Studying the spatial distribution of cabbage aphids, Brevicoryne brassicae L. in commercial canola field sites, Severtson et al. also found significantly higher counts of this important pest within 20–30 m from field edges compared to further inwards into canola fields. Based on logistic regression, the population density of cabbage aphids was found to be negatively correlated with the distance from field edges in dryland canola host plants. Besides aphids, cabbage seed weevils, Ceutorhynchus assimilis Paykull , displayed a similar spatiotemporal pattern of distribution in winter oilseed rape . A study describing the distribution of Andean potato weevils, Premnotrypes spp. , showed heavier infestation of potato tubers along field edges . Edge-biased distribution was also reported regarding wheat stem sawflies, Cephus cinctus Norton , in dryland wheat fields .In the context of stored products, warehouse walls can be considered as physical or environmental edges. Insects associated with stored products have been shown to aggregate along warehouse walls and near physical edges. A study of the spatial distribution of red flour beetles, Tribolium castaneum Herbst , in stored wheat warehouse showed consistent aggregations along warehouse walls . This wall-biased distribution has also been observed regarding other stored product pests, such as Trogoderma variabile Ballion . Similarly, a study of the distribution of insect pests in a botanical warehouse in Florida found higher abundance of both moths and beetles [Cadra cautella Walker , Lasioderma serricorne Fabricius , Oryzaephilus mercator Fauvel , Typhaea stercorea L. , and Indianmeal moths, Plodia interpunctella Hübner ] along the walls and corners of the warehouse . In an experimental study with pheromone traps placed in 1-m intervals along a vertical gradient from the floor level to the ceiling in a 6-m tall warehouse,nft growing system most Indian meal moths were caught predominantly either near the ground level or near the ceiling , thus showing a vertical edge-biased distribution.

Interestingly, the same study showed that the moths’ preference for vertical edges could be eliminated through addition of landing surfaces to pheromone traps or by placing traps near walls. Thus, the study by Nansen et al. showed important ways to enhance moth trap captures through a combination of manipulation and targeted placements of traps near walls, and both improvements hinged on the importance of recognizing edge bias of moth captures.Several small-scale laboratory studies have indicated the occurrence of edge-biased distributions of insects. As an example, female almond moths, C. cautella, were released into a 120-cm-square arena with uniform layers of intact or cracked peanuts, and the spatial distribution of eggs laid by these female was recorded after 48 h . The results indicated that when peanuts filled the entire arena, female almond moths significantly aggregated their oviposition along arena edges. Moreover, when only the central 25% of the arena was filled with peanuts, the majority of the eggs were found along the edges of the peanut patches instead of the edge of the arena. Similarly, the infestation pattern of the red flour beetles, T. castaneum, also showed insect aggregations along arena edges .Given the prevalence of edge-biased distributions of insects in agricultural systems, it seems of considerable importance to unravel the driving mechanisms of the phenomenon. One of the common approaches used in the study of edge-biased distributions is the development of models that can simulate the edged-biased pattern of insect distributions. Although these models are theoretical and based on assumptions that are difficult to validate, they have been used widely on a conceptual basis and also to produce meaningful predictions of insect distributions.In Eq. , the factor D is known as the diffusion coefficient, which can be estimated through the mean square difference of displacement of insects over time . Predicted dispersal distributions based on Eq. 1 are presented in Fig. 2, and it is seen that they follow a normal distribution with population density being highest at the center of dispersal and gradually decreasing over distance.

Based on simple diffusion, an animal is predicted to have highest abundance near edges due to spillover , as individuals transition from one habitat into other and unlikely move far into the new habitat . A series of mark release and recapture experiments with multiple insect pest species [Phyllotreta cruciferae Goeze , Phyllotreta striolata Fabricius , and Trirhabda sericotrachyla Blake ] displayed distribution patterns characterized by highest population density at the point of release and gradual decrease over distance away from the original point of release . In addition, Severtson et al. conducted an experimental release study with alate cabbage aphids released into centers of small plots of canola and found that the distribution of cabbage aphids also followed a diffusive pattern. These experiments, as well as the predicted frequency distributed depicted in Fig. 2, assume dispersal from a single point. In reality, the actual insect distribution in agricultural systems would more likely involve multiple points of dispersal which, depending on their relative distances to each other and relative positions to field edges, can result in different distribution patterns. If centers of dispersal are located outside an agricultural system, simple diffusion models will predict that the colonization of insects will lead to higher population densities along field edges as compared to inwards into an agricultural system. However, if dispersal centers are located within an agricultural field, the bell-shaped curve distribution of insects will result in lower population density along field edges and higher population density in the interior. Such a counter-edge effect distribution pattern has been noted in nymphs of potato psyllid, Bactericera cockerelli Sulc , in commercial fields of potato .Despite support for the simple diffusion model, this model does not explain the initial aggregation point and therefore what is driving the establishment of insect populations near edges. In addition, Liebhold and Tobin argue that the relevance of simple diffusion models to predict spatial distributions of insects is limited to small spatial scales and fails to account for greater rate of diffusion at large spatial scales. In addition, largescale insect distributions show a certain degree of aggregation and patchiness that varies over time . To account for the patchiness of insect distributions and the faster speed of insect dispersal at a large spatial scale, Liebhold and Tobin propose stratified diffusion model to consider the effects of stochastic events, such as accidental spread of insects due to human activities and prevailing wind .

