In most models of collective motion in animal groups each individual updates its heading based on the current positions and headings of its neighbors. Several authors have investigated the effects of including anticipation into models of this type . Key findings include that anticipation inhibits polarized collective motion in alignment based models and promotes milling and swarming in the one attraction-repulsion model studied. However, it was recently reported that polarized collective motion do emerge in an alignment based asynchronous lattice model with mutual anticipation. To our knowledge this is the only reported case where polarized collective motion has been observed in a model with anticipation. Here we show that including anticipation promotes polarized collective motion in a synchronous, off lattice, attraction based model. Establishing that anticipation can be a promoter of polarized collective motion in certain models and that asynchrony, mutual anticipation , or motion restricted to a lattice are not necessary requirements for polarized collective motion to emerge in models with anticipation . In addition, unlike alignment based models the attraction based model used here does not produce any type of polarized collective motion in the absence of anticipation. So here anticipation is a direct polarization inducing mechanism and we believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.
In most models of collective motion in animal groups each individual updates its heading based on the current positions and headings of its neighbors. Several authors have investigated the effects of including anticipation into models of this type , and have found that anticipation inhibits polarized collective motion in alignment based models and promotes milling and swarming in the one attraction-repulsion model studied. However, it was recently reported that polarized collective motion does emerge in an alignment based asynchronous lattice model with mutual anticipation. To our knowledge this is the only reported case where polarized collective motion has been observed in a model with anticipation. Here we show that including anticipation induces polarized collective motion in a synchronous, off lattice, attraction based model. This establishes that neither asynchrony, mutual anticipation nor motion restricted to a lattice environment are strict requirements for anticipation to promote polarized collective motion . In addition, unlike alignment based models the attraction based model used here does not produce any type of polarized collective motion in the absence of anticipation. Here anticipation is a direct polarization inducing mechanism . We believe that utilizing anticipation instead of frequently used alternatives such as explicit alignment terms, asynchronous updates and asymmetric interactions to generate polarized collective motion may be advantageous in some cases.
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