# Diagnosing and Predicting the Earth’s Health via Ecological Network Analysis

Authors: Zi-Ke Zhang; Ye Sun; Chu-Xu Zhang; Kuan Fang; Xiang Xu; Chuang Liu; Xueqi Wang; Kui Zhang
Journal: Discrete Dynamics in Nature and Society
 (2013)

---

## Abstract

Ecological balance is one of the most attractive topics in biological, environmental, earth sciences, and so on. However, due to the complexity of ecosystems, it is not easy to find a perfect way to conclusively explain all the potential impacts. In this paper, by considering several important elements, we seek to build a dynamic network model to predict the Earth’s health, trying to identify and explain how the human behavior and policies affect the model results. We firstly empirically analyze both the topological properties and time-dependent features of nodes and propose an Earth’s health index based on Shannon Entropy. Secondly, we identify the importance of each element by a machine learning approach. Thirdly, we use a spreading model to predict the Earth’s health. Finally, we integrate the topological property and the proposed health index to identify the influential nodes in the observed ecological network. Experimental results show that the oceans are the key nodes in affecting the Earth’s health, and Big countries are also important nodes in influencing the Earth’s health. In addition, the results suggest a possible solution that returning more living lands might be an effective way to solve the dilemma of ecological balance.


---

## Body

## 1. Introduction

Ecological balance is one of the most attractive topics in biological, environmental, Earth sciences and many other related disciplines [1], especially since the industrialization has been undergoing for about two hundred years. To better understand how biosphere responds to the increasing pressure (e.g., population explosion, water and air pollution, climate change), there is a vast class of researches devoted to discovering possible solutions in alleviating pains of the Earth. However, due to the complexity of ecosystems, it is not easy to find a perfect way to conclusively explain all the potential impacts [2] that is responsible for the ecological fragility [3, 4]. Among various studies, Ecological Network Analysis (ENA) [5, 6] is regarded as one promising methodology to assess the Earth’s health [7].Ecological networks can be extracted from various information, resulting in different kinds of networks, where each node represents a nation, a continent, an ocean, a habitat, or a park, and an edge is present when two nodes are directed or mutually influenced, varying from economic impact, population flow to environmental pollution, economic level, and so forth [5, 8].Since the network information is not explicitly provided, we start our research by constructing the global ecological network via extracting nodes and links from the world geography map (see Figure1). We consider each nation or ocean as one node, and a link is present if the two countries/oceans (or country and ocean) are geographically neighboring. For example, the two nodes, China and Russia, are connected since they are neighboring countries. In addition, there is also a link between the Pacific Ocean and China since they are also mutually connected. Figure 2 shows the constructed network. Furthermore, we also consider five time-dependent factors of each node, including the population size, economic level, habitats area size, energy consumption, and air pollution, which might affect the global ecological environment.Figure 1
Illustration of the world map.Figure 2
The 145-nation (including 19 oceans) network, where edges represent the geographically neighboring relationship. The positions of the nodes are drawn according to their respective centrality index, regardless of the geographical positions. The size of each node is set according to the stationary value of (14).After constructing the time-dependent ecological network, we start our research as follows.(i)
Firstly, we observe network topological properties by formulating both local features of a node and global topology of the network.(ii)
Secondly, we investigate how the dynamical factors evolve and how they affect the Earth’s health.(iii)
Thirdly, we use a machine learning algorithm to identify the influential factors of the ecological network.(iv)
Fourthly, we design a spreading model to predict the Earth’s health and perform sensitive analysis to test its robustness.(v)
Finally, we use thek-core deposition method [9] to identify the influential nodes by considering factors as weights.Many researches have adopted operation researches (OR) methods, such as minimum spanning tree (MST), to discover mathematical solutions (e.g., the minimum cost/maximum flow). Hill proposed a matrix solution to solve the number of paths with certain length from any two nodes [10]. Finn presented three important indices to evaluate the ecosystem flows, including the Total System Through-Flow (TST), the Average Path Length of an Inflow (APL), and the Cycling Index (CI), which are widely adopted in discussing the mass and energy flow mechanism [11]. However, researches from Network Science (NS) [12–19] consider the ecosystem problem from a very novel perspective. It not only abstracts nodes and affiliated properties, but also takes into account various kinds of interactions and functions among them. Therefore, NS-based methods, including link prediction and navigation, have been introduced, trying to discover the potential global topology via analyzing the local structure and dynamics [20, 21].


## 2. Methods

In this paper, we adopt theNetwork Science to analyze the ecological networks mainly because of its robustness and explainable solution in simulating both the static and dynamical properties of graphs. In this section, we shall describe the construction of our network model, including nodes and edges information, property formulation, and the dynamical evolution as well. In particular, we begin our study based on several necessary assumptions.(i)
All the data and information about the ecological network are collected from reliable statistical database;(ii)
Both the properties and topological position of a node in the network are important to evaluate its influence for the Earth’s health;(iii)
The spatial network has similar structure and features with real ecological network.