That means there will be groups of insect colonies leaping ahead of the main population front line. Each of these new groups become new centers of dispersal. Although stratified diffusion model has been shown to improve predictions of insect distributions compared to simple diffusion models, they are also known to have limitations. Stratified diffusion models,vertical hydroponic nft system just like simple diffusion models, rely on the concept of insect population density over distance as a time-dependent function. As time elapses, insects will eventually spread randomly and evenly across crop fields with little population density variance, failing to account for the aggregation and patchiness in insect distribution in many agricultural systems in the long term.To overcome the limitations of simple and stratified diffusion models, there is a need to revisit the major assumptions of these two models. Both models rely on the assumption that insect movement and dispersal, to a large extent, are intrinsic to their biological processes, such as their natural mobility and population growth rate. Thus, the complex influences of external environment have been simplified. Although stratified diffusion model does factor in the effects of stochastic events on insect distribution, these events often occur at irregular frequencies and within very short duration of time. After these short events, pockets of insects are still expected to spread via simple diffusion mechanism. Therefore, in relation to edge effect, the interest of modeling would be to directly address the question: How far does an edge environment affect the spatial distribution of insects in agricultural systems? The theoretical response to such a question entails three possibilities: Edges have no effect, repelling effect, and aggregating effect on insect spatial distribution. Several influential edge models have been developed to reflect the above mentioned possibilities of edge influence, including null-edge, attractive-edge, and reflective-edge models by Olson and Andow ; absorptive-edge model by Fagan et al. ; and the edge resource model . Therefore, nulledge model is essentially a simple diffusion model, which predicts a bell-shaped distribution of insects within an agricultural system . Unlike null-edge model, reflective-edge model considers edges as unfavorable environments that directly bounce insects back into the interior by altering their direction of movement . Meanwhile, absorptive-edge model assumes that the environment outside an edge is lethal for insects, resulting in declining population density towards the edge. Similarly, attractive-edge model assumes the ability of an edge to pull insects and/or trap them, leading to their aggregation along the edge . Although both absorptive-edge and attractive-edge models produce mathematical simulations for the aggregation of insects along edges, their difference lies in whether or not insects are lost to the adjacent habitat. In absorptive-edge model, once insects cross the edge boundary to the lethal habitat, they are lost from the original habitat. Meanwhile, in attractive-edge model, insects crossing the boundary to less favorable habitat can return to the original and more favorable habitat, leading to their accumulation along edges.

Ries and Sisk argued that accumulation of species at habitat edges is widely accepted to be driven by three mechanisms: spillover, edges as enhanced habitats, and complementary resource distributions. Moreover, they argued that a conceptual model based on resource availability and quality of bordering habitats can be used to predict the likelihood of edge-biased distributions. Of all the influential edge models, the attractive-edge model and the edge resource model most closely resemble the discussed edge biased distribution of insects, providing conceptual basis for the understanding of edge-biased distributions. The strength of attractive-edge modeling approach, as compared to simple diffusion modeling approaches, is its consideration of the constraints imposed by edge environment on insect spatial distribution. These constraints most likely stem from the inherent features of the edge environment , which are relatively stable. Therefore, the attractive-edge model can potentially provide the explanation of edge-biased distribution of insects in the long term as seen from certain case studies of edge effect.In light of an attractive edge as a potential explanation for the occurrence of edge-biased insect distributions in agricultural systems, the following question needs to be discussed: What set of conditions would make an agricultural edge attractive? Before further discussion of this question, it is worth mentioning that the term “attractive edge,” as described by Olson and Andow , should be broadly understood as an edge environment that leads to higher insect density than further inwards into agricultural systems. Therefore, an attractive edge does not necessarily act as favorable environment that attracts insects, but it can also or simply act as a trapping environment that reduces insects’ dispersal.Within the large body of literature on factors affecting insect movement, wind has been investigated extensively. Small-bodied, weak flying, or airborne insect pests often rely on air flows for their dispersal and colonization of crop fields . Studies of small-bodied flies and bark beetles showed less likelihood of dispersal under strong winds. However, in a study of fruit flies [Ceratitis capitata Wiedemann ] dispersal into an area of 3600 ha which was treated with chemosterilant bait stations, Navarro-Llopis et al. concluded that the fruit flies showed an edge effect but traveled over 1 km into the treated area. Wind patterns are relevant to a discussion about edge-biased insect distributions in agricultural landscapes, because the presence of hedgerows and artificial windbreaks along field edges has been shown to create a triangular region right behind it known as the “quiet zone” whose length extends to around twice the height of the barriers . This region is characterized by very weak or no winds . Right next to the quiet zone is the “wake zone” where wind speed starts to increase to its original value . Accordingly, Lewis conducted a series of studies to quantify the distribution of insects in relation to distance from artificial windbreaks in fields. The studies found that there were several fold higher densities of gall midges , moth flies , and seven times more fruit flies and day-flying thrips on the leeward side at a distance equivalent to one wind break height away from the windbreak as compared to unsheltered fields. A similar windbreak-skewed distribution was observed in the lettuce root aphid, Pemphigus bursarius L. .