Seed mix selection model

The three data files, presented as matrices, comprise a plant-bee interaction data set that is previously published (Lane et al. 2020; Lane et al. 2022). The previously published data set includes 8,572 native bee specimens representing 144 species or morphospecies associated with 79 plant species (Lane et al. 2020; Lane et al. 2022). We built these matrices and the associated seed mix model (see R script) to improve seed mix design. Therefore, the three data matrices are a subset of the original data including only plant species on the CP42 list for Minnesota (57 species) because these species are commercially available and practical for use in seed mixes. The matrices thus contain 5,860 bee specimens collected from 32 CP42 plant species and representing 127 bee species.

The seed mix model is adapted from the seed mix selection model published by Williams and Lonsdorf (2018), which was based on M’Gonigle et al. (2017). The model objective is to maximize the total number of bee species that would be supported over their entire flight season by a given seed mix. The model thus requires three types of data presented as matrices in order to calculate the maximum number of bee species supported by a given seed mix: 1) adult phenology of each bee species, where each cell represents whether or not that bee species was observed in the data during a given time period, 2) flowering phenology of plants, where each cell represents whether or not a bee was collected from that plant species during a given time period, and 3) pairwise interactions between plant species and bee species, where each cell represents whether each plant-bee species pair was observed interacting in the data.

We applied the seed mix selection model using a binary genetic algorithm to select seed mixes (R package ‘GA’; Scrucca 2013; Scrucca 2017). Classic genetic algorithms consider a population of chromosomes and apply principles of natural selection (selection, mutation, and crossover processes) to generate optimal solutions. In our application, a seed mix is analogous to a chromosome and fitness is the potential bee richness supported by a mix. For each data set, we initialized a starting population of plant species equal to the desired number of plant species in the mix. The genetic algorithm then operated over 1000 iterations, applying crossover and mutation processes to optimize bee richness. We used default values for the probability of crossover, the probability of mutation, and elitism (percentage of top-performing mixes that “survive” each iteration): 0.8, 0.1, and 0.05, respectively. We repeated this process 100 times for each plant seed mix size: 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 plant species.

REFERENCES  

Lane, I. G., Herron-Sweet, C. R., Portman, Z. M., & Cariveau, D. P. (2020). Floral resource diversity drives bee community diversity in prairie restorations along an agricultural landscape gradient. Journal of Applied Ecology, 57, 2010-2018. doi: 10.1111/1365-2664.13694

Lane, I. G., Portman, Z. M., Herron-Sweet, C. R., Pardee, G. L., & Cariveau, D. P. (2022). Differences in bee community composition between restored and remnant prairies are more strongly linked to forb community differences than landscape differences. Journal of Applied Ecology, 59, 129-140. doi: 10.1111/1365-2664.14035

M’Gonigle, L. K., Williams, N. M., Lonsdorf, E., & Kremen, C. (2017). A tool for selecting plants when restoring habitat for pollinators. Conservation Letters, 10, 105-111. doi: 10.1111/conl.12261

Scrucca, L. (2013). GA: A Package for Genetic Algorithms in R. Journal of Statistical Software, 53, 1-37. http://www.jstatsoft.org/v53/i04

Scrucca, L. (2017). On some extensions to GA package: hybrid optimization, parallelization and islands evolution. The R Journal, 9/1, 187-206. https://journal.r-project.org/archive/2017/RJ-2017-008

Williams, N. M., & Lonsdorf, E. V. (2018). Selecting cost-effective plant mixes to support pollinators. Biological Conservation, 217, 195-202. doi: 10.1016/j.biocon.2017.10.032