### 2.1. Static Properties

In the constructed network, a graphG(V,E) is used to describe its structure, where V is the node set and E is the edge set (Table 1 shows the basic information of the observed ecological network). Here, we consider four respective indices to analyze the static properties of the ecological network.Table 1
Basic statistics of the observed ecological network.
|
V
|
145
|
E
|
403
D
9.65
×
1
0
-
3
|
V
| denotes the number of nodes, |E| denotes the number of edges, and D=2|E|/(|V|*(|V|-1)) denotes the network density, respectively.(i) Degree Index. Degree index [22] indicates how many nodes that a nation/ocean connects to. Naturally, the degree index of node i is defined as
(1)SD(i)=∑j=1|V|‍eij,
where eij=1 if there is a link between node i and j; otherwise eij=0.(ii) Betweenness Index. Betweenness [22] is defined as how many shortest paths pass through the target node. The larger the Betweenness is, the more connective role the target node plays. In a given network, the Betweenness is denoted as
(2)SB(i)=∑j=1|V|‍∑k<j|V|‍Pkji,k≠j,
where Pkji=1 if there is a shortest path between node k and j passing node i.(iii) Closeness Index. Closeness [22] is defined as the reverse distance between the target node and other nodes. The larger the Closeness is, the closer they would be and vice versa. In a given network, the Closeness is denoted as
(3)SC(i)=1∑j=1|V|Lij,i≠j,
where Lij=1 denotes the length of the shortest path between nodes i and j.(iv)
k
-Core Index. k-core [23], denoted as SK(i), is the core number of a node which is the largest value k of a k-core containing that node. It is obtained as follows: (i) remove from the graph all nodes of degree less than k and (ii) then remove these vertices repeatedly until no further removal is possible. The remaining result, if exists, is the k-core. Thus, a network is organized as a set of successively enclosed k-cores.


### 2.2. Dynamical Factors

Besides the static network properties, we collect various data from World Bank (http://data.worldbank.org/) to investigate the dynamical factors of all the nodes in the ecological network. The dataset includes population size, per capita GDP, area of land and marine, energy consumption per unit of GDP, and carbon dioxide emission of each country from year 1962 to 2011. Specifically, we observe the five following factors for each node.(i)
Population size, denoted as PSti, is the total population of node i in the year t.(ii)
Economic level, denoted as ELti, is the per capita GDP of node i in the year t.(iii)
Habitats area, denoted as HAti, is the total area of land and marine of node i in the year t.(iv)
Energy consumption, denoted as ECti, is energy consumption per unit of GDP of node i in the year t.(v)
Air pollution, denoted as APti, is the total amount of carbon dioxide emission of node i in the year t.Figure3 shows how the five factors change from the year 1961 (HA starts from 1990 and EC starts from 1980 due to the data absence) to 2011. It can be seen that, generally, the values of all the factors increase year by year. It also shows that the population size has highly positive relationship with economic level. For example, the population size of China (CHN) and USA are both in the top five nations, and their average GDP also have high ranks among all the 126 nations. Meanwhile, their air pollution is ranked in the worst five nations, which might suggest that the development of economy would have negative impact on the environment. Furthermore, we list the top 20 nodes for both static properties and dynamical factors in Table 2. It can be seen that the Atlantic Ocean (ATO) holds the most significant role in maintaining the robustness of the ecological network because it connects the largest number of nodes (Table 3). Russia (RUS) has high network property, with degree rank number 5, Betweenness rank number 2, and Closeness rank number 2, but simultaneously has a relatively bad air quality (rank number 3). Other nations, such as China (CHN), have the similar situation. Comparatively, USA is not ranked in the top network structure list but has a large population (rank number 3) and a high economic  level (rank number 6), which might promote its impact in affecting the global Earth’s health.Table 2
Top 20 nodes of the static and dynamical properties.
Rank
S
D
S
B
S
C
S
K
PS
EL
HA
EC
AP
1
ATO
ATO
ATO
ATO
CHN
NOR
VEN
PER
USA
2
PCO
RUS
RUS
PAK
IND
CHE
DEU
COL
CHN
3
CHN
CHN
FRA
TKM
USA
DNK
ECU
CHE
RUS
4
MSO
PCO
NHO
UZB
IDN
ISL
ZMB
BWA
IND
5
RUS
MSO
ZAF
KAZ
BRA
IRL
NIC
IRL
JPN
6
INO
INO
MRT
AFG
PAK
USA
BWA
PAN
DEU
7
DEU
FRA
CHN
AZE
RUS
SWE
SAU
CRI
CAN
8
IRN
ABO
MDG
IRN
BGD
JPN
GTM
GAB
GBR
9
COD
UKR
JPO
TUR
NGA
NLD
TZA
ITA
KOR
10
ABO
JPO
PCO
FRA
JPN
FIN
ZWE
DNK
IRN
11
CBO
ZAF
CAN
FIN
MEX
AUT
DOM
ALB
ITA
12
KAZ
IRN
USA
SWE
PHL
GBR
CHE
GRC
MEX
13
UKR
MRT
ARG
AUT
DEU
BEL
SEN
TUR
ZAF
14
SDN
ERI
MEX
CZE
VNM
CAN
AUT
PRT
FRA
15
FRA
IDN
HND
DEU
EGY
DEU
SVK
GBR
SAU
16
HUN
NHO
CRI
HUN
ETH
FRA
BRA
ESP
AUS
17
POL
TUR
PAN
POL
IRN
AUS
EST
AUT
BRA
18
AUT
DEU
INO
SVK
TUR
ITA
KHM
NAM
IDN
19
BSO
BBO
NAM
CHE
THA
SGP
CIV
ECU
UKR
20
AFG
SDN
DZA
BLR
FRA
ESP
POL
SGP
ESP
S
D denotes the degree index, SB denotes the Betweenness index, SC denotes the Closeness index, and SK denotes the k-core index, respectively. PS, EL, HA, EC, and AQ, respectively, denote the population size, economic level, habitats area size, energy consumption, and air pollution in the year of 2011.Table 3
Abbreviations of ocean nodes.
Abbr.
Full name
ATO
Atlantic Ocean
PCO
Pacific Ocean
INO
Indian Ocean
ARO
Arctic Ocean
MSO
Mediterranean Sea
CBO
Caribbean Sea
BSO
Black Sea
ABO
Arabian Sea
BLO
Baltic Sea
NOO
Norwegian Sea
CPO
Caspian Sea
ACO
Antarctic Ocean
JPO
Sea of Japan
NSO
North Sea
RSO
Red Sea
CSO
South China Sea
BBO
Bay of Bengal
GMO
Gulf of Mexico
GTO
Gulf of ThailandFive factors of evolution of all nodes versus time. (a) Population; (b) economic level; (c) habitats area; (d) energy consumption per GDP; (e) air pollution. In each subgraph, five nations with top amount of corresponding property are highlighted.
(a)
(b)
(c)
(d)
(e)


