtained results

were compared with other results obtained with least squared method. It was obtained that Moran – Ricker

model without time lag and with time lag in one year is not suitable for fitting of time series. Best

correspondences on quantitative and qualitative levels between model trajectories and empirical dataset were

found for cases with time lag in 3 years.

Keywords larch bud moth dynamics; time series; fitting; Moran - Ricker model with time lag.

1 Introduction

For estimation of ecological model parameters various methods and approaches can be used – from expert

estimations up to Bayesian approach (Bard, 1974; Borovkov, 1984; Draper and Smith, 1981; Wood, 2001 a, b

and others). For one and the same model which is used for fitting of one and the same time series we can get

various estimations for model parameters: expert estimations, estimations obtained with least square method,

obtained with method of maximum likelihood etc. Naturally, in some situations question about better

estimations does not arise, and in some situations question about correspondence of model and time series

does not arise too.

Let us assume that parameters of following discrete-time model must be estimated:

Selforganizology     ISSN 2410­0080   URL: http://www.iaees.org/publications/journals/selforganizology/online­version.asp RSS: http://www.iaees.org/publications/journals/selforganizology/rss.xml E­mail: selforganizology@iaees.org Editor­in­Chief: WenJun Zhang Publisher: International Academy of Ecology and Environmental Sciences 

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),(1 kk xFx . (1)

In (1) kx is population size at moment k , ...2,1,0k ; is vector of model parameters; F is

non-negative function (for non-negative values kx and admissible values of parameters). Let us additionally

to assume that at initial time moment 0k population size is equal to 0x and it is unknown amount which

must be estimated too.

Let }{ *kx , Nk ,...,1,0 , be empirical time series of population size changing in time; 1N is

sample size. Using this sample }{ *kx we have to estimate model parameters and initial population size

0x .

Use of least square method (LSM) (Bard, 1974; Borovkov, 1984) is based on assumption that best

estimations of model parameters can be found with minimizing of sum of squared deviations between

theoretical (model) and empirical datasets. If time series is approximated by model trajectory (global fitting;

Wood, 2001 a, b) loss-function can be presented in the following form:

N

kkk xxxxQ

0

2*00 ),(),( . (2)

In (2) )},({ 0xxk is model (1) trajectory obtained for fixed values of and 0x . Let’s also assume

that for certain point ),( **0

** x there is a global minimum in (2):

N

kkk

xxxxxQ

0

2*0

,

**0

** ),(min),(0

r

. (3)

Following a traditional approach (Bard, 1974; Borovkov, 1984; Draper and Smith, 1981) after

determination of estimations ),( **0

** x analysis of set of deviations }{ ke between theoretical and

empirical datasets must be provided:

***0

** ),( kkk xxxe . (4)

Model (1) is recognized to be suitable for fitting of considering time series if following conditions are

truthful: deviations }{ ke are values of independent stochastic variables with Normal distribution and with

zero average. Following these assumptions Kolmogorov – Smirnov, Lilliefors, Shapiro – Wilk or other tests

are used for checking of Normality of deviations (Bolshev and Smirnov, 1983; Lilliefors, 1967; Shapiro et al.,

1968). For checking of independence of stochastic variables Durbin – Watson and/or Swed – Eisenhart tests

are used (Draper and Smith, 1981; Hollander and Wolfe, 1973; Likes and Laga, 1985).

If in the sequence of residuals (4) serial correlation is observed it gives a background for conclusion that

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Selforganizology, 2016, 3(1): 25-40

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considering model isn’t suitable for fitting and needs in modification. It means also that some of important

factors or processes were not taken into account within the framework of model. Similar conclusion about

model and its applicability to fitting can be made in situation when hypothesis about Normality of deviations

must be rejected (for selected significance level). In other words, final conclusion about suitability of model

for approximation of considering time series is based on analysis of properties of unique point ),( **0

** x in

the space of model parameters.

In our opinion, this is one of basic problems of LSM: a’priori it is impossible to exclude from

consideration a situation when nearest to ),( **0

** x points have required properties. One more problem of

LSM is absence of a background for assumption about Normality of deviations. This is very strong condition

and it must be reduced to two other conditions – symmetry of distribution with respect to origin and monotonic

behaviour of branches of density function (Nedorezov, 2012, 2015a, b).

