The Role of Modeling in Monarch Butterfly Research and Conservation

Abstract

Models are an integral part of the scientific endeavor, whether they be conceptual, mathematical, statistical, or simulation models. Models of appropriate complexity facilitate comprehension and improve understanding of the variables driving system processes. In the context of conservation planning decision-making or research efforts, a useful model can aid interpretation and avoid overfitting by including only essential elements. Models can serve two related, but different purposes: understanding and prediction of future system behavior. Predictive models can require several iterations of refinement and empirical data gathering to be useful for conservation planning. Models with less predictive ability can be used to enhance understanding of system function and generate hypotheses for empirical evaluation. Modeling monarch butterfly systems, whether it be landscape-scale movement in breeding habitats, migratory behavior, or population dynamics at monthly or yearly timeframes, is challenging because the systems encompass complex spatial and temporal interactions across nested scales that are difficult, if not impossible, to empirically observe or comprehend without simplification. We review mathematical, statistical, and simulation models that have provided insights into monarch butterfly systems. Mathematical models have provided understanding of underlying processes that may be driving monarch systems. Statistical models have provided understanding of patterns in empirical data, which may represent underlying mechanisms. Simulations models have provided understanding of mechanisms driving systems and provide the potential to link mechanisms with data to build more predictive models. As an example, recently published agent-based models of non-migratory eastern North American monarch butterfly movement and egg-laying may provide the means to explore how different spatial patterns of habitat, habitat quality, and the interaction of stressors can influence future adult recruitment. The migratory process, however, has not been addressed with agent-based modeling. Using western monarch migration as an example, we describe how modeling could be used to provide insights into migratory dynamics. Future integration of migratory models with non-migratory and population dynamics models may provide better understanding and ultimately prediction of monarch butterfly movement and population dynamics at a continental scale.

Assessing Field‐Scale Risks of Foliar Insecticide Applications to Monarch Butterfly (Danaus plexippus) Larvae

“…Characterizing risks of foliar insecticides to nonmigratory monarch populations in agricultural ecosystems requires landscape‐scale analyses (Uhl and Brühl 2019). Adult monarchs are vagile (Zalucki et al 2016), which requires that attributes of their movement and reproductive behavior be integrated with spatial and temporal heterogeneity of monarch breeding habitat, agricultural fields, pastures, rural road rights‐of‐way, weather conditions, and pest pressure (Grant and Bradbury 2019). Results from the present study, ongoing acute contact exposures to egg and pupae from foliar insecticides, chronic larval dietary exposures to foliar and seed treatment insecticides, and acute adult oral exposures to seed treatment insecticides are being incorporated into an individual‐based model (Grant et al 2018) to obtain a more complete picture of landscape‐scale risks.…”

“…We are developing a landscape‐scale approach (Grant and Bradbury 2019; Uhl and Brühl 2019) to test the hypothesis that conservation benefits of establishing monarch breeding habitat in close proximity to maize and soybean fields will outweigh the risks of increased insecticide exposure. However, the current paucity of insecticide toxicity data precludes the means to assess field‐scale and landscape‐scale mortality rates.…”

The Integrated Monarch Monitoring Program: From Design to Implementation

“…Statewide collaboratives such as Missourians for Monarchs 13 employ it to track progress toward achieving their statewide milkweed stem goals. IMMP data were used to parameterize a milkweed density index in a model of monarch reproductive use on an Iowa landscape (Grant et al, 2018;Grant and Bradbury, 2019…”

Estimating arthropod survival probability from field counts: a case study with monarch butterflies

“…Continental-scale population models of monarch butterflies suggest larval survival probabilities are an important component of population growth rate and critical to conservation of this species (Flockhart et al 2015, Oberhauser et al 2017. While survival probabilities of egg and larval stages are critical for understanding monarch population dynamics, limited techniques are available to estimate survival probabilities of these life stages (Grant and Bradbury 2019). In some cases, researchers have attempted to follow individual monarch eggs and larvae (De Anda andOberhauser 2015, Myers et al 2019).…”