### 2.3. Definition of the Earth’s Health Index

Inspired by previous analyses, we consider that the Earth’s health is not just affected by a single factor, but a joint influence resulting from many complicated factors. In this paper, we use theShannon Entropy [24–26] to integrate the impact of all possible factors to characterize the Earth’s health, denoted by EH, as
(4)EH=-∑i=1|V|‍∑j=1|F|‍pfij′logpfij′,
where fij′=(fij-fminj)/(fmaxj-fminj) is the normalized fraction of factor j for node i, |F| denotes the set of all the factors defined in Section 2.2, and the final Earth’s health value, EH, runs over the sum of all nodes. According to the original definition of Shannon Entropy, the larger the entropy value is, the more equal the distribution will be. Therefore, a large value of EH suggests a good situation of ecological balance both among nations and factors and hence indicates good Earth’s health and vice versa (Table 4).Table 4
Abbreviations of nation nodes.
Abbr.
Full name
Abbr.
Full name
AFG
Afghanistan
AGO
Angola
ALB
Albania
ARE
United Arab Emirates
ARG
Argentina
AUS
Australia
AUT
Austria
AZE
Azerbaijan
BEL
Belgium
BFA
Burkina Faso
BGR
Bulgaria
BGD
Bangladesh
BIH
Bosnia and Herzegovina
BLR
Belarus
BOL
Bolivia
BRA
Brazil
BWA
Botswana
CAF
Central African Republic
CAN
Canada
CHE
Switzerland
CHL
Chile
CHN
China
CIV
Cote D'Ivoire
CMR
Cameroon
COD
Congo
COL
Colombia
CRI
Costa Rica
CUB
Cuba
CZE
Czech Republic
DEU
Germany
DNK
Denmark
DOM
Dominican Republic
DZA
Algeria
ECU
Ecuador
ERI
Eritrea
ESP
Spain
EST
Estonia
ETH
Ethiopia
FIN
Finland
FRA
France
GAB
Gabon
GBR
United Kingdom
GHA
Ghana
GIN
Guinea
ALB
Albania
GTM
Guatemala
HND
Honduras
HRV
Croatia
HTI
Haiti
HUN
Hungary
IDN
Indonesia
IND
India
IRL
Ireland
IRN
The Islamic Republic of Iran
IRQ
Iraq
ISL
Iceland
ITA
Italy
JAM
Jamaica
JOR
Jordan
JPN
Japan
KAZ
Kazakhstan
KEN
Kenya
KGZ
Kyrgyzstan
KHM
Cambodia
KOR
Korea
LAO
Laos
LBR
Liberia
LBY
Libya
LKA
Sri Lanka
LTU
Lithuania
LVA
Latvia
MDA
Moldova
MDG
Madagascar
MEX
Mexico
MKD
Macedonia
MLI
Mali
MMR
Myanmar
MNG
Mongolia
MOZ
Mozambique
MRT
Mauritania
MYS
Malaysia
NAM
Namibia
NER
Niger
NGA
Nigeria
NIC
Nicaragua
NLD
Netherlands
NOR
Norway
NPL
Nepal
NZL
New Zealand
OMN
Oman
PAK
Pakistan
PAN
Panama
PER
Peru
PHL
Philippines
POL
Poland
PRK
North Korea
PRT
Portugal
ROU
Romania
RUS
Russian Federation
SAU
Saudi Arabia
SDN
Sudan
SEN
Senegal
SGP
Singapore
SLV
El Salvador
SOM
Somalia
SRB
Serbia
SSD
Southern Sudan
SVK
Slovak Republic
SVN
Slovenia
SWE
Sweden
TCD
Chad
THA
Thailand
TJK
Tajikistan
TKM
Turkmenistan
TUR
Turkey
TZA
Tanzania
UGA
Uganda
UKR
Ukraine
USA
United States
UZB
Uzbekistan
VEN
Bolivarian Republic of Venezuela
VNM
Vietnam
YEM
Republic of Yemen
ZAF
South Africa
ZMB
Zambia
ZWE
Zimbabwe


### 2.4. Identifying the Influential Factor via Machine Learning Approach

#### 2.4.1. Random Forest

We useRandom Forest [27] to evaluate the importance of factors. Random Forest is an ensemble regressor/classifier that consists of many decision trees and then outputs the value that is the mode of the values/classes output by individual trees. In this scenario, we apply this method in a regression way and use it to evaluate each feature’s importance. Compared with other regression models, we choose the Random Forest model because of its following advantages for our solution:(i)
it can tackle high-order variable interactions or correlated predictor variables;(ii)
it can be used not only for prediction, but also to assess variable importance;(iii)
it can partially overcome the overfitting problem.


#### 2.4.2. Base Learner: Classification and Regression Tree (CART)

Given a training vectorxi∈Rn, i=1,…,l and a label vector yi∈Rl, the decision tree recursively partitions the space such that the samples with the same labels can be classified together. Let the data at node m be represented by Q, for each candidate split θ=(j,tm) consisting of a feature j and threshold tm; partition data into two parts:
(5)Qright(θ)=QQleft(θ),(6)Qleft(θ)=(x,y)∣xj⟸tm.
The impurity at m is computed using an impurity function H, the choice of which depends on the task being solved:
(7)G(Q,θ)=nleftNmH(Qleft(θ))+nrightNmH(Qright(θ)).
Then, select the parameters that minimize the impurity:
(8)θ*=argminθG(Q,θ).
After this recurse for subsets Q1eft(θ*) and Qright(θ*) until the maximum allowable depth is reached, Nm<minSamples. In regression problem, for a node m, representing a region Rm with Nm observations, we choose the criterion of Mean Squared Error (MSE) as impurity function H:
(9)cm=1Nm∑i∈Nm‍yi,H(Xm)=1Nm∑i∈Nm‍(yi-c)2.