Next problem of LSM is following: there are no criterions for selection of loss-function. This function

may have form (2) (with or without system of weights), it can be a sum of absolute values of deviations etc.

This freedom in selection of loss-function is based on absence of real correlation with biological problem, and

it is based on desire for obtaining of one point only but not set of points. Note that even in a case when model

(1) is a law of population dynamics with natural values of parameters, there are no reasons for assumption that

it must give minimum of any abstract loss-function.

Before finding of any special point in a space of parameters basic criterions for sets of deviations between

theoretical and empirical datasets must be determined. On the next step it will allow determination of a feasible

set – this is a set in the space of model parameters where all statistical criterions demonstrate required results.

After that it is possible to use any loss-functions within the limits of feasible set. It is possible but not

obligatory step – structure of feasible set depends on significance levels, and changing of these levels it will be

possible to find points with extreme properties. These extreme points give best approximation for time series

from the standpoint of selected criterions (but not from standpoint of loss-function).

In current publication this alternative approach is under consideration. Moran – Ricker model with time

lags is applied for fitting of larch bud moth (LBM) time series (Zeiraphera diniana Gn.; Baltensweiler, 1964,

1978). For every considering particular case (which are determined by length of time lags) obtained results

compare with results obtained with LSM and biological imaginations about LBM dynamics.

In our previous publication (Nedorezov and Sadykova, 2015) we applied Moran – Ricker model with

time lags for fitting of larch bud moth time series. But not all basic dynamic regimes were presented in pointed

out publication. In current publication we analyze wider spectrum of dynamic regimes which may have

relation to larch bud moth dynamics.

2 Basic Requirements to Model and Set of Deviations

Mathematical model can be recognized as suitable for approximation of time series if following requirements

are truthful:

1. Deviations between theoretical and empirical datasets must have a symmetric distribution with respect to

origin. Branches of density function must be monotonic curves – it must increase in negative part of straight

line, and it must decrease in right part.

Let }{ ke be a set of positive deviations, and }{ ke is a set of negative deviations (4) with sign minus.

Distribution has symmetry with respect to origin if and only if samples }{ ke and }{ ke have one and the

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Selforganizology, 2016, 3(1): 25-40

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same distribution function. It allows using criterions for homogeneity – Kolmogorov – Smirnov test, Lehmann

– Rosenblatt test, and Mann – Whitney test ((Bolshev and Smirov, 1983; Hollander and Wolfe, 1973; Likes

and Laga, 1985). For testing of property of monotonic behavior of branches of density function Spearman rank

correlation coefficient was used.

2. Hypotheses about existence of serial correlation in sequences of residuals must be rejected. For testing of

this property Swed – Eisenhart test (Draper and Smith, 1981) and test “jump up –jump down” (Likes and Laga,

1985) were used below.

3. Behavior of model trajectory must correspond to behavior of time series. If for every increasing of values in

time series model demonstrates decreasing of values there are no backgrounds for conclusion about suitability of model for fitting of considering sample. Thus, quota q of cases when time series and model trajectory

demonstrate different changes must be rather small. In other words, Null hypothesis :0H 5.0q with

alternative hypothesis :1H 5.0q must be rejected.

Pointed out set of statistical criterions was used as for determination of points of feasible sets as for

finding points with strongest properties. For example, if hypothesis about symmetry of distribution cannot be

rejected with 5% significance level it does not mean that Null hypothesis must be accepted (p-value can be

rather small and close to 0.05). But if this hypothesis cannot be rejected with 95% significance level it means

that we have to accept it.

Changing of values of significance levels allows finding small number of points in a space of model

parameters with extreme properties. These points can be used as estimations for parameters. This is the first

basic idea of considering approach. The second idea is following: assuming that every point of feasible set can

be used as estimation of model parameters stochastic point with uniform distribution within the limits of

feasible set will allow obtaining a distribution of possible dynamic regimes. This distribution can also be used

as background for conclusion about population dynamics.

