The data used in all the studies reviewed here comprised the presence and absence of pest species in different countries and regions in the world. This information was extracted with permission from the CABI Crop Protection Compendium (2003, 2007) and CABI’s Plantwise Knowledge Bank (http://www.plantwise.org/knowledgebank), which are interactive multimedia encyclopaedias edited by CABI, a not-for-profit science-based development and information organization.

Data presented by country or geographical regions where pest presence or absence is represented by binary data, with 0 corresponding to absence and 1 corresponding to presence of species in a specific geographical area. Incomplete data from the database were discarded. Depending on the taxa of interest in the study, different numbers of pest species and regions comprised the actual database used for analysis.

A detailed description of self-organising maps (SOM) can be found in Kohonen (1982) and Kohonen (2001), and examples of its application to pest risk data in Worner and Gevrey (2006) as well as Gevrey et al. (2006). The self-organising map is an unsupervised learning algorithm that is a type of neural network. A SOM consists of two layers of artificial neurons, 1) the input layer that represents the input data (pest profiles comprising, presence = 1 or absence = 0 for each species in each region) and the output layer or map, which is usually arranged in a two-dimensional structure (Fig. 1). Every input neuron or vector (pest profile) is connected to every output neuron (map neuron or node), and each connection has a weight attached to it. The batch SOM algorithm can be summarized as follows: (i) Initialize the values of the virtual (node) vectors (VVi, 1 ≤ i ≤c) using random values. (ii) Repeat steps (iii) to (vi) until convergence. (iii) Read all the sample vectors (SV or pest profiles) one at a time. (iv) Compute the Euclidean distance between SV and VV. (v) Assign each SV to the nearest VV according to the distance results. (vi) Modify each VV with the mean of the SV that were assigned to it (Worner and Gevrey 2006). In other words, when the input vectors (pest profiles for global sites) are presented to the SOM algorithm, random weight values are assigned to each virtual (weight) vector associated with each neuron (node) of the map. For each input vector (pest profile) the Euclidean distance between the input vector (pest profile) and the incoming weight (node or virtual) vector of each map neuron, is calculated. Each input vector is then assigned to the closest virtual vector (the winner, also known as the best matching unit (BMU)) according to the Euclidean distance. Each virtual vector is then updated during an iterative learning process, where weights are modified according to equation (1.1).

w_{i, j}(t+1)=w_{i, j}(t)+h(t)(x_i-w_{i, j}(t))      (1.1)

where w_{i, j}(t) is the connection weight from input i to map neuron j at time t, x_i is element i of input vector x, and h is the neighbourhood function. In other words, the neighbourhood function determines how strongly the neurons or nodes are connected to each other, as defined in equation (2).

h(t)= α exp(-d2/(2σ2(t)))      (1.2)

where α is the learning rate, which decays towards zero as time progresses, d is the Euclidean distance between the winning unit (BMU) and the current unit j, and σ is the neighbourhood width parameter, which also decays towards zero (Watts and Worner 2009b).

Basically, the large number of data vectors, or pest profiles are sorted such that those pest profiles that are most similar are associated with a particular node, neuron or cell on the map. Additionally, pest profiles associated with cells that are close to each other are more similar than those cells that are further away. While the SOM algorithm is essentially a clustering algorithm, the detail within each cluster is very useful for questions concerning the invasive species of interest. The analysis shows similarities between pest profiles of countries and regions despite that intuitively many regions may not appear to have analogous climates and environmental conditions. Clearly, however, such similarity requires close study and indeed, if the percentage similarity between any two countries in a cluster is examined one usually finds a level of similarity that is often unexpected. Clearly, the SOM analysis is only the start of a more detailed analysis into what the clusters mean. The most important result of the SOM analysis is that the SOM weights can be used to create a risk list where the weight assigned to each species (element in the vector of species) can be used as an index of the risk of those species of establishing in the target area Gevrey et al. (2006). In this way, a subset of the original 844 species can be targeted for more in-depth risk assessment.