#### 2.4.3. Construction of Random Forest

Let the number of training cases beN and let the number of variables in the regressor be M. We are told the number m of input variables to be used to determine the decision at a node of the tree; m should be much less than M.(i)
Choose a training set for this tree by choosingn times with replacement from all N available training cases (i.e., take a bootstrap sample). Use the rest of the cases to estimate the error of the tree.(ii)
For each node of the tree, randomly choosem variables on which to base the decision at that node. Calculate the best split based on these m variables in the training set.(iii)
Each tree is fully grown and not pruned (as may be done in constructing a normal tree classifier). For prediction a new sample is pushed down the tree. It is assigned the value of the training sample in the terminal node it ends up in.


#### 2.4.4.Out-of-Bag (OOB) Evaluation

To evaluate theRandom Forest model, we use 2/3 of the data as training set and remaining 1/3 (saying Out-of-Bag) are regarded as the test set when constructing the base learner. We calculate the average result from 50-round simulations to alleviate the random fluctuations. For each tree t, the Out-of-Bag (OOB) simulation is tested in detail as follows.(i)
Consider the associatedOOBt sample.(ii)
Denote by errOOBt the error of a single tree t on this OOBt sample.(iii)
Randomly permute the values ofXj in OOBt to get a permuted sample denoted by OOBtj, the error of predictor t on the perturbed sample:
(10)err(Xj)=1Ntree∑t‍(errOOBtj-errOOBt),where Xj represents jth variable of each data. Then we can get err(Xj) for each j and normalize it. The bigger the err(Xj) is, the more important the variable is. Figure 4 shows the err(X) result for all the five features. It can be seen that, among all the features, the err(Xj) value of habitats area size is the biggest, hence the most important factor for the Earth’s health, which is in the agreement with reports by public media that people, especially humans living cities, now occupy smaller and smaller space than before, resulting in comparatively a much worse living condition.Figure 4
err(Xj) values of five representative factors versus time.


### 2.5. Predicting the Earth’s Health in Ecological Networks

We use a dynamic spreading model [28] to predict the Earth’s health by considering the observed ecological network structure. The model runs as follows.(i)
At the initial step, each nodei is set a health value by averaging the Earth’s health index (EHi0 defined by (4)) from the most recent five years.(ii)
We then choose 10% of the nodes as “seed” nodes and addΔEHi0 to each seed node. The ΔEHi0 is calculated by averaging over the incremental EH values of the most recent five years.(iii)
At each time stept+1, each node i will affect all its neighbouring nodes’ Earth’s health index by
(11)ΔEHi→jt+1=α*ΔEHit*(EHit*EHjt)β,
where ΔEHi→jt+1 is the Earth’s health influence from node i to j and α and β are tunable parameters.(iv)
Then, the nodej’s Earth’s health index at time step t+1 is summed over all j’s neighbours as
(12)EHjt+1=EHjt+∑eij∈E‍ΔEHi→jt+1,
where eij=1 if there is a link between node i and node j, and eij=0 otherwise.(v)
Finally, the global Earth’s health, at time stept+1, is summarized over all the nodes:
(13)EHt+1=∑i=1|V|‍EHit+1.


## 2.1. Static Properties

In the constructed network, a graphG(V,E) is used to describe its structure, where V is the node set and E is the edge set (Table 1 shows the basic information of the observed ecological network). Here, we consider four respective indices to analyze the static properties of the ecological network.Table 1
Basic statistics of the observed ecological network.
|
V
|
145
|
E
|
403
D
9.65
×
1
0
-
3
|
V
| denotes the number of nodes, |E| denotes the number of edges, and D=2|E|/(|V|*(|V|-1)) denotes the network density, respectively.(i) Degree Index. Degree index [22] indicates how many nodes that a nation/ocean connects to. Naturally, the degree index of node i is defined as
(1)SD(i)=∑j=1|V|‍eij,
where eij=1 if there is a link between node i and j; otherwise eij=0.(ii) Betweenness Index. Betweenness [22] is defined as how many shortest paths pass through the target node. The larger the Betweenness is, the more connective role the target node plays. In a given network, the Betweenness is denoted as
(2)SB(i)=∑j=1|V|‍∑k<j|V|‍Pkji,k≠j,
where Pkji=1 if there is a shortest path between node k and j passing node i.(iii) Closeness Index. Closeness [22] is defined as the reverse distance between the target node and other nodes. The larger the Closeness is, the closer they would be and vice versa. In a given network, the Closeness is denoted as
(3)SC(i)=1∑j=1|V|Lij,i≠j,
where Lij=1 denotes the length of the shortest path between nodes i and j.(iv)
k
-Core Index. k-core [23], denoted as SK(i), is the core number of a node which is the largest value k of a k-core containing that node. It is obtained as follows: (i) remove from the graph all nodes of degree less than k and (ii) then remove these vertices repeatedly until no further removal is possible. The remaining result, if exists, is the k-core. Thus, a network is organized as a set of successively enclosed k-cores.


