A general characterization of networks with N nodes and E edges can be

provided by different metrics. The centrality metrics we evaluated here (Table

1) were average degree (2E/N), maximum degree, average shortest path

(average number of edges separating any two nodes in the network when a

path exists), connectance (E divided by the total possible number of edges),

and transitivity (defined for any node as the fraction of nodes connected to it

that are also connected to each other).

Global cropland connectivity as a risk factor for pathogen and pest saturation and crop losses: the case of banana, cassava, potato, sweetpotato, and yam

J. Hernandez Nopsa1*, Y. Xing1, J. Andrade-Piedra2, F. Beed3, G. Blomme4, M. Carvajal Yepes5, D. Coyne10, G. Forbes6, J. Kreuze7, J. Kroschel7, L. Kumar8, J. Legg3, M. Parker9, E. Schulte-Geldermann9, and K.A. Garrett1,11

1Kansas State University, Manhattan, KS, USA, 2International Potato Center (CIP), Quito, Ecuador, 3International Institute of Tropical Agriculture (IITA), Dar es Salaam, Tanzania, 4Bioversity, Kampala, Uganda, 5International Center for Tropical Agriculture (CIAT), Cali, Colombia, 6CIP, Beijing,

China, 7CIP, Lima, Peru, 8IITA, Ibadan, Nigeria, 9CIP, Nairobi, Kenya, 10IITA, Nairobi, Kenya, , 11University of Florida, Gainesville, FL, USA. *Contact information: Ph. 785-532-1346, e-mail: nopsa@ksu.edu

We characterize the cropland networks for the six crops (Fig. 2, left) and

identify differences among their structures reflected in their metrics (Table 1).

Nodes that are linked to many other nodes (nodes that have high degree) may

be particularly important for the spread of invasive pathogens and pests.

Nodes that act as bridges between cropland regions (nodes that have high

betweenness centrality (BE)) represent another important type of invasion and

saturation risk (e.g., Russia and Poland, Fig. 2C.).

We also propose a novel index to represent the component of invasion

risk based on cropland connectivity (mapped in Fig. 2, right). This index is

constructed as a weighted mean of the components below, giving half the

weight to a measure of the importance of the node as a bridge (BE), and half

the weight to other metrics that measure how strongly a node and its

neighbors are connected. The cropland connectivity risk index was defined as:

• 1/2 Betweenness centrality (the number of shortest paths crossing a node)

• 1/6 Node strength (the sum of the edge weights)

• 1/6 Mean nearest neighbor node degree (mean number of edges for

neighbors of the focal node)

• 1/6 Eigenvalue centrality (gives each node a score proportional to the sum

of the scores of its neighbors and their neighbors)

All metrics were scaled as a proportion of their maximum value. As an overall

measure of cropland connectivity risk for this set of crops, we also evaluated a

general index for these six crops by adding the individual risk indices (Fig. 3).

The maps illustrate the invasion and saturation risk due to cropland

connectivity for each crop (Fig. 2). High risk areas may be priorities for

surveillance and management strategies to control emerging pests and

diseases affecting each crop. The map of combined cropland connectivity risk

(Fig. 3) suggests that two regions in Africa (Great Lakes Region and the region

between Ghana and Nigeria) have a very high risk component for multiple

crops. Central China and Eastern Europe have some high risk areas, as well.

Cropland connectivity risk can be combined with other risk components, such

as the structure of trade networks and patterns of environmental

conduciveness to disease, in an integrated program to manage emerging

diseases and pests.

Fig. 1. Root, tuber, and banana crops are a primary source of calories for most of the world.

Clockwise from top left: banana, potato, cassava, and sweetpotato.

Introduction

We analyzed global cropland area data from ca. 2000 (Monfreda et al.