3 Larch Bud Moth Population Dynamics

3.1 Used time series and models

Regular observations of the changing of larch bud moth (Zeiraphera diniana Gn.) population densities in time

in Swiss Alps (Upper Engadine valley) had been started in 1949 (Auer, 1977; Baltensweiler, 1964, 1978). In

current publication time series on larch bud moth dynamics were used which can be free downloaded in

Internet (NERC Centre for Population Biology, Imperial College (1999) The Global Population Dynamics

Database, N 1407). Unit of measurement is number of larva per kilogram of branches. As it was pointed out in

GPDD, data were collected on 1800 m above sea level that corresponds to optimal zone of species living

(Isaev et al., 1984, 2001). Sample contains 38 values (first point corresponds to 1949).

Below we’ll follow one of basic concepts about larch bud moth dynamics: periodicity of population

fluctuations can be explained by influence of time lag in a reaction of self-regulation mechanisms (Isaev et al.,

1984, 2001; Berryman and Stark, 1985; Berryman, 1981, 2002; Sadykova and Nedorezov, 2013; Nedorezov

and Utyupin, 2011). Moran – Ricker model is one of well-known and well-studied models, and it has very rich

set of dynamic regimes (Moran, 1950; Ricker, 1954):

m

jjkjkk xaAxx

01 exp , 3,2,1,0m . (5)

In (5) all parameters are non-negative, k 0, constaA k . Initial values of population sizes must be

28

Selforganizology, 2016, 3(1): 25-40

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positive, 00 kx , 3,2,1,0k . Note, that it was proved that model (5) with 1m can give good

approximation for some time series of larch bud moth dynamics (McCallum, 2000).

3.2 Moran – Ricker model with 0m

Within the framework of traditional approach following estimations were obtained (Nedorezov, Sadykova,

2015): 7.465435min Q , 44.530 x , 0.517A , 1168.00 a . minQ is minimum value of

functional form (2)-(3). Obtaining values of stochastic points with uniform distribution in

]1,0[]1000,0[]100,0[ we get a possibility to analyze structure of feasible set . In Fig. 1 there is a

projection of feasible set onto plane ),( 0aA (for all criterions one and the same 5% significance level was

used). As one can see in fig. 1 LSM-estimation is far from a domain of maximum of point’s concentration:

705.18 A , 05.00 a approximately. Moreover, LSM-estimation doesn’t belong to .

For LSM-estimations analysis of properties of deviations }{ ke (4) allowed obtaining following results:

hypothesis about Normality of deviations must be rejected with 0.1% significance level (Shapiro – Wilk test).

Probability that distribution of deviations is symmetry is very small: 002507.0p for Wald – Wolfowitz

test and 025.0p for Kolmogorov – Smirnov test. Thus, within the framework of traditional approach we

have to conclude that Moran – Ricker model (5) with 0m is not suitable for fitting of considering time

series.

Fig. 1 Projection of feasible set for Moran – Ricker model without time lag onto plane ),( 0aA . Crest corresponds to point of minimum of functional form (2)-(3).

29

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Selforganizology, 2016, 3(1): 25-40

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Let be a stochastic variable with uniform distribution on feasible set which is equal to length of

(asymptotic) cycle which is realized for respective point of the space of model parameters. In such a case

probability }{ kP is equal to quota of respective dynamic regimes among all dynamic regimes which can

be observed for points from feasible set. Distribution of stochastic variable can be as element of

background of final conclusion about population dynamic regime. For considering situation it was obtained

that probability of event }1000{ is equal to 0.935 approximately. Some other probabilities have

following values: 0184.0}4{ P , 0102.0}5{ P , 015.0}6{ P , 0029.0}8{ P

(other probabilities are much smaller). Probability of event }100029{ is equal to zero.

It allows concluding that regimes with strongest properties, most probable regimes, and regimes with

LSM-estimations don’t correspond to biological imaginations about larch bud moth fluctuations (Isaev et al.,

1984, 2001; Auer, 1977; Baltensweiler, 1964, 1978).

3.3 Moran – Ricker model with 1m

Within the framework of traditional approach following results were obtained (Nedorezov and Sadykova,

2015): 4.154148min Q , 1400 10148.4 x , 1274.00

1 x , 3.8A , 30 10205.2 a ,

02214.01 a . For these parameters asymptotic stable regime is 18-cycle with rather close values of cyclic

coordinates (Fig. 3). It looks like double 9-cycle, and in this occasion it corresponds to biological imagination

about larch bud moth dynamics (Auer, 1977; Baltensweiler, 1964, 1978). But analysis of deviations shows that

hypothesis about Normality must be rejected with 1% significance level; serial correlation is also observed in

sequence of residuals (Swed – Eisenhart test).