## 2.2. Dynamical Factors

Besides the static network properties, we collect various data from World Bank (http://data.worldbank.org/) to investigate the dynamical factors of all the nodes in the ecological network. The dataset includes population size, per capita GDP, area of land and marine, energy consumption per unit of GDP, and carbon dioxide emission of each country from year 1962 to 2011. Specifically, we observe the five following factors for each node.(i)
Population size, denoted as PSti, is the total population of node i in the year t.(ii)
Economic level, denoted as ELti, is the per capita GDP of node i in the year t.(iii)
Habitats area, denoted as HAti, is the total area of land and marine of node i in the year t.(iv)
Energy consumption, denoted as ECti, is energy consumption per unit of GDP of node i in the year t.(v)
Air pollution, denoted as APti, is the total amount of carbon dioxide emission of node i in the year t.Figure3 shows how the five factors change from the year 1961 (HA starts from 1990 and EC starts from 1980 due to the data absence) to 2011. It can be seen that, generally, the values of all the factors increase year by year. It also shows that the population size has highly positive relationship with economic level. For example, the population size of China (CHN) and USA are both in the top five nations, and their average GDP also have high ranks among all the 126 nations. Meanwhile, their air pollution is ranked in the worst five nations, which might suggest that the development of economy would have negative impact on the environment. Furthermore, we list the top 20 nodes for both static properties and dynamical factors in Table 2. It can be seen that the Atlantic Ocean (ATO) holds the most significant role in maintaining the robustness of the ecological network because it connects the largest number of nodes (Table 3). Russia (RUS) has high network property, with degree rank number 5, Betweenness rank number 2, and Closeness rank number 2, but simultaneously has a relatively bad air quality (rank number 3). Other nations, such as China (CHN), have the similar situation. Comparatively, USA is not ranked in the top network structure list but has a large population (rank number 3) and a high economic  level (rank number 6), which might promote its impact in affecting the global Earth’s health.Table 2
Top 20 nodes of the static and dynamical properties.
Rank
S
D
S
B
S
C
S
K
PS
EL
HA
EC
AP
1
ATO
ATO
ATO
ATO
CHN
NOR
VEN
PER
USA
2
PCO
RUS
RUS
PAK
IND
CHE
DEU
COL
CHN
3
CHN
CHN
FRA
TKM
USA
DNK
ECU
CHE
RUS
4
MSO
PCO
NHO
UZB
IDN
ISL
ZMB
BWA
IND
5
RUS
MSO
ZAF
KAZ
BRA
IRL
NIC
IRL
JPN
6
INO
INO
MRT
AFG
PAK
USA
BWA
PAN
DEU
7
DEU
FRA
CHN
AZE
RUS
SWE
SAU
CRI
CAN
8
IRN
ABO
MDG
IRN
BGD
JPN
GTM
GAB
GBR
9
COD
UKR
JPO
TUR
NGA
NLD
TZA
ITA
KOR
10
ABO
JPO
PCO
FRA
JPN
FIN
ZWE
DNK
IRN
11
CBO
ZAF
CAN
FIN
MEX
AUT
DOM
ALB
ITA
12
KAZ
IRN
USA
SWE
PHL
GBR
CHE
GRC
MEX
13
UKR
MRT
ARG
AUT
DEU
BEL
SEN
TUR
ZAF
14
SDN
ERI
MEX
CZE
VNM
CAN
AUT
PRT
FRA
15
FRA
IDN
HND
DEU
EGY
DEU
SVK
GBR
SAU
16
HUN
NHO
CRI
HUN
ETH
FRA
BRA
ESP
AUS
17
POL
TUR
PAN
POL
IRN
AUS
EST
AUT
BRA
18
AUT
DEU
INO
SVK
TUR
ITA
KHM
NAM
IDN
19
BSO
BBO
NAM
CHE
THA
SGP
CIV
ECU
UKR
20
AFG
SDN
DZA
BLR
FRA
ESP
POL
SGP
ESP
S
D denotes the degree index, SB denotes the Betweenness index, SC denotes the Closeness index, and SK denotes the k-core index, respectively. PS, EL, HA, EC, and AQ, respectively, denote the population size, economic level, habitats area size, energy consumption, and air pollution in the year of 2011.Table 3
Abbreviations of ocean nodes.
Abbr.
Full name
ATO
Atlantic Ocean
PCO
Pacific Ocean
INO
Indian Ocean
ARO
Arctic Ocean
MSO
Mediterranean Sea
CBO
Caribbean Sea
BSO
Black Sea
ABO
Arabian Sea
BLO
Baltic Sea
NOO
Norwegian Sea
CPO
Caspian Sea
ACO
Antarctic Ocean
JPO
Sea of Japan
NSO
North Sea
RSO
Red Sea
CSO
South China Sea
BBO
Bay of Bengal
GMO
Gulf of Mexico
GTO
Gulf of ThailandFive factors of evolution of all nodes versus time. (a) Population; (b) economic level; (c) habitats area; (d) energy consumption per GDP; (e) air pollution. In each subgraph, five nations with top amount of corresponding property are highlighted.
(a)
(b)
(c)
(d)
(e)