Databases often contain errors and the concern is that such error will significantly affect the confidence in any analysis that is based on the database. Paini et al. (2010a) evaluated the sensitivity of the SOM method by altering the original presence/absence data by an increasing percentage and compared estimates of risk with those generated by a national coordinating body (Plant Health Australia) utilizing expert stakeholder opinion. The same species distribution data set as used by Worner and Gevrey (2006), described above, was used in this study. Additionally, Impact Risk Assessments (IRAs) generated by the Australian Government’s Department of Agriculture, Forestry, and Fisheries (http://www.daff.gov.au/ba/ira/final-plant) were analysed to estimate the error rate in a sample of the CABI data and to determine the range of data alteration required. To simulate database error, data from all regions in the original database (459) were altered by 5%, 10%, 20%, and 30%. To do that, a set percentage of species were randomly selected from each regional pest profile and their presence or absence records reversed. Each region was altered separately so that no two regions were altered in the same way. Paini et al. (2010a) found that evaluation of the risk posed by the species based on the SOM analysis remained unaffected by alterations of up to 20% of data over all regions (Fig. 2). Of interest was the comparison of species indicated as high risk by the SOM with expert stakeholder methodology. Unsurprisingly, the comparison revealed significant differences in the estimates of establishment risk.

Clearly, no data set is complete and the impact of potentially inaccurate or incomplete data was tested in another study where species profiles were bootstrapped (resampling with replacement) 1000 times and the change in each species rank (highest weight to the lowest) was recorded (Watts and Worner 2009b). The New Zealand regional pest profile was used. For the top 50 most highly ranked species, that were not established in New Zealand, their ranks changed on average only 14 places out of a possible 800, indicating considerable confidence in the method.

Another question is whether a SOM analysis could have helped identify those pest species that actually established in a target region. As a means of validation Worner and Soquet (2010) carried out a new SOM analysis on an updated CABI data base (CABI 2007). New Zealand’s pest profile again was used where the status of each currently established pest species was changed one at a time. In other words, if a species is established/present (1) its status was changed to not established/absent (0). The objective was to determine whether changing a species status from present to absent changes its risk index significantly. After the status of a single species was changed from present to absent, a new self-organizing map was created using the modified data and the new risk index for the target species recorded. Following that, the species status was reinstated to its original before repeating the process with the next established/present species.

By using the same initial parameters for a SOM (map size, initial weight values, number of epochs), the same clusters were formed and for each trial, the same regions were associated with the same neuron or node (cell on the map).

A rank was also associated with each species depending on its weight or risk value. Before validation the species were sorted in descending order from the species with the highest risk allocated the first rank and so on. Using ranks is a good way to measure the change in the risk by evaluating the change of rank before and after alteration. If a species rank hardly changes, in other words, if a previously present species that is changed to absent, maintains a high rank or risk index on re-analysis of the data then the self-organizing map has performed well.

The Spearman’s rank correlation between ranks obtained before and after data modification was r = 0.987, showing high correlation. Altering the data did not have a significant influence on risk assessment. A species that is highly ranked remains highly ranked even though its status is changed. Notably, the cluster to which New Zealand was assigned also never changed, nor were the adjacent neurons modified. Those results once again, illustrated the stability of the method.

The average change in risk values for the top 100 pests was 0.07 and the ranks changed on average, 14 places (Fig. 2) for the 120 established species when their status was changed to absent (Worner and Soquet 2010). Clearly, their initial high risk index barely changed after data transformation thus a SOM analysis would have identified these species as high risk before they established in New Zealand. Despite this, a change of status of 4 of the 120 species currently present in New Zealand resulted in a change of cluster. For these 4 species the risks values also changed considerably. Some species have low initial risk simply because of low prevalence. Any interpretation of risk for low prevalence species, in other words less than about 20 occurrences, requires much caution and should be based on additional information. It is clear however that this tool is robust enough to not be influenced by even quite large variations for a large number of known global crop pests.

Suiter (2011) carried out a SOM analysis on USA data. The data bases used were the Global Pest and Disease Database (GPDD) which is an archive of information for pests of concern to the USA. The study also used data extracted from the CABI Crop Protection Compendium (CPC) as described above for comparative analysis. The GPDD comprised over 3000 species and is well used by many agencies such as the United States Department of Agriculture (USDA), Customs and Border Protection (CBP), Department of Homeland Security (DHS) and State Co-operators. In contrast to the study carried out by Worner and Gevrey (2006) and Gevrey et al. (2006), Suiter (2011) included all pest species recorded in the respective data bases, from bacteria to weeds, in the analysis. World pest distribution data extracted from both databases included only distributions marked as “Present”. “Unverified, Uncertain, Eradicated, Intercepted” and “Questionable” citations were discarded. The resulting analysis of the GPDD data comprised 45, 051 unique distribution records and for the CABI database, there were 47, 411 unique distribution records. Interestingly, there was only 9.8% overlap in the species recorded in each database (Fig. 4). Of particular interest with respect to validation of the SOM method was the number of high risk species, as determined by the SOM method, that were not established in 2007, that subsequently established by 2011. A 10 X 15 SOM map was used for the analysis and the databases were analysed separately.

