Generational Spreading Speed and the Dynamics of Population Range Expansion

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Online enhancement: appendix.abstract: Some of the most fundamental quantities in population ecology describe the growth and spread of populations. Population dynamics are often characterized by the annual rate of increase, l, or the generational rate of increase, R 0 . Analyses involving R 0 have deepened our understanding of disease dynamics and life-history complexities beyond that afforded by analysis of annual growth alone. While range expansion is quantified by the annual spreading speed, a spatial analog of l, an R 0 -like expression for the rate of spread is missing. Using integrodifference models, we derive the appropriate generational spreading speed for populations with complex (stage-structured) life histories. The resulting measure, relevant to locations near the expanding edge of a (re)colonizing population, incorporates both local population growth and explicit spatial dispersal rather than solely growth across a population, as is the case for R 0 . The calculations for generational spreading speed are often simpler than those for annual spreading speed, and analytic or partial analytic solutions can yield insight into the processes that facilitate or slow a population's spatial spread. We analyze the spatial dynamics of green crabs, sea otters, and teasel as examples to demonstrate the flexibility of our methods and the intuitive insights that they afford.

Trophic biology of the twospot livebearer, Pseudoxiphophorus bimaculatus, an invasive fish in Teuchitlán River, central Mexico

“…22201/ib.20078706e.2021.92.3533 These results, as well as other biological traits such as continuous reproduction, a high proportion of female individuals (Ramírez-García et al, 2017), parental care associated with viviparity (Gross & Shine, 1981), and high tolerance to environmental degradation (Mercado-Silva et al, 2002) are consistent with successful invasive species (Sakai et al, 2001), since this success is related to their establishment, spread, and abundance (Hayes & Barry, 2008;Marchetti et al, 2004;Ricciardi, 2013;Ricciardi et al, 2013). Moreover, in the present study we found ontogenetic trophic overlap of P. bimaculatus and, considering the iteroparous reproductive biology of the species in the site (Ramírez-García et al, 2017), a clear generational overlap over time, facilitating the potential for spread and colonization and giving rise to the apparently rapid and successful establishment of P. bimaculatus in the Teuchitlán River (Bateman et al, 2015;Herrerías-Diego et al, 2019).…”

Moving forward: insights and applications of moving‐habitat models for climate change ecology

“…) and calculating more accurate spread speeds for stage‐structured invasives (Bateman et al . ). An interesting way to incorporate climate change would be to develop the IDE analogue of the RDE found in Li et al .…”

“…IDEs have a long history of use for invasive species. Recent developments include modelling competing genotypes of pest species (Kanary et al 2014) and calculating more accurate spread speeds for stage-structured invasives (Bateman et al 2015). An interesting way to incorporate climate change would be to develop the IDE analogue of the RDE found in Li et al (2014).…”

“…They are the discrete-time analogues of RDEs. Recent IDE models have considered a variety of spatial problems, including optimal pest control (Martinez, Lenhart & White 2015), measuring spread speeds for structured populations (Bateman et al 2015), competition in patchy landscapes (Williams, Snyder & Levine 2016) and the influence of dispersal on Allee effects (Goodsman & Lewis 2016). IDEs are well suited for both applied and theoretical problems; they are easy to construct and implement; and, along with simple extensions, they can address nearly all of the challenges (at least partially) for prediction and management outlined above.…”

A mechanistic statistical approach to infer invasion characteristics of human-dispersed species with complex life cycle

“…Another potential issue in estimating parameters may arise if multiple combinations of two or more parameters produce the same ecological outcome. For example, two species with different life-history strategies can generate the same spread patterns (Bateman et al 2015). This issue of non-identifiability of parameters makes it statistically challenging to infer the life-history tactics of an invader, which, in turn, can limit our ability to determine which life-history parameters play an outsized role in the species spread and, therefore, should be the target of management efforts (Crouse et al 1987).…”