Within the boundaries of set ]1,0[]1,0[]1000,0[]100,0[]100,0[ 50000 points of feasible

set were found (with the help of stochastic variable with uniform distribution). Probability to find a point

in belonging to is equal to 5103356.5 approximately. Final picture is close to presented in fig. 1

(it is obvious that set for Moran – Ricker model with 0m is a subset for new one). New domains of

point’s concentration on the plane ),( 0aA were not identified.

The following point 705.4400 x , 333.530

1 x , 01.719A , 0318.00 a , 0017.01 a has

best characteristics with respect to symmetry. Value of Kolmogorov – Smirnov test is equal to 0.4425

(hypothesis about symmetry cannot be rejected with 98.7411% significance level); value of Lehmann –

Rosenblatt test is equal to 0.03305 (93.315%); value of Mann – Whitney test is equal to 0.0908 (92.04%). It

means that Null hypothesis about symmetry of distribution of residuals must be accepted.

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IAEES

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about absence

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p

%

e

c

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32

Selforganizology, 2016, 3(1): 25-40

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of serial correlation were minimized.

Analysis of points of feasible set shows that cycles of various lengths can correspond to considering time

series: 1-cycle (regime of asymptotic stabilization or rather small fluctuations near stable level with variance

which is less than 10-40), 2,…, 7, 11, 15, 16, 19, 27, 30, 56. 8-cycles and 9-cycles were not found. Cycles with

lengths 16 and 27 don’t look like double or triple 8-cycle or 9-cycle: in these cases dynamic regimes with very

long phases of population increasing were observed.

For considering case 0164.0}1{ P , 0131.0}2{ P . Other probabilities are much less

these values. Biggest probability is equal to 0.9546 for event }1000{ . Thus, in both considered cases

( 0m and 1m ) dynamic regimes don’t correspond to existing imaginations about population dynamics.

3.4 Moran – Ricker model with 2m

Let’s consider situation when time lag is equal to 2. Minimum of squared deviations (3) 1.92099min Q

was observed for the following values of model parameters: 1500 10638.5 x , 160

1 10653.2 x ,

07208.002 x , 076.20A , 3

0 10155.8 a , 31 106994.1 a , 02097.02 a . Analysis of

deviations showed that for Kolmogorov–Smirnov test p < 0.05; for Lilliefors test p < 0.01; for Shapiro – Wilk

test p < 10-5 (Bolshev and Smirnov, 1983; Shapiro et al., 1968; Lilliefors, 1967). Thus, model (5) with

LSM-estimations cannot be used for fitting of empirical time series.

Within the boundaries of set : 1.00 0 kx , 400 A , 03.00 ka , 2,1,0k , – 50000

points of feasible set were found. Probability to find in a point belonging to is equal to

000915.0 approximately.

Point 06564.000 x , 02832.00

1 x , 0211.002 x , 607.27A , 01207.00 a ,

000138.01 a , 01257.02 a of the feasible set has following properties: hypothesis about symmetry of

deviations cannot be rejected with 99.9991% significance level (Kolmogorov – Smirnov test), with 99.7%

(Lehmann – Rosenblatt test), and with 98.81% (Mann – Whitney test). Hypothesis about equivalence of

Spearman rank correlation coefficient to 0 must be rejected with 0.1% significance level (t-test is equal to

0.7947). Hypothesis about absence of serial correlation cannot be rejected with 10.37% significance level

(Swed – Eisenhart test); value of test “jump up – jump down” is equal to 22: hypothesis about absence of serial

correlation cannot be rejected with 20% significance level. This point with extreme properties doesn’t

correspond to biological imaginations about larch bud moth dynamics: asymptotic stable dynamic regime is

strong 7-cycle.

Another point with extreme properties is following: 0098.000 x , 0902.00

1 x , 0585.002 x ,

758.27A , 0174.00 a , 00655.01 a , 0181.02 a . Hypothesis about symmetry of deviations

cannot be rejected with 99.9996% significance level (Kolmogorov – Smirnov test), with 99.7% (Lehmann –

Rosenblatt test), and with 89.31% (Mann – Whitney test). Hypothesis about equivalence of Spearman rank

33

Selforganizology, 2016, 3(1): 25-40

IAEES www.iaees.org

correlation coefficient to 0 must be rejected with 0.1% significance level (t-test is equal to 0.8947). Hypothesis

about absence of serial correlation cannot be rejected with 28.37% significance level (Swed – Eisenhart test);

value of test “jump up – jump down” is equal to 20: hypothesis about absence of serial correlation cannot be

rejected with 5% significance level.

