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 >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 (cm²) 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

1. 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 (cm²/minute)
   • LMeanDisp - ln mean distance dispersed

Data were analyzed using the R-code: Density dependent sex displacement.R

1. 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 (cm²/minute)

R-code: Density-dependent movement.R

1. 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 (cm²/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