A Delayed Response in the Area‐Concentrated Search Can Improve Foraging Success

Area-concentrated search (ACS) is a simple movement rule implying that an animal searches for resources using a "state-dependent correlated random walk." Accordingly, a forager increases its searching intensity by reducing the directionality of movement ("intensive search mode" or ISM) when it detects a resource item, but if it searches unsuccessfully for a while, it returns to a more straight-line movement to search for new resource locations elsewhere ("extensive search mode" or ESM). We propose a modified ACS, called delayed-response ACS (dACS), which is more efficient in resource collection than standard ACS. Instead of immediately switching from ESM to ISM when encountering a resource, as is done in standard ACS, an individual foraging in the dACS mode delays this switch by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow> </mml:mrow> </mml:math> steps so that it continues moving in a straight line for a while before switching to ISM. Our results showed that an individual with a suitable delay parameter <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow> </mml:mrow> </mml:math> for the dACS achieved substantially higher foraging success than an individual with standard ACS ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>x</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn></mml:mrow> </mml:mrow> </mml:math> ). Optimal foraging success occurred when <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow> </mml:mrow> </mml:math> was approximately similar to the patch radius <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>r</mml:mi></mml:mrow> </mml:mrow> </mml:math> . This is because, with dACS, an individual can penetrate deeper into and stay longer within a cluster, ultimately increasing the number of resources collected. Modifying the half-saturation constant <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow> </mml:mrow> </mml:math> also affected the success of foraging, but the effects depended on resource density and cluster size. Generally, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>h</mml:mi></mml:mrow> </mml:mrow> </mml:math> modulated the optimal <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow><mml:mrow><mml:mi>x</mml:mi></mml:mrow> </mml:mrow> </mml:math> value only slightly. dACS can be interpreted as a survey movement within a resource cluster before switching from ESM to ISM. The dACS rule does not rely on complex spatial memory but only on memorizing how long ago resources were found or not. It may thus occur in a wide range of taxa, from organisms without a central nervous system to animals with complex brain systems.