The analysis of the GPDD database showed six species with high risk indices that had not established in 2007 had established by 2011 and also six species with high risk indices in the CABI database. These species were not the same, so 12 high risk species have subsequently established by 2011. It is not known whether any of these species were regulated at the time or whether they were on any agency risk list. It appears that the SOM analysis is a useful filter that may alert risk assessors to potential threats that require a closer analysis.

Suiter (2011) found that the SOM analysis was quite robust and provided a consistent fit of the neural network to the pest distribution data. Suiter (2011) pointed out that the results of the analysis may be subject to data over- or under-sampling artefacts. For example, countries that have been heavily sampled for invasive pests (i.e., USA, China, Australia) consistently cluster together on the SOM neural net. Suiter (2011) concluded that this could be due to one or more of several factors, 1) a high probability of overlap in pest assemblages for countries with a large number of pests, 2) the countries are vast with a wide range of climates that may be very similar, 3) the countries with high pest numbers may be major trading partners and the similarities in current pest assemblages are most likely historical in nature due to trade and human movement, and 4) these countries have the resources and capacity to survey for invasive pests, unlike poorer countries. However, comparing the results of Suiter (2011) with the findings of Worner and Gevrey (2006) it appears that oversampling does not completely explain why some clusters occur. For example, Worner and Gevrey (2006) found that some countries (e.g., Tasmania, 63 species) in the New Zealand cluster had only half the number of species as some other countries (Canary Islands, 125) in the same cluster. Also the fact that trading history is important has always been proposed as one of the reasons why some pest assemblages are similar (Worner and Gevrey 2006, Paini et al. 2010b).

The Suiter (2011) study found that of the 2600 GPDD pests and 2500 CABI pests, only 505 (9.8%) (Fig. 4) were shared by both datasets and despite that, the GPDD and CABI geopolitical SOM projections looked very similar. When risk rankings were used to produce a prioritized pest list, the species compositions generated for the United States for both datasets were quite different. The study illustrates that the composition of the pest species complex present in a dataset and the distribution of species in the country of interest, are important. When there are many endemic pests in the data matrix for a large area like USA, the Euclidean distance values (risk ratings) for pests tend to be significantly lower in general than if the majority of species in the pest profile are not present in the country. That result highlights the need to analyse and interpret the results of each database separately and be mindful of endemic species that may have very low global prevalence and therefore tend not to co-occur with many other species. The fact that each database was able to highlight the risk of a number of species that had not established in 2007 but subsequently established by 2011 (Suiter 2011), illustrates that the information in each database, despite being different, is valid.

Paini et al. (2011) tested the ability of the SOM to rank fungal species that could establish in a region above those species that couldn’t establish according to simulated data. The authors did this in a virtual world in which regions had particular characteristics and species had particular requirements. Surprisingly, there was little or no difference between species that had low prevalence and species that were widely distributed and the success rate was above 90% for all species.

K-means is an unsupervised algorithm that performs clustering (Lloyd 1982). In other words, the algorithm finds the best way to partition data into groups or clusters. The name k-means comes from the fact that the user decides how many clusters (k clusters) are necessary to partition data. The k-means algorithm proceeds as follows:

1. Choose k initial centres. These centres (vectors) can be generated randomly or they can be vectors that are randomly selected from the data set.
2. For each data vector (eg. regional pest profile), calculate the distance to each of the k cluster centres.
3. Assign each data vector (pest profile) to its nearest cluster.
4. Calculate new cluster centres, corresponding to the mean of all vectors in each cluster.
5. Repeat steps 2-4 until a stopping condition is reached. This is usually when vectors no longer change the cluster they are assigned to, that is, the clusters are stable.

