A periodic matrix population model for monarch butterflies

Abstract

The migration pattern of the eastern monarch butterfly (Danaus plexippus) consists of a sequence of generations of butterflies that originate in Mexico each spring, travel as far north as Southern Canada, and ultimately return to the original location in Mexico the following fall. Estimates of monarch populations in the Oyamel firs in Mexico have caused concern within the scientific community about the long-term stability of this phenomenon. We use periodic population matrices to model the life cycle of the eastern monarch butterfly and find that, under this linear model, this migration is not currently at risk. We extend the model to address the three primary obstacles for the long-term survival of this migratory pattern: deforestation in Mexico, increased extreme weather patterns, and milkweed decline. Incorporating these obstacles into the model shows that there is a definite need to take action to alleviate the aforementioned obstacles. K E Y W O R D SDanaus plexippus, mathematical model, monarch butterfly, periodic matrix population model Natural Resource Modeling. 2017;e12123.wileyonlinelibrary.com/journal/nrm

An Evaluation of Studies on the Potential Threats Contributing to the Decline of Eastern Migratory North American Monarch Butterflies (Danaus plexippus)

“…Field studies constituted one of the principal methods documenting the effects of sudden changes in environmental conditions and adverse weather patterns in the decline of monarch butterflies (50% of total studies on adverse weather events, Brower et al, 2015Brower et al, , 2017, but only a single study considered the effect of extreme weather patterns before fall migration (25% of total studies on adverse weather events, Hunt and Tongen, 2017). Field studies examined the physiological response of monarchs to changes in environmental conditions in the southern portion of the migratory range , but controlled studies that assessed field-realistic, shortterm changes in environmental variables such as temperature, humidity, precipitation, or solar radiation on the physiological condition and survival during the breeding season were absent.…”

“…Field studies examined the physiological response of monarchs to changes in environmental conditions in the southern portion of the migratory range , but controlled studies that assessed field-realistic, shortterm changes in environmental variables such as temperature, humidity, precipitation, or solar radiation on the physiological condition and survival during the breeding season were absent. Similarly, few studies applied modeling techniques that evaluated the impact of weather extremes on monarch population viability (Flockhart et al, 2015;Hunt and Tongen, 2017). The peer-reviewed literature suggested a negative impact of adverse weather patterns on monarch butterflies (50% of total studies on adverse weather events, Brower et al, 2017;Hunt and Tongen, 2017) and these conditions could impact monarchs at each stage of their life cycle (Hunt and Tongen, 2017).…”

“…Similarly, few studies applied modeling techniques that evaluated the impact of weather extremes on monarch population viability (Flockhart et al, 2015;Hunt and Tongen, 2017). The peer-reviewed literature suggested a negative impact of adverse weather patterns on monarch butterflies (50% of total studies on adverse weather events, Brower et al, 2017;Hunt and Tongen, 2017) and these conditions could impact monarchs at each stage of their life cycle (Hunt and Tongen, 2017). Though sporadic events may result in considerable losses, the timing of the events is also suggested to alter the severity of the impact.…”

“…Brower et al (2015) noted that nectar sources available in the southern portion of the migratory range might offset the energetic cost of adverse conditions experienced earlier in migration, therefore having less impact than extreme weather on overwintering populations. Further, though Hunt and Tongen (2017) showed a negative effect of increasing extreme weather events on monarch butterflies, no studies evaluated the effect of adverse weather patterns in long-term datasets or the extent to which populations are capable of recovering afterwards.…”

“…Changes in suitable environmental conditions (Barve et al, 2012;Thogmartin et al, 2017b) and habitat at both breeding (Pleasants, 2017;Thogmartin et al, 2017a) and overwintering sites, as well as contaminant exposure (Oberhauser et al, 2006Pecenka and Lundgren, 2015), are thought to be foremost threats to monarch butterfly populations. Suboptimal environmental conditions during the overwintering period, such as unseasonably warm temperatures (Hunt and Tongen, 2017) or cold and wet microclimates that pose a risk of freezing (Anderson and Brower, 1996), can accelerate lipolysis that quickly depletes lipid stores needed for overwinter survival (Alonso-Mejía et al, 1997). Overwintering lipid stores may be further reduced by limited availability of nectar sources due to habitat loss and a northward shift in monarch movements expected with climate change (Batalden et al, 2007;Brower et al, 2015;Lemoine, 2015).…”