Mathematically similar movement kernels yield contrasting ecological outcomes in insect trapping

Danish A. Ahmed

Insect movement is often described using random-walk models but comparing ecological outcomes of short- and long-distance movement can depend on how their underlying movement kernels are related. Here, thin- and heavy-tailed step-length distributions are linked through a common survival probability and then optimally compared using a similarity measure, providing an objective comparison when an independent ecological basis is lacking. Because the optimal relationship differs among spatial dimensions, we examine its consequences across three insect-trapping systems: one-dimensional trap cropping, where pests are attracted from a cash crop to a terminal trap crop and may be retained, removed or emigrate; two-dimensional pitfall trapping, where randomly moving ground-dwelling arthropods encounter passive traps; and three-dimensional flight interception, where flying insects may encounter, be captured by, or bypass a finite panel. Across these systems, optimally related movement kernels produced contrasting ecological outcomes. In trap-cropping, the relative advantage of long-distance movement depended on attraction strength and trap-crop allocation, reversing from greater to lower removal as attraction increased. In pitfall trapping, long-distance movement generally increased cumulative capture within a confined spatial domain, with trap counts increasing with survival probability. However, non-optimal values could produce similar capture to short-distance movement, potentially masking the effect of movement type. In the flight interception model, long-distance movement reduced panel interception and capture while increasing edge leakage. Thus, mathematically optimal similarity between movement kernels does not ensure ecological equivalence. Rather, the remaining differences in displacement structure interact with behavioural responses, boundary effects and trapping geometry, producing outcomes that vary among ecological contexts.