Copepods counter dispersion to maintain high mating-encounter rates
Authors: Shnapp Ron , Holzner Markus 
Published: March 2022

&lt;p&gt;&lt;span&gt;Finding mating partners can be challenging for copepods: the ocean is vast and turbulent, the average animal's concentration is sparse, and their swimming ability is limited. Therefore, the probability for locating a mate assuming a homogeneous distribution of animals and a random motion leads to low mating encounter rates. However, zooplankton distribution is not homogeneous; field observations since the 1950s have shown that plantkon have patchy distributions over multiple scales - from thousand of kilometers down to the millimeter scale&lt;sup&gt;1&lt;/sup&gt;. Of relevance to mating is patchiness at small scales (on the order of the animal's size), leading to increased probability for sexual encounters due to higher local concentrations. Indeed, such mating clusters have been identified in ship transect observations&lt;sup&gt;2&lt;/sup&gt;. However, how such clusters form in the diffusive turbulent environment is not fully understood.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;In certain species, males actively search for females to achieve sexual encounters. When a male locates a female it pursuits her to achieve contact&lt;sup&gt;3&lt;/sup&gt;, and this behavior is thought to drive small-scale clustering&lt;sup&gt;4&lt;/sup&gt;. Nevertheless, the details of this process are not so straightforward. Specifically, the random swimming pattern males perform in their search, and the (super) diffusive nature of turbulence&lt;sup&gt;5&lt;/sup&gt;, both increases the animals'&lt;/span&gt;&lt;span&gt; dispersion, thus opposing patch formation. Therefore, the existence of mating clusters requires a detailed balance between diffusion and pair-interactions. However, this equilibrium in zooplankton patch formation was not examined in the past. &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;Our study examines the equilibrium between diffusion and pair-interactions in zooplankton. Specifically, we have formulated a numerical framework, &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;the pair-interaction model&lt;/span&gt;&lt;/em&gt;&lt;/span&gt;&lt;span&gt;, which allows to study patch formation. Remarkably, we observe that pair-interactions can lead to patches of numerous particles, similar to the field observations&lt;sup&gt;2&lt;/sup&gt;. We thus explore the model's parameter space, to reveal what is required for patchiness to be sustained. Furthermore, we compare our model's results with laboratory measurements of calanoid copepod trajectories&lt;sup&gt;3&lt;/sup&gt; and show good agreement between the model and the experiment. Our results support the hypothesis that small-scale patchiness is driven by the animal's behavior and thus explain the details of how zooplankton achieve high mating encounter rates in their complex environment. &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;sup&gt;1&lt;/sup&gt; B. Pinel-Alloul and A. Ghadouani (2007). &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;Spatial heterogeneity of planktonic microorganisms in aquatic systems&lt;/span&gt;&lt;/em&gt;&lt;/span&gt;&lt;span&gt;, Springer Netherlands, Dordrecht.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;sup&gt;2&lt;/sup&gt; C. S. Davis, S. M. Gallager and A. R. Solow (1992). &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;Science&lt;/span&gt;&lt;/em&gt;&lt;/span&gt; &lt;span&gt;&lt;strong&gt;&lt;span&gt;257&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;, 230-232. &lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;sup&gt;3&lt;/sup&gt; F.-G. Michalec et al. (2017). &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;Proc. Natl. Acad. Sci. U.S.A&lt;/span&gt;&lt;/em&gt;&lt;/span&gt;&lt;span&gt;. &lt;/span&gt;&lt;span&gt;&lt;strong&gt;&lt;span&gt;114&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;&amp;#160;; F.-G. Michalec et al. (2020). &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;eLife&lt;/span&gt;&lt;/em&gt;&lt;/span&gt; &lt;span&gt;&lt;strong&gt;&lt;span&gt;9&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;, e62014.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;sup&gt;4&lt;/sup&gt; C. L. Folt and C. W. Burns (1999). &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;Trends in Ecology and Evolution&lt;/span&gt;&lt;/em&gt;&lt;/span&gt;&lt;span&gt;, &lt;/span&gt;&lt;span&gt;&lt;strong&gt;&lt;span&gt;14&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;, 300&amp;#8211;305.&lt;/span&gt;&lt;/p&gt;&lt;p&gt;&lt;span&gt;&lt;sup&gt;5&lt;/sup&gt; J. P. Salazar and L. R. Collins (2009). &lt;/span&gt;&lt;span&gt;&lt;em&gt;&lt;span&gt;Ann. Rev. Fluid Mech.&lt;/span&gt;&lt;/em&gt;&lt;/span&gt; &lt;span&gt;&lt;strong&gt;&lt;span&gt;41&lt;/span&gt;&lt;/strong&gt;&lt;/span&gt;&lt;span&gt;, 405-432&lt;/span&gt;&lt;span&gt;.&lt;/span&gt;&lt;/p&gt;