An agent-based model of cattle grazing toxic Geyer's larkspur

<div><p>By killing cattle and otherwise complicating management, the many species of larkspur (<i>Delphinium</i> spp.) present a serious, intractable, and complex challenge to livestock grazing management in the western United States. Among the many obstacles to improving our understanding of cattle-larkspur dynamics has been the difficulty of testing different grazing management strategies in the field, as the risk of dead animals is too great. Agent-based models (ABMs) provide an effective method of testing alternate management strategies without risk to livestock. ABMs are especially useful for modeling complex systems such as livestock grazing management, and allow for realistic bottom-up encoding of cattle behavior. Here, we introduce a spatially-explicit, behavior-based ABM of cattle grazing in a pasture with a dangerous amount of Geyer’s larkspur (<i>D</i>. <i>geyeri</i>). This model tests the role of herd cohesion and stocking density in larkspur intake, finds that both are key drivers of larkspur-induced toxicosis, and indicates that alteration of these factors within realistic bounds can mitigate risk. Crucially, the model points to herd cohesion, which has received little attention in the discipline, as playing an important role in lethal acute toxicosis. As the first ABM to model grazing behavior at realistic scales, this study also demonstrates the tremendous potential of ABMs to illuminate grazing management dynamics, including fundamental aspects of livestock behavior amidst ecological heterogeneity.</p></div

Results of multiple linear regression for the standard deviation of maximum individual daily alkaloid intake as predicted by herd-cohesion-factor (HCF) and stocking-density (SD).

<p>Adj. R² = 0.47. No significant interaction was present.</p

Box plots of various model evaluation data demonstrating effect of distinct persistent subherds.

<p>(a) Mean individual travel distance per grazing day (m) by herd cohesion factor (HCF); (b) Proportion of use of assess herd procedure (versus environmental movement) to choose a new grazing patch, a measure of herd-based versus individual optimization, by HCF; (c) Standard deviation of times-grazed count for all patches at end of model run, a measure of grazing heterogeneity, by HCF; (d) Total model run length, an inverse indicator of grazing efficiency, by HCF at stocking density = 0.5.</p

The effect of varying herd-cohesion-factor (HCF) on herd patterns, displayed at different levels of pasture usage (AUMs).

<p>Note that the cows depicted in these images are drawn 200 times larger than they really are to aid visualization, which makes them appear closer to one another than they are. Pasture size is 1.66 km x 1.58 km, and stocking density for all images is 1.0 AU • ha^-1. White cows are leaders, black followers, and gray independents. Yellow indicates patches that have been grazed twice, red three times. (a) HCF = 10, AUMs = 14; (b) HCF = 7, AUMs = 68; (c) HCF = 4, AUMs = 119; (d) HCF = 1, AUMs = 163. Typical usage for this pasture (258.82 ha) is 150 AUMs.</p

Results of multiple linear regression for the standard deviation of individual daily alkaloid intake as predicted by herd-cohesion-factor (HCF) and stocking-density (SD).

<p>Adj. R² = 0.76.</p

Results of multiple linear regression for the mean of maximum individual daily alkaloid intake as predicted by herd-cohesion-factor (HCF) and stocking-density (SD).

<p>Adj. R² = 0.82. β coefficients are from the same model without the interaction present.</p

Results of GLM with negative binomial distribution and log-link function for count of lethal acute toxicosis as predicted by herd-cohesion-factor (HCF) and stocking-density (SD).

<p>β coefficients are from the same GLM without the interaction present. GLM fit: Fisher scoring iterations = 1; residual deviance = 516.94 on 476 degrees of freedom; AIC = 1686.3.</p

Pseudo-coded flow chart of model processes, with role of cows executing each process in parentheses.

<p>1 = leader, 2 = follower, 3 = independent.</p

Appendix C. Nine wildebeest migratory pathways that evolved using average monthly surfaces in the additive model and yearly pathways refined in a learning phase.

Nine wildebeest migratory pathways that evolved using average monthly surfaces in the additive model and yearly pathways refined in a learning phase

Appendix B. Locations on the 15th of each month of wildebeest simulated in the evolutionary stage for models influenced by rainfall and new vegetation growth, as reflected in NDVI.

Locations on the 15th of each month of wildebeest simulated in the evolutionary stage for models influenced by rainfall and new vegetation growth, as reflected in NDVI