Evolutionary response of a native butterfly to concurrent plant invasions: Simulation of population dynamics

Abstract

The habitat of the green-veined white butterfly Pieris oleracea in eastern North America has undergone invasions by the exotic plant garlic mustard (Alliaria petiolata), which is replacing native hosts of P. oleracea such as Cardamine diphylla. A. petiolata was originally lethal to most larvae of the native butterfly but during the past 20+ years it has been incorporated successfully into the larval diet, likely through evolutionary change. The region was also invaded by another exotic plant, Cardamine pratensis, on which the native butterfly larvae readily develops, allowing the possibility of population rescue. Further complicating the butterfly's reproductive dynamics, it is multigenerational within a summer, and host plant availability and location change during the summer. Our goal is to model the expected dynamics of the native butterfly population in this evolving, dynamic landscape by using a new bio-inspired paradigm known as membrane computing.In this context, a Probabilistic Guarded Scripted P system has been designed to model and explore the conditions under which an allele conferring ability of P. oleracea larvae to develop on A. petiolata might have proliferated. The design describes a population dynamics model whose parameter values are derived from experimental and observational data. Our modeling framework is spatially explicit and our model integrates seasonal as well as annual dynamics. The simulation results from our model qualitatively match our field observations and experimental laboratory results, and agree with the results from a previous model on the genotypic adaptation of this butterfly species. From the simulations we identified the likely trajectories for the spatio-temporal distribution of alleles enabling P. oleracea to use the invasive plant species across this selective and phenological mosaic.

Developmental trap or demographic bonanza? Opposing consequences of earlier phenology in a changing climate for a multivoltine butterfly

“…Despite these long‐term trends of decline over the past century, some populations seem to be rebounding particularly in western Massachusetts, consistent with our results. Many of these rebounds have been attributed to its release from an introduced braconid parasitoid ( Cotesia glomerata ; Benson et al, ; Herlihy et al, ; Keeler, Chew, Goodale, & Reed, ; Van Driesche, ); the naturalization of a suitable new plant host ( Cardamine pratensis ; Chew et al, ; García‐Quismondo, Reed, Chew, Martínez‐del‐Amor, & Pérez‐Jiménez, ); and its ability to successfully consume garlic mustard (Chew et al, ; Keeler & Chew, ), which previously acted as a sensory oviposition trap (Huang, Renwick, & Chew, ). However, the effects of a warming climate in triggering an additional fourth generation might also be contributing to these rebounds in the southern parts of New England.…”

Modeling diel vertical migration with membrane computing

“…We created a membrane computing model structured in three sets of object rewriting rules and discrete-time equations (modules), with each module capturing the dynamics of a trophic level (abiotic resources, phytoplankton and Daphnia). The membrane graph that defines the structure of a membrane computing model provides a natural manner to represent regions with different properties, and permits to express local phenomena in a straightforward way [18,19,33,34]. In the case of the present model, membranes represent regions in a bidimensional space, and the adjacency between membranes in this graph encodes naturally the adjacency between spatial regions.…”

“…In the case of the present model, membranes represent regions in a bidimensional space, and the adjacency between membranes in this graph encodes naturally the adjacency between spatial regions. Likewise, objects are a natural manner to encode discrete entities such as animals or groups of animals [3,18,19,34].…”

“…Nevertheless, the discrete nature of P systems makes it difficult to represent continuous quantities that are inherent to virtually any ecological process. Therefore, it is necessary to introduce features in P systems modeling population dynamics that are capable of representing and processing continuous values [31,34]. To this end, we propose a model in which the transition steps between computations are defined both by object rewriting rules that capture the dynamics of groups of individuals and discrete-time equations that handle continuous values.…”

An interactive timeline of simulators in membrane computing

“…A later contribution, by 2014, to the practical application of membrane computing in biology, making use of P-Lingua framework, was MeCoGUI [159], incorporating probabilistic guarded P systems [107]. This application was used recently for the simulation of the ecosystem of Pieris napi oleracea in eastern North America [108,161]. In addition, another interesting application related to the study of regenerative processes using these tools was recently published [109].…”