## 2.3. Definition of the Earth’s Health Index

Inspired by previous analyses, we consider that the Earth’s health is not just affected by a single factor, but a joint influence resulting from many complicated factors. In this paper, we use theShannon Entropy [24–26] to integrate the impact of all possible factors to characterize the Earth’s health, denoted by EH, as
(4)EH=-∑i=1|V|‍∑j=1|F|‍pfij′logpfij′,
where fij′=(fij-fminj)/(fmaxj-fminj) is the normalized fraction of factor j for node i, |F| denotes the set of all the factors defined in Section 2.2, and the final Earth’s health value, EH, runs over the sum of all nodes. According to the original definition of Shannon Entropy, the larger the entropy value is, the more equal the distribution will be. Therefore, a large value of EH suggests a good situation of ecological balance both among nations and factors and hence indicates good Earth’s health and vice versa (Table 4).Table 4
Abbreviations of nation nodes.
Abbr.
Full name
Abbr.
Full name
AFG
Afghanistan
AGO
Angola
ALB
Albania
ARE
United Arab Emirates
ARG
Argentina
AUS
Australia
AUT
Austria
AZE
Azerbaijan
BEL
Belgium
BFA
Burkina Faso
BGR
Bulgaria
BGD
Bangladesh
BIH
Bosnia and Herzegovina
BLR
Belarus
BOL
Bolivia
BRA
Brazil
BWA
Botswana
CAF
Central African Republic
CAN
Canada
CHE
Switzerland
CHL
Chile
CHN
China
CIV
Cote D'Ivoire
CMR
Cameroon
COD
Congo
COL
Colombia
CRI
Costa Rica
CUB
Cuba
CZE
Czech Republic
DEU
Germany
DNK
Denmark
DOM
Dominican Republic
DZA
Algeria
ECU
Ecuador
ERI
Eritrea
ESP
Spain
EST
Estonia
ETH
Ethiopia
FIN
Finland
FRA
France
GAB
Gabon
GBR
United Kingdom
GHA
Ghana
GIN
Guinea
ALB
Albania
GTM
Guatemala
HND
Honduras
HRV
Croatia
HTI
Haiti
HUN
Hungary
IDN
Indonesia
IND
India
IRL
Ireland
IRN
The Islamic Republic of Iran
IRQ
Iraq
ISL
Iceland
ITA
Italy
JAM
Jamaica
JOR
Jordan
JPN
Japan
KAZ
Kazakhstan
KEN
Kenya
KGZ
Kyrgyzstan
KHM
Cambodia
KOR
Korea
LAO
Laos
LBR
Liberia
LBY
Libya
LKA
Sri Lanka
LTU
Lithuania
LVA
Latvia
MDA
Moldova
MDG
Madagascar
MEX
Mexico
MKD
Macedonia
MLI
Mali
MMR
Myanmar
MNG
Mongolia
MOZ
Mozambique
MRT
Mauritania
MYS
Malaysia
NAM
Namibia
NER
Niger
NGA
Nigeria
NIC
Nicaragua
NLD
Netherlands
NOR
Norway
NPL
Nepal
NZL
New Zealand
OMN
Oman
PAK
Pakistan
PAN
Panama
PER
Peru
PHL
Philippines
POL
Poland
PRK
North Korea
PRT
Portugal
ROU
Romania
RUS
Russian Federation
SAU
Saudi Arabia
SDN
Sudan
SEN
Senegal
SGP
Singapore
SLV
El Salvador
SOM
Somalia
SRB
Serbia
SSD
Southern Sudan
SVK
Slovak Republic
SVN
Slovenia
SWE
Sweden
TCD
Chad
THA
Thailand
TJK
Tajikistan
TKM
Turkmenistan
TUR
Turkey
TZA
Tanzania
UGA
Uganda
UKR
Ukraine
USA
United States
UZB
Uzbekistan
VEN
Bolivarian Republic of Venezuela
VNM
Vietnam
YEM
Republic of Yemen
ZAF
South Africa
ZMB
Zambia
ZWE
Zimbabwe


## 2.4. Identifying the Influential Factor via Machine Learning Approach

### 2.4.1. Random Forest

We useRandom Forest [27] to evaluate the importance of factors. Random Forest is an ensemble regressor/classifier that consists of many decision trees and then outputs the value that is the mode of the values/classes output by individual trees. In this scenario, we apply this method in a regression way and use it to evaluate each feature’s importance. Compared with other regression models, we choose the Random Forest model because of its following advantages for our solution:(i)
it can tackle high-order variable interactions or correlated predictor variables;(ii)
it can be used not only for prediction, but also to assess variable importance;(iii)
it can partially overcome the overfitting problem.


### 2.4.2. Base Learner: Classification and Regression Tree (CART)

Given a training vectorxi∈Rn, i=1,…,l and a label vector yi∈Rl, the decision tree recursively partitions the space such that the samples with the same labels can be classified together. Let the data at node m be represented by Q, for each candidate split θ=(j,tm) consisting of a feature j and threshold tm; partition data into two parts:
(5)Qright(θ)=QQleft(θ),(6)Qleft(θ)=(x,y)∣xj⟸tm.
The impurity at m is computed using an impurity function H, the choice of which depends on the task being solved:
(7)G(Q,θ)=nleftNmH(Qleft(θ))+nrightNmH(Qright(θ)).
Then, select the parameters that minimize the impurity:
(8)θ*=argminθG(Q,θ).
After this recurse for subsets Q1eft(θ*) and Qright(θ*) until the maximum allowable depth is reached, Nm<minSamples. In regression problem, for a node m, representing a region Rm with Nm observations, we choose the criterion of Mean Squared Error (MSE) as impurity function H:
(9)cm=1Nm∑i∈Nm‍yi,H(Xm)=1Nm∑i∈Nm‍(yi-c)2.


### 2.4.3. Construction of Random Forest

Let the number of training cases beN and let the number of variables in the regressor be M. We are told the number m of input variables to be used to determine the decision at a node of the tree; m should be much less than M.(i)
Choose a training set for this tree by choosingn times with replacement from all N available training cases (i.e., take a bootstrap sample). Use the rest of the cases to estimate the error of the tree.(ii)
For each node of the tree, randomly choosem variables on which to base the decision at that node. Calculate the best split based on these m variables in the training set.(iii)
Each tree is fully grown and not pruned (as may be done in constructing a normal tree classifier). For prediction a new sample is pushed down the tree. It is assigned the value of the training sample in the terminal node it ends up in.