This point with extreme properties doesn’t also correspond to biological imaginations about larch bud

moth dynamics: asymptotic stable dynamic regime is non-periodic. Values of autocorrelation function belong

to close interval ]4088.0,2284.0[ . Asymptotic stable regime constructed for 20000 points (after 106 free

steps of model) on the plane )log,(log 1010 yx is presented in Fig. 5a. Approximation of considering time

series by initial part of model trajectory is presented in Fig. 5b. Visual analysis of these pictures shows that we

have not a background for conclusion that in this case Moran – Ricker model gives good fitting. In particular,

number of extreme points of trajectory (Fig. 5b) is much bigger than number of extreme points of time series.

Asymptotic trajectory of model is rather difficult, and we cannot say it has relation to larch bud moth dynamics

or not.

Analysis of points of feasible set shows that cycles of various lengths belong to this set. Like in previous

case biggest probability is equal to 0.9 for event }1000{ . For 1-cycle probability is equal to 0.01634; for

9-cycle 01202.0}9{ P , and for 8-cycle 00892.0}8{ P . In a group of regimes which are close

to 9-cycle, it is possible to point out strong 9-cycles, double 9-cycles (cycles of the length 18), and fuzzy

9-cycles with close coordinates (every ninth step values of autocorrelation function is bigger than 0.999). It

allows concluding that within the boundaries of feasible set it is possible to find dynamic regimes which are

close to biological imaginations about larch bud moth dynamics. But quota of these regimes is rather small.

3.5 Moran – Ricker model with 3m

Let us consider the situation with 3m . Minimum 9.92018min Q of squared deviations (3) was

observed for the following values of model parameters: 1400 1097.4 x , 160

1 1061.1 x ,

1602 102.4 x , 4837.10

3 x , 8439.19A , 0081.00 a , 0018.01 a , 0186.02 a ,

0021.03 a . Analysis of deviations showed that for Kolmogorov–Smirnov test 05.0p ; for Lilliefors

test 01.0p ; for Shapiro– Wilk test 510p (Bolshev and Smirnov, 1983; Shapiro et al., 1968;

Lilliefors, 1967). Thus, Moran – Ricker model with LSM-estimations of model parameters cannot be applied

for fitting of considering time series. Asymptotic stable dynamic regime is not cycling with length of cycle in

1000 years or less.

34

IAEES

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38

Selforganizology, 2016, 3(1): 25-40

IAEES www.iaees.org

when time lag is in three years. In this situation correspondence of theoretical and empirical datasets is

observed on quantitative (all statistical criterions are satisfied with extreme values of significance levels) and

qualitative (behavior of model trajectory corresponds to behavior of empirical time series) levels. Provided

analysis allows concluding that asymptotic stable dynamic regime of larch bud moth is strong 28-cycle (cycle

in 28 years with three maximum points) or fuzzy 16-cycle (cycle in 16 years).

References

Auer C. 1977. Dynamik von Larchenwicklerpopulationen langs des Alpenbogens. Mitteilungen der

Eidgenossischen Anstalt fiir forstliches Versuchswesen, 53: 71-105

Berryman AA. 1981. Population Systems: A General Introduction. Plenum Press, New York, USA

Berryman AA. 2002. Population regulation, emergent properties, and a requiem for density dependence. Oikos,

99(3): 600-606

Berryman AA, Stark RW. 1985. Assessing the risk of the forest insect outbreaks. Z. angew. Entomology, 99(2):

199-208

Baltensweiler W. 1964. Zeiraphera griceana Hubner (Lepidoptera, Tortricedae) in the European Alps. A

contribution to the problem of cycles. Canadian Entomologist, 96(5): 792-800

Baltensweiler W. 1978. Ursache oder Wirkung? Huhn oder Ei?. Mitteilungen der Schweizerischen