The approach of using k-means to analyse the regional pest profiles is the same as the self-organizing one where geographical regions are clustered together based on their pest species assemblage (pest profiles) to determine which species are more likely to establish in a new region. In k-means, the risk index of a species establishing in a specific region is assessed by its frequency of presence in the vectors/pest profiles in the cluster to which the target region has been assigned. Watts and Worner (2009a, 2009b, 2011, 2012) have reported a number of analyses of the CABI data set (2003, 2007) described above, using k-means clustering. In Watts and Worner (2009b) the results of clustering insect assemblages with SOM were compared with the results of the k-means algorithm. While that study found that in some ways k-means could be superior to SOM, several issues were left unaddressed such as the effect of noise or small random changes to the performance of each algorithm.

Watts and Worner (2012) compared the performance of SOM maps with the performance of equivalent k-means algorithms over assemblages of bacterial crop diseases and also investigated the effects of adding noise to the assemblages and measuring cluster quality. Cluster quality for each algorithm was measured using quantisation error (Hansen and Jaumard 1997), which is the mean distance between each vector and the centre of its cluster. In addition, the computational efficiency of each algorithm was also considered. While the Watts and Worner (2012) study found differences in the performance of the clustering algorithms in most instances the difference are not significant. More important, however, in this study as well as previous studies, the different algorithms give high to medium risk indices to basically the same species. For example, in the Watts and Worner (2012) study only 12 species out of the top 80 used for the comparisons, were not in both the SOM and k-means risk lists.

Borgatti (1994) and Hastie et al. (2009) give good explanations of hierarchical clustering as a means of classifying similar samples or objects. Given a set of N items to be clustered, the start of the hierarchical agglomerative clustering is to:

Assign each item to its own cluster. In each of the subsequent steps, two clusters are merged and a new cluster is formed until all clusters are merged into a single cluster. There are various methods to determine which clusters are merged, for example using the most similar pair of observations in two clusters (single linkage), the most dissimilar pair of observations (complete linkage) or the dissimilarity between the average of the observations in each cluster (group average; Hastie et al. 2009). The method used to merge clusters determines the size of the clusters and the relationships between them. A dendrogram provides a graphical representation of the relationship between the clustered items by plotting each merge at the similarity (distance) between the merged groups. It is important to note that, like the other clustering techniques discussed in this paper the clustering result does not imply a causal relationship and should be interpreted with caution.

An example of a hierarchical cluster analysis of the CABI data is provided by Eschen and Kenis (2012) who investigated the trade in woody plants for planting in Europe, as a major pathway for the introduction of alien forest pests and diseases. While phytosanitary inspections at the import stage are essential to prevent such introductions, Eschen and Kenis (2012) suggest they are limited and tend to target recognised pests, particular hosts and shipments that are likely to contain them. Such phytosanitary inspections tend to be biased, moreover, the identification of risk depends to some extent on expert judgement. The aim of the Eschen and Kenis (2012) analysis was to provide an objective assessment of the risk posed by individual species and identification or prediction of potential sources of invasive species based on the global distribution of known pests. Eschen and Kenis (2012) analysed distribution data (presence/absence data) obtained from CABI’s Plantwise Knowledge Bank (http://www.plantwise.org/knowledgebank) for 1009 invertebrate pests and pathogens of woody hosts in 351 global regions within 183 countries. Seven large countries were subdivided into regions. The 1009 taxa were divided into twelve groups (4 micro-organism and 8 invertebrate taxa).

Countries and regions with similar pest species assemblages were identified for each organism group using hierarchical cluster analysis and the likelihood of establishment of those species was calculated as the proportion or frequency of countries within the cluster containing EU and European Free Trade Association countries (EFTA) where each species has been recorded as present. Taxa recorded in fewer than six regions were excluded from the analysis to reduce the influence of rare species and outliers. Eschen and Kenis (2012) used Ward minimum variance method (Ward 1963) to determine which clusters were merged, as it consistently produced interpretable clusters, while other methods did not. The optimal number of clusters was determined for each of the twelve groups of taxa using the Davies-Bouldin Index, a measure based on the ratio between the variation within and between clusters (Davies and Bouldin 1979).

Interpretable clusters were formed for all groups of taxa, except for the Oomycetes, where the European countries were spread over all clusters. Clusters for micro-organisms contained nearly twice as many regions as clusters for invertebrates (111 vs. 61 regions per cluster). The non-EU regions with the most similar pest species assemblages to EU regions were North America, the Mediterranean region, the northern part of Eurasia and Australia/New Zealand (Fig. 5), which have a broadly similar climatic range as the EU and a long history of intensive trade. Most pest species in the database used for hierarchical analysis were already present in one or more EU countries at the time of the study, which indicated that the risk of these species primarily comes from within the EU and is similar to the result of Paini et al. (2010b), who used a SOM to identify potential new invasive agricultural invertebrate pests for the USA and also found that the majority of species in their dataset were already recorded in one or more states. Moreover, the high proportion of species already recorded in the target region lowered the risk values (Suiter 2011). Eschen and Kenis (2012) suggested that combining the results of this analysis with economic data could provide a clearer indication about the likely origin of unidentified, future alien species establishing in Europe, that should be considered when assessing the risks associated with the import of woody plants for planting.