### 2.4.4.Out-of-Bag (OOB) Evaluation

To evaluate theRandom Forest model, we use 2/3 of the data as training set and remaining 1/3 (saying Out-of-Bag) are regarded as the test set when constructing the base learner. We calculate the average result from 50-round simulations to alleviate the random fluctuations. For each tree t, the Out-of-Bag (OOB) simulation is tested in detail as follows.(i)
Consider the associatedOOBt sample.(ii)
Denote by errOOBt the error of a single tree t on this OOBt sample.(iii)
Randomly permute the values ofXj in OOBt to get a permuted sample denoted by OOBtj, the error of predictor t on the perturbed sample:
(10)err(Xj)=1Ntree∑t‍(errOOBtj-errOOBt),where Xj represents jth variable of each data. Then we can get err(Xj) for each j and normalize it. The bigger the err(Xj) is, the more important the variable is. Figure 4 shows the err(X) result for all the five features. It can be seen that, among all the features, the err(Xj) value of habitats area size is the biggest, hence the most important factor for the Earth’s health, which is in the agreement with reports by public media that people, especially humans living cities, now occupy smaller and smaller space than before, resulting in comparatively a much worse living condition.Figure 4
err(Xj) values of five representative factors versus time.


## 2.4.1. Random Forest

We useRandom Forest [27] to evaluate the importance of factors. Random Forest is an ensemble regressor/classifier that consists of many decision trees and then outputs the value that is the mode of the values/classes output by individual trees. In this scenario, we apply this method in a regression way and use it to evaluate each feature’s importance. Compared with other regression models, we choose the Random Forest model because of its following advantages for our solution:(i)
it can tackle high-order variable interactions or correlated predictor variables;(ii)
it can be used not only for prediction, but also to assess variable importance;(iii)
it can partially overcome the overfitting problem.


## 2.4.2. Base Learner: Classification and Regression Tree (CART)

Given a training vectorxi∈Rn, i=1,…,l and a label vector yi∈Rl, the decision tree recursively partitions the space such that the samples with the same labels can be classified together. Let the data at node m be represented by Q, for each candidate split θ=(j,tm) consisting of a feature j and threshold tm; partition data into two parts:
(5)Qright(θ)=QQleft(θ),(6)Qleft(θ)=(x,y)∣xj⟸tm.
The impurity at m is computed using an impurity function H, the choice of which depends on the task being solved:
(7)G(Q,θ)=nleftNmH(Qleft(θ))+nrightNmH(Qright(θ)).
Then, select the parameters that minimize the impurity:
(8)θ*=argminθG(Q,θ).
After this recurse for subsets Q1eft(θ*) and Qright(θ*) until the maximum allowable depth is reached, Nm<minSamples. In regression problem, for a node m, representing a region Rm with Nm observations, we choose the criterion of Mean Squared Error (MSE) as impurity function H:
(9)cm=1Nm∑i∈Nm‍yi,H(Xm)=1Nm∑i∈Nm‍(yi-c)2.


## 2.4.3. Construction of Random Forest

Let the number of training cases beN and let the number of variables in the regressor be M. We are told the number m of input variables to be used to determine the decision at a node of the tree; m should be much less than M.(i)
Choose a training set for this tree by choosingn times with replacement from all N available training cases (i.e., take a bootstrap sample). Use the rest of the cases to estimate the error of the tree.(ii)
For each node of the tree, randomly choosem variables on which to base the decision at that node. Calculate the best split based on these m variables in the training set.(iii)
Each tree is fully grown and not pruned (as may be done in constructing a normal tree classifier). For prediction a new sample is pushed down the tree. It is assigned the value of the training sample in the terminal node it ends up in.


## 2.4.4.Out-of-Bag (OOB) Evaluation

To evaluate theRandom Forest model, we use 2/3 of the data as training set and remaining 1/3 (saying Out-of-Bag) are regarded as the test set when constructing the base learner. We calculate the average result from 50-round simulations to alleviate the random fluctuations. For each tree t, the Out-of-Bag (OOB) simulation is tested in detail as follows.(i)
Consider the associatedOOBt sample.(ii)
Denote by errOOBt the error of a single tree t on this OOBt sample.(iii)
Randomly permute the values ofXj in OOBt to get a permuted sample denoted by OOBtj, the error of predictor t on the perturbed sample:
(10)err(Xj)=1Ntree∑t‍(errOOBtj-errOOBt),where Xj represents jth variable of each data. Then we can get err(Xj) for each j and normalize it. The bigger the err(Xj) is, the more important the variable is. Figure 4 shows the err(X) result for all the five features. It can be seen that, among all the features, the err(Xj) value of habitats area size is the biggest, hence the most important factor for the Earth’s health, which is in the agreement with reports by public media that people, especially humans living cities, now occupy smaller and smaller space than before, resulting in comparatively a much worse living condition.Figure 4
err(Xj) values of five representative factors versus time.


## 2.5. Predicting the Earth’s Health in Ecological Networks

We use a dynamic spreading model [28] to predict the Earth’s health by considering the observed ecological network structure. The model runs as follows.(i)
At the initial step, each nodei is set a health value by averaging the Earth’s health index (EHi0 defined by (4)) from the most recent five years.(ii)
We then choose 10% of the nodes as “seed” nodes and addΔEHi0 to each seed node. The ΔEHi0 is calculated by averaging over the incremental EH values of the most recent five years.(iii)
At each time stept+1, each node i will affect all its neighbouring nodes’ Earth’s health index by
(11)ΔEHi→jt+1=α*ΔEHit*(EHit*EHjt)β,
where ΔEHi→jt+1 is the Earth’s health influence from node i to j and α and β are tunable parameters.(iv)
Then, the nodej’s Earth’s health index at time step t+1 is summed over all j’s neighbours as
(12)EHjt+1=EHjt+∑eij∈E‍ΔEHi→jt+1,
where eij=1 if there is a link between node i and node j, and eij=0 otherwise.(v)
Finally, the global Earth’s health, at time stept+1, is summarized over all the nodes:
(13)EHt+1=∑i=1|V|‍EHit+1.