2008) for banana and plantain (combined in one analysis), cassava, potato,

sweetpotato, and yam. Data were aggregated by finding the mean for each

crop across 24x24 units of 5’x5’ for a final resolution of 120’x120’ (2ox2o) in

each cropland node. We retained nodes for which the mean proportion

cropland area was greater than 0.002. We described the risk component for

pathogen or pest movement between each pair of nodes as a function of the

distance between the nodes and the cropping density at the nodes. The

distance effect on the risk was calculated as a function of Euclidean distance

between nodes i and j (dij) as dij-β, where higher β reflects lower likelihood of

long-distance dispersal.

Data Source and Evaluation

Acknowledgements

We appreciate the support of CGIAR Research Program on Roots, Tubers, and Bananas, and the Kansas Agricultural Experiment Station. Special thanks to Dr. Thomas-Sharma.

The geographic connectedness of cropland is an important risk factor for

invasion and saturation by crop-specific pathogens. Understanding the

structure of cropland networks supports sampling, management, and

mitigation strategies. We evaluated global networks of six vegetatively–

propagated crops (banana and plantain, cassava, potato, sweetpotato, and

yam, Fig. 1), because of their major role as a source of energy in the tropics,

and their importance to smallholder farmers in developing countries. Plant

diseases and pests are notorious for their negative effect, reducing yields and

affecting food security, especially in developing countries. The objectives of

the present work are to i) characterize the network structure of global cropland

for banana and plantain, cassava, potato, sweetpotato, and yam, ii) evaluate

the network structure in terms of its potential impact on pest and disease risk

globally and develop an index for cropland connectivity risk, and iii) use the

network structure to identify priorities for surveillance and management of

emerging pests and diseases.

Metrics Used to Describe the Networks Cropland Networks and Maps of Connectivity Index

Banana Cassava Potato Sweetpotato Yam WH EH WH EH WH EH WH EH WH EH

Average Degree

0.11 1.03 0.06 2.16 0.04 2.89 - 2.48 - 4.12

Maximum Degree

2 12 2 36 1 59 - 31 - 20

Connectance 0.001 0.004 0 0.005 0 0.003 - 0.007 - 0.061

Transitivity 0 0.84 0 0.43 - 0.56 - 0.55 - 0.59

Average Shortest path 1.25 1.42 1.33 2.21 1.00 2.36 - 2.03 - 1.67

Fig. 3. Combined cropland connectivity risk index (the sum of the indices for the six individual

crops). Higher values of the index reflect greater connectivity for geographic locations based

on cropland area, a risk factor for invasions (β=1).

Fig. 2. Network of cropland connectivity (left) and map of cropland connectivity risk index

(right, defined in third column) in the Eastern Hemisphere. Nodes in the network represent

areas of production and links show the risk component for pathogen/pest movement between

nodes.

Cropland Connectivity Risk Index

Table 1: Characterization of network metrics in the Western Hemisphere (WH) and Eastern

Hemisphere (EH) for the six crops. Examples given are for β=1. Values presented are for

networks where there were enough nodes above the threshold for analysis.

E. Yam

Cropping area data

(5’x5’) for each crop

Risk associated with pair of nodes

is product of power law function

of distance between nodes and

gravity model product of

cropland area in the

nodes

Data aggregation

2ox2o to produce

cropland nodes

Mapping of cropland connectivity

risk index (Fig. 2, right)

Characterization and construction of

networks of cropland connectivity (Fig.2, left)

Mapping of combined cropland connectivity risk

index (Fig. 3) by summing individual crop risk

B. Cassava

A. Banana and plantain

C. Potato

D. Sweetpotato

The risk due to greater cropland area for any two nodes i and j was

accounted for using a gravity model, by multiplying together the mean cropland

area (c) in each of the nodes (ci cj). Thus in the first step, the weights in the

adjacency matrix, indicating the overall risk of movement between two

geographic nodes, were ci cj dij-β. We then used a threshold minimum value of

0.0001 and set weights below that to 0. Network models of cropland

connectivity for the six crops analyzed here are illustrated for the Eastern

Hemisphere (Fig. 2) and evaluated globally (Table 1). We used the R

programming environment (R Core Team, 2013), the igraph package (Csardi

and Nepusz, 2006) and the raster package (Hijmans, 2014).