DOI: 10.5061/dryad.xgxd254nx
title: Density-dependent within-patch movement behavior of two competing species

description: Movement behavior is central to understanding species distributions,
 population dynamics and coexistence with other species. At present,
 relatively little is known about how conspecific and interspecific
 competitor density affect movement behavior. We conducted releases of two
 species of competing Tribolium flour beetles at different densities, alone
 and together in homogeneous microcosms, and tested whether their
 recaptures-with-distance were well described by a random-diffusion model.
 We also determined whether mean displacement distances varied with the
 release density of conspecific and heterospecific beetles. A diffusion
 model provided a good fit to the redistribution of T. castaneum and T.
 confusum at all release densities, explaining an average of &gt;60% of
 the variation in recaptures. For both species, mean displacement (directly
 proportional to the diffusion rate) exhibited a humped-shaped relationship
 with conspecific density. Finally, we found that both species of beetle
 impacted the within-patch movement rates of the other species, but it
 depended on density. For T. castaneum in the highest density treatment,
 the addition of equal numbers of T. castaneum or T. confusum had the same
 effect, with mean displacements reduced by approximately one-half. The
 same result occurred for T. confusum released at an intermediate
 density. In both cases, it was total beetle abundance, not species
 identity that mattered to mean displacement. We suggest that displacement
 or diffusion rates that exhibit a nonlinear relationship with density or
 depend on the presence or abundance of interacting species should be
 considered when attempting to predict the spatial spread of populations.
description: # Density-dependent within-patch movement behavior of two competing
 species James T\. Cronin1\,\* \| Jerome Goddard II2 \| Aaron Krivchenia1
 \| Ratnasingham Shivaji3 1Department of Biological Sciences, Louisiana
 State University, Baton Rouge, LA 70803 2Department of Mathematics and
 Computer Science, Auburn University Montgomery, Montgomery, AL 36124, USA
 3Department of Mathematics and Statistics, University of North Carolina
 Greensboro, Greensboro, NC 27402, USA \*Corresponding author:
 jcronin@lsu.edu, +12255787218 Abstract Movement behavior is central to
 understanding species distributions, population dynamics and coexistence
 with other species. Although the relationship between conspecific density
 and emigration has been well studied, little attention has been paid to
 how interspecific competitor density affects another species’ movement
 behavior. We conducted releases of two species of competing *Tribolium*
 flour beetles at different densities, alone and together in homogeneous
 microcosms, and tested whether their recaptures-with-distance were well
 described by a random-diffusion model. We also determined whether mean
 displacement distances varied with the release density of conspecific and
 heterospecific beetles. A diffusion model provided a good fit to the
 redistribution of *T. castaneum* and *T. confusum* at all release
 densities, explaining an average of &gt;60% of the variation in
 recaptures. For both species, mean displacement (directly proportional to
 the diffusion rate) exhibited a humped-shaped relationship with
 conspecific density. Finally, we found that both species of beetle
 impacted the within-patch movement rates of the other species, but the
 effect depended on density. For *T. castaneum* in the highest density
 treatment, the addition of equal numbers of *T. castaneum* or *T.
 confusum* had the same effect, with mean displacements reduced by
 approximately one half. The same result occurred for *T. confusum*
 released at an intermediate density. In both cases, it was total beetle
 abundance, not species identity that mattered to mean displacement. We
 suggest that displacement or diffusion rates that exhibit a nonlinear
 relationship with density or depend on the presence or abundance of
 interacting species should be considered when attempting to predict the
 spatial spread of populations or scaling up to heterogeneous landscapes.
 KEYWORDS Density-dependent movement, Diffusion, Microcosm experiment,
 Spatial spread, Tribolium castaneum, Tribolium confusum ### Data Source
 and R-code for Analyses All data are provided as comma-separated value
 tables. The data for each set of analyses is divided into separate files.
 The contents of each file is summarized below. 1. Diffusion model fit.csv.
 This dataset summarizes the mean number of flour beetle recaptured with
 distance from the point of release. Releases were conducted at different
 beetle densities. Codes for each column of data are as follows:
 Replicates: number of replicate releases of adult flour beetles Species:
 RFB = T. castaneum, CFB = T. confusum Density: numbers of adult beetles
 released Distance: midpoint of the 15-cm distance category Captures:
 number of beetles captured in each distance category LCaptures:
 ln-transformed number of beetles captured in each distance category Dist2:
 distance category squared (cm<sup>2</sup>) PCaptures:
 proportion captured in each distance category LPCaptures: ln-transformed
 proportion of beetles released that were recaptured in each distance
 category. Data were analyzed using the R-code: Diffusion model fit2.R 2.
 Mean displacement by sex.csv. This dataset summarizes the mean
 displacement and diffusion rate for male and female flour beetles of each
 species. Codes for each column of data are as follows: * Rep - Replicate
 number * Density - Number beetles released for that sex * Sex - male or
 female * Species - RFB (T. castaneum) or CFB (T. confusum) * Status -
 Released as a single species (1) or with the other species (2) * Recovered
 - number of beetles recovered at the end of the dispersal period *
 MeanDisp - mean distance dispersed (cm) * Diffusion - the diffusion rate =
 mean squared displacement/4t (cm<sup>2</sup>/minute) *
 LMeanDisp - ln mean distance dispersed Data were analyzed using the
 R-code: Density dependent sex displacement.R 3. Mean displacement combined
 sexes.csv. This worksheet includes all replicates, including those in
 which the sex of the beetles was identified, where the mean displacement
 and diffusion rate was quantified for each replicate release of beetles.
 Codes for each column of data are as follows: * Species - RFB (T.
 castaneum) or CFB (T. confusum) * Duration - number of minutes that the
 experimental trial lasted. In all cases, 60 minutes * Density - release
 density for that replicate * Recovered - number of beetles recovered at
 the end of the dispersal period * Together - Beetles were released either
 alone (1) or together with the other species (2) * MeanDisp - mean
 distance dispersed (cm) * Diffusion - the diffusion rate = mean squared
 displacement/4t (cm<sup>2</sup>/minute) R-code:
 Density-dependent movement.R 4. Two-species movement\_5.csv, Two-species
 movement\_25.csv, Two-species movement\_50.csv. These three worksheets
 represent the data used in our Experiment 2: Heterospecific effects on
 within-patch redistribution. Each worksheet shows the data for the focal
 species when it is alone at density x, combined with the other species
 each at a density of x, and when the focal species is alone at density 2x.
 Codes for each column of data are as follows: * Species - RFB (T.
 castaneum) or CFB (T. confusum) * Time - duration of each trial (min) *
 Density - number of beetles released for that replicate * Recovered -
 number of beetles recovered at the end of the dispersal period * Status -
 Released as a single species (1) or with the other species (2) * MeanDisp
 - mean distance dispersed by the focal species (cm) * Diffusion - the
 diffusion rate of the focal species = mean squared displacement/4t
 (cm<sup>2</sup>/minute) * State - character variable that
 reports the number of the focal species released and whether it was
 released alone or together with the other species. * LMeanDisp- ln mean
 distance dispersed (cm) Data were analyzed using the R-code:
 Density-dependent movement - two species.R