Random Walks in Biology

Berg, Howard C.

doi:10.1515/9781400820023

Cited by 455 publications

(663 citation statements)

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“…where ∆x is a change in distance and ∆t is a time step of duration t. In general, diffusivity can be derived from a random walk (Skellam 1951, Okubo and Levin 2001, Ovaskainen and Crone 2009). The 'random walk' has been derived previously (Berg 1993). A Levy walk, which is a probability distribution with a heavy tail, is another possible way to model this process (Nathan andMuller-Landau 2000, Levin et al 2003) for other potential animal seed distribution functions.…”

Section: Estimate Of Dmentioning

confidence: 99%

Megafauna extinction, tree species range reduction, and carbon storage in Amazonian forests

et al. 2015

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During the Late Pleistocene and early Holocene 59 species of South American megafauna went extinct. Their extinction potentially triggered population declines of large‐seeded tree species dispersed by the large‐bodied frugivores with which they co‐evolved, a theory first proposed by Janzen and Martin (1982). We tested this hypothesis using species range maps for 257 South American tree species, comparing 63 species thought to be primarily distributed by megafauna with 194 distributed by other animals. We found a highly significant (p < 0.001) decreased mean range size of 26% for the megafauna dispersed fruit (n = 63 species) versus fruit dispersed by other animals (n = 194), results which support the hypothesis. We then developed a mathematical model of seed dispersal to estimate the theoretical impact of megafauna extinction on tree species range and found the estimated dispersal capacity (Φseed) of a 2 g seed decreases by > 95% following disperser extinction. A numerical gap dynamic simulations suggests that over a 10 000 yr period following the disperser extinctions, the average convex hull range size of large‐seeded tree species decreased by ∼ 31%, while the estimated decrease in population size was ∼ 54%, indicating a likely greater decrease in species population size than indicated by the empirical range patterns. Finally, we found a positive correlation between seed size and wood density of animal‐dispersed tree species implying that the Late Pleistocene and early Holocene megafaunal extinctions reduced carbon content in the Amazon by ∼ 1.5 ± 0.7%. In conclusion, we 1) provide some empirical evidence that megafauna distributed fruit species have a smaller mean range size than wind, water or other animal‐dispersed species, 2) demonstrate mathematically that such range reductions are expected from megafauna extinctions ca 12 000 yr ago, and 3) illustrate that these extinctions may have reduced the Amazon's carbon storage capacity.

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Section: Estimate Of Dmentioning

confidence: 99%

Megafauna extinction, tree species range reduction, and carbon storage in Amazonian forests

et al. 2015

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“…This approach is similar to one used in the classic work of Denny and Shibata (1989), but generalizes it and corrects a subtle bias. In essence, the model tracks the time to contact the bottom for propagules taking numerous, short, randomly directed steps either up or down (i.e., a ''random walk''; see Berg 1983), when released from a given height. The probability of stepping to a new vertical position is a function of the degree of mixing which varies with elevation in the water column.…”

Section: The Calculation Of Hitting Timesmentioning

confidence: 99%

A Physically Based Model of Macroalgal Spore Dispersal in the Wave and Current-Dominated Nearshore

Gaylord

Reed

Raimondi

et al. 2002

Ecology

163

127

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Propagule dispersal in seaweeds is a process influenced by a variety of biological and physical factors, the complexity of which has hindered efforts to understand colonization, persistence, post‐disturbance recovery, and dynamics of algal populations in general. In view of this limitation, we employ here modifications to an existing turbulent‐transport model to explore the mechanics of nearshore macroalgal spore dispersal and its relationship to coastal hydrodynamic conditions. Our modeling efforts focus on four example species of seaweed whose reproductive propagules span a wide range in sinking speed and height of release above the sea floor: the giant kelp Macrocystis pyrifera, the erect fucoid Sargassum muticum, the small filamentous brown alga Ectocarpus siliculosus, and the flaccid red alga Sarcodiotheca gaudichaudii. Results indicate that both propagule sinking speed and release height can affect dispersal distance substantially, but that the influence of these biological parameters is modulated strongly by the intensity of turbulence as dictated by waves and currents. In rapid flows with larger waves, it is primarily fluid dynamic processes, in particular current velocities, that determine dispersal distance. Additional simulations suggest that patterns of spore dispersal are highly skewed, with most propagules encountering the sea floor within a few meters to hundreds of meters of their parents, but with a sizeable fraction of spores also dispersing as far as kilometers. Such model predictions imply a much greater potential for longer range dispersal than has typically been assumed, a finding with important implications for understanding the demographics of algal populations and for predicting levels of connectivity among them.

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“…Using the techniques of Kareiva ( 1983), the observed recapturewith-distance curve (for first-day recaptures only, since so few butterflies were captured on days 2-5) was much more leptokurtic than would be expected under passive diffusion in a homogeneous environment (Kolmogorov-Smirnov D = 0.348, n = 56, P < .01). However, a leptokurtic curve is to be expected when the target, in this case the habitat patch, is absorbing (Berg 1983). Thus, a diffusion model modified by the inclusion of an appropriate "settling" term might better fit the data.…”

Section: Out-of-habitat Release Experimentsmentioning

confidence: 99%

Long‐Distance Dispersal and Colonization in the Bay Checkerspot Butterfly, Euphydryas Editha Bayensis

Harrison¹

1989

Ecology

128

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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. This content downloaded from 138.Abstract. Dispersal, patch finding, and colonization abilities of the Bay checkerspot butterfly (Euphydryas editha bayensis) were measured in field experiments. Butterflies released in non-habitat were capable of moving several kilometres to reach a distant habitat patch. However, their interhabitat movements appeared to be non-oriented, unless they were within 50 m of a suitable patch. To quantify colonization ability, I transplanted propagules of 100 postdiapause larvae each to 38 vacant habitats. Twenty-four transplants (63%) produced adults in the initial year, and 6 (25%) of these initially successful transplants persisted to produce adults one year later. Thus the chances of successful population establishment, given the presence of a gravid female on a vacant habitat, appear to be low (i.e., at most a 6.25% chance of persisting 2 yr). The