Plant-parasitic nematodes (PPN) cause estimated losses of $157 billion/year worldwide (Abad et al. 2008) and documented losses of $600 million/year in Australia (Hodda 2009). Fortunately, Australia does not have many of the globally damaging and quarantinable PPN species and the current losses result from the activities of a relatively few damaging species, such as root-knot nematodes, root lesion nematodes, cereal cyst nematode, Heterodera avenae and potato cyst nematode, Globodera rostochiensis (in the state of Victoria only). Despite this, trade is increasing, as it is in many other countries, thus providing multiple pathways for introduction of more exotic nematode species. Based on the need for a system to prioritize risks from many PPN species and to predict their potential biosecurity threats, Singh et al. (2012) carried out a study that analysed the distribution data of 250 PPN species from 355 regions worldwide using a SOM. As in the previous studies, Singh et al. (2012) compared the presence and absence of pest species in Australia to other regions of the world by clustering regions with species assemblages similar to Australia and her component states. The SOM was also used to determine regions which could act as a donor for potential invasive species.

Singh et al. (2012) considered that in addition to distribution, there are other criteria that contribute towards the risks and impact of a species. Additionally, there are often biases in the distribution data as thorough nematode surveys are lacking in countries where there is very limited nematological expertise available. In consideration of all these factors, Singh et al. (2012) devised an assessment including the following nine criteria. For example, 1) the existence of particular pathways, 2) survival adaptations, 3) pathogenicity, 4) host range, 5) whether the species is an emerging pest, 6) its taxonomy, 7) the existence of particular pathotypes and, 8) association in disease complexes, and, 9) the level of knowledge that exists about the species. For each of the nine criteria, a probability scale was established indicating the level of risk. For example, for the pine wilt nematode, Bursaphelenchus xylophilus, and the criterion “Pathways”, they define the probability scale as, a) association with propagative material p ≥ 0.6, b) association as a contaminant, p < 0.6 > 0.3, c) not directly associated with trade p < 0.3. For each criterion, probability values were estimated based on both literature search and expert judgment. Following that, weights were assigned based on the relative contribution of each criterion towards the biosecurity risk. The SOM index from the analysis of PPN distributions was combined with the values from the nine criteria and the sum of the weighted average values was calculated to determine the overall biosecurity risk.

Initial SOM clustering indicated that potential donor regions or regions from where species are most likely to pose the greatest threat were unsurprisingly, Australia’s major trading partners. Bursaphelenchus xylophilus is a well known quarantine nematode species and based on the SOM analysis of the distribution data the resulting SOM index of 0.37 indicated the species to be of medium risk. Singh et al. (2012) used SOM index risk scale, > 0.7 = High, < 0.7 > 0.3 = Medium and < 0.3 = Low risk. When the criteria based assessment was included, the resulting risk value was much higher than that estimated by the SOM index alone (Table 1).

The higher risk is the result of considering the potential economic impacts of the species and additional information such as recent spread and availability of pathways as indicated by the number of interceptions in wood packaging materials and pine timber products. Another example is the carrot cyst nematode, Heterodera carotae, an economically important pest which currently has a restricted distribution. However, despite this restricted distribution, there is evidence of its spread and also its good survival adaptations by the formation of cysts. The SOM estimate ranked the species as low risk, but based on the multicriteria analysis, it becomes categorised as a medium risk species (Table 2).

The study by Singh et al. (2012) illustrates, as Worner and Gevrey (2006) suggested, that relying only on SOM estimates alone may lead to under- or overestimation of risks depending on the species. SOM remains a useful method for initial prioritization and can be incorporated with criteria based methods to better estimate a species biosecurity risks. A similar suggestion was made by Eschen and Kenis (2012), who found that their analysis did not identify Asia as a potentially important source or donor region for new invasive pests, despite a recent, strong increase in trade in plants for planting from that region.