Entomologischen Geselschaft, 51: 261-267

Bard Y. 1974. Nonlinear Parameter Estimation. Academic Press Inc., New York, USA

Bolshev LN, Smirnov NV. 1983. Tables of Mathematical Statistics. Nauka, Moscow, USSR

Borovkov АА. 1984. Mathematical Statistics. Nauka, Moscow, USSR

Draper NR, Smith H. 1981. Applied Regression Analysis. Wiley and Sons Inc., New York, USA

Hollander MDA, Wolfe DA. 1973. Nonparametric Statistical Methods. John Wiley and Sons Inc., New York,

London, Sydney, Toronto

Isaev AS, Khlebopros RG, Nedorezov LV, Kondakov YuP, Kiselev VV. 1984. Forest Insect Population

Dynamics. Nauka, Novosibirsk, USSR

Isaev AS, Khlebopros RG, Nedorezov LV, Kondakov YuP, Kiselev VV, Soukhovolsky VG, 2001. Population

Dynamics of Forest Insects. Nauka, Moscow, Russia

Likes J, Laga J. 1985. Basic Tables of Mathematical Statistics. Finance and statistics, Moscow, USSR

Lilliefors HW. 1967. On the Kolmogorov–Smirnov test for normality with mean and variance unknown.

Journal of American Statistical Association, 64: 399-402

McCallum H. 2000. Population parameters estimation for ecological models. Blackwell Sciences Ltd.,

Brisbane, Australia

Moran PAP. 1950. Some remarks on animal population dynamics. Biometrics, 6(3): 250-258

Nedorezov LV. 2012. Chaos and Order in Population Dynamics: Modeling, Analysis, Forecast. LAP Lambert

Academic Publishing, Saarbrucken, Germany

Nedorezov LV. 2015a. Paramecia aurelia dynamics: non-traditional approach to estimation of model

parameters (on an example of Verhulst and Gompertz models). Ecological Modelling, 317: 1-5

Nedorezov LV. 2015b. Lotka-Vo0lterra Model of Competition Between Two Species and Gause Experiments:

Is There Any Correspondence? Biofizika, 60(5): 1039-1040

Nedorezov LV, Sadykova DL. 2015. Dynamics of larch bud moth populations: application of Moran - Ricker

models with time lags. Ecological Modelling, 297: 26-32

Nedorezov LV, Utyupin YuV. 2011. Continuous-Discrete Models of Population Dynamics: An Analytical

39

Selforganizology, 2016, 3(1): 25-40

IAEES www.iaees.org

Overview. State Public Scientific-Technical Library, Novosibirsk, Russia

Ricker WE, 1954. Stock and recruitment. Journal of Fishery Res. Board of Canada, 11(5): 559-623

Sadykova DL, Nedorezov LV. 2013. Larch bud moth dynamics: can we explain periodicity of population

fluctuations by the time lag dependence in birth rate? Population Dynamics: Analysis, Modelling,

Forecast, 2(4): 154-181

Shapiro SS, Wilk MB, Chen HJ. 1968. A comparative study of various tests of normality. Journal of the

American Statistical Association, 63: 1343-1372

Wood SN. 2001a. Minimizing model fitting objectives that contain spurious local minima by bootstrap

restarting. Biometrics, 57: 240-244

Wood SN. 2001b. Partially specified ecological models. Ecological Monographs, 71: 1-25

40

Selforganizology, 2016, 3(1): 41-42

IAEES www.iaees.org

Book Review

A review on the book, Selforganizology: The Science of Self-

Organization GuangHua Liu Guangdong AIB Polytech College, Guangzhou 510507, China

E-mail: ghliu@gdaib.edu.cn

Received 15 January 2016; Accepted 20 January 2016; Published online 1 March 2016

Abstract

The book, Selforganizology: The Science of Self-Organization, authored by WenJun Zhang and published by

World Scientific, was briefly reviewed in present report.

Keywords selforganizology; self-organization; book; review.

This invaluable book is the first of its kind on "selforganizology", the science of self-organization. It covers a

wide range of topics, such as the theory, principle and methodology of selforganizology, agent-based

modelling, intelligence basis, ant colony optimization, fish/particle swarm optimization, cellular automata,

spatial diffusion models, evolutionary algorithms, self-adaptation and control systems, self-organizing neural

networks, catastrophe theory and methods, and self-organization of biological communities, etc. Readers will

have an in-depth and comprehensive understanding of selforganizology, with detailed background information

provided for those who wish to delve deeper into the subject and explore research literature. This book is a

valuable reference for research scientists, university teachers, graduate students and high-level undergraduates

in the areas of computational science, artificial intelligence, applied mathematics, engineering science, social

science and life sciences.