## 3. Results

### 3.1. Performance Comparison

To test the performance of our spreading model, we setα=4 and β=0.65 to predict the global Earth’s health in the computer simulation. In addition, we also use Gaussian Fitting to compare with our model. Figure 5 shows the comparison results. It can be seen that our model can better fit the real data, comparing with Gaussian Fitting. In addition, the proposed EH index shows that the Earth’s health is getting worse from 2008, which gives us the warning that we should put much more attention to our environment. Correspondingly, results from Section 2.4.4 suggest for us a possible solution that returning more living lands might be the most effective way to solve this dilemma.Figure 5
Earth health (EH) tendency comparisons for(1) empirical data, (2) our model, and (3) for Gaussian Fitting (GF).


### 3.2. Sensitivity Analysis

We then perform the sensitivity analysis to test the robustness of our model. We randomly deleteP fraction of the links and see whether our model is reliable or not. Figure 6 reports different prediction results of model for various values of P. It can be seen that the prediction result of model is quite robust that even a large fraction of links, 60% for instance, is removed. Therefore, it can be concluded that our model is reliable for predicting the Earth’s health.Figure 6
Comparisons with the original network for various fractions of links are removed from the network forP=0.2, 0.4, 0.6, respectively.


### 3.3. Identifying the Influential Node in Ecological Networks

Our Earth’s health index tries to diagnose and predict the global Earth’s health status. In addition, in order to find which node (saying nation or ocean) plays the most important role in affecting the Earth’s health, we additionally perform analysis to rank the node importance. We integrate thek-core value, SK(i) (see Section 2.1), and the Earth’s health index EHi to evaluate the node i’s importance, Ii, which is consequently defined as
(14)Ii=EHi*SK(i).Figure7 illustrates the node importance in affecting the Earth’ health by Ii versus the corresponding rank, where some typical nodes are marked. The oceans (with the highest rank) indeed are the key nodes in affecting the Earth’s health; USA, Russia, and China are also important nations in influencing the Earth’s health. Some small nations, such as Madagascar (MDG) and Iraq (IRQ), play less important roles for the Earth’s health.Figure 7
Node importance versus corresponding rank.


## 3.1. Performance Comparison

To test the performance of our spreading model, we setα=4 and β=0.65 to predict the global Earth’s health in the computer simulation. In addition, we also use Gaussian Fitting to compare with our model. Figure 5 shows the comparison results. It can be seen that our model can better fit the real data, comparing with Gaussian Fitting. In addition, the proposed EH index shows that the Earth’s health is getting worse from 2008, which gives us the warning that we should put much more attention to our environment. Correspondingly, results from Section 2.4.4 suggest for us a possible solution that returning more living lands might be the most effective way to solve this dilemma.Figure 5
Earth health (EH) tendency comparisons for(1) empirical data, (2) our model, and (3) for Gaussian Fitting (GF).


## 3.2. Sensitivity Analysis

We then perform the sensitivity analysis to test the robustness of our model. We randomly deleteP fraction of the links and see whether our model is reliable or not. Figure 6 reports different prediction results of model for various values of P. It can be seen that the prediction result of model is quite robust that even a large fraction of links, 60% for instance, is removed. Therefore, it can be concluded that our model is reliable for predicting the Earth’s health.Figure 6
Comparisons with the original network for various fractions of links are removed from the network forP=0.2, 0.4, 0.6, respectively.


## 3.3. Identifying the Influential Node in Ecological Networks

Our Earth’s health index tries to diagnose and predict the global Earth’s health status. In addition, in order to find which node (saying nation or ocean) plays the most important role in affecting the Earth’s health, we additionally perform analysis to rank the node importance. We integrate thek-core value, SK(i) (see Section 2.1), and the Earth’s health index EHi to evaluate the node i’s importance, Ii, which is consequently defined as
(14)Ii=EHi*SK(i).Figure7 illustrates the node importance in affecting the Earth’ health by Ii versus the corresponding rank, where some typical nodes are marked. The oceans (with the highest rank) indeed are the key nodes in affecting the Earth’s health; USA, Russia, and China are also important nations in influencing the Earth’s health. Some small nations, such as Madagascar (MDG) and Iraq (IRQ), play less important roles for the Earth’s health.Figure 7
Node importance versus corresponding rank.


## 4. Conclusion and Discussion

In this paper, we collect various data and construct a 145-nation (including 126 nations, 19 oceans/seas, and 403 edges) world ecological network, with each node representing a nation or an ocean and each edge representing geographical neighboring relationship of the corresponding two nodes. Firstly, we analyze both the topological properties and time-dependant features of nodes. Secondly, we propose an Earth’s health index based onShannon Entropy. Thirdly, we identify the importance of elements by a machine learning approach (Random Forest). Fourthly, we design a spreading model to predict the Earth’s health and perform sensitive analysis to test its robustness. Finally, we integrate the topological property (k-core index) and the health index to identify the influential nations in the observed ecological network.The model results indicated that the oceans (with the highest rank) indeed are the key nodes in affecting the Earth’s health. TheBig countries, for example, USA, Russia, and China, are also important nations in influencing the Earth’s health. Correspondingly, it suggests for us a possible solution that returning more living lands might be the most effective way to solve this dilemma. The combination of topological properties and local factors leads to good performance in both predicting the good and bad trends of the Earth’s health. The model can be easily extended by considering more factors. However, our model needs empirical support from more sufficient data. Also, the incremental mechanism may hinder long-term prediction.



---

*Source: 741318-2013-12-31.xml*