Major contents of the book include

Organization and Organizational Theory

Selforganizology: The Science of Self-organization

Agent-based Modeling

Intelligence Principles

Catastrophe Theory and Methods

Self-adaptation and Control Systems

Cellular Automata and Spatial Diffusion Models

Artificial Neural Networks

Selforganizology     URL: http://www.iaees.org/publications/journals/selforganizology/online­version.asp RSS: http://www.iaees.org/publications/journals/ selforganizology /rss.xml E­mail: selforganizology@iaees.org Editor­in­Chief: WenJun Zhang Publisher: International Academy of Ecology and Environmental Sciences 

Selforganizology, 2016, 3(1): 41-42

IAEES www.iaees.org

Ant Colony Optimization

Fish and Particle Swarm Optimization

Synergy, Coevolution, and Evolutionary Algorithms

Synergy: Correlation Analysis

Community Succession and Assembly

Mathematical Foundations

The readers of the book will be research scientists, university teachers, graduate students and high-level

undergraduates in the areas of computational science, artificial intelligence, applied mathematics, engineering

science, social science and life sciences.

Reference

Zhang WJ. 2016. Selforganizology: The Science of Self-Organization. World Scientific, Singapore

(http://www.worldscientific.com/worldscibooks/10.1142/9685)

42

Selforganizology

The Selforganizology (ISSN 2410-0080) is an open access (BOAI definition), peer/open reviewed online journal that considers scientific articles in all different areas of selforganizology. The goal of this journal is to keep a record of the state-of-the-art research and promote the research work in these fast moving areas. The topics to be covered by Selforganizology include, but are not limited to:

Innovative theories and methods on self-organization. Applications of evolution-, interaction-, behavior-, organization-, intelligence- and

feedback-based theories, such as coevolution theory, coextinction theory, community succession theory, correlation analysis, parrondo’s paradox, game theory, neural networks, artificial intelligence, behavioral theory, organization theory, and automation theory, in self-organization.

Simulation and modeling of self-organization systems. Algorithms of self-organization, including intelligence computation (swarm intelligence

algorithms, genetic algorithms, etc.), cellular automata, self-adaptation and automation, etc.

Various self-organization phenomena in nature.

We are particularly interested in short communications that clearly address a specific issue or

completely describe a new self-organization phenomenon.

Authors can submit their works to the email box of this journal, selforganizology@iaees.org. All

manuscripts submitted to this journal must be previously unpublished and may not be considered

for publication elsewhere at any time during review period of this journal. Authors are asked to

read and accept Author Guidelines and Publication Ethics & Malpractice Statement before

submitting manuscripts.

In addition to free submissions from authors around the world, special issues are also accepted.

The organizer of a special issue can collect submissions (yielded from a research project, a

research group, etc.) on a specific research topic, or submissions of a scientific conference for

publication of special issue.

Editorial Office: selforganizology@iaees.org

Publisher: International Academy of Ecology and Environmental Sciences

Address: Unit 3, 6/F., Kam Hon Industrial Building, 8 Wang Kwun Road, Kowloon Bay, Hong Kong

Tel: 00852-2138 6086 Fax: 00852-3069 1955

E-mail: office@iaees.org

Selforganizology ISSN 2410-0080

Volume 3, Number 1, 1 March 2016

Articles

A random network based, node attraction facilitated network

evolution method

WenJun Zhang 1-9

A review on research of the predator-prey interactions

H. A. Wahab, Hazrat Ali, Muhammad Naeem, et al. 10-15

Validity process for refactored coupling based non-dispatchable flaws

in the design model

Syed Uzair Ahmad, Muhammad Naeem 16-24 Non-traditional approach to fitting of time series of larch bud moth dynamics: Application of Moran – Ricker model with time lags

L.V. Nedorezov 25-40

Book Review A review on the book, Selforganizology: The Science of Self- Organization GuangHua Liu 41-42

IAEES http://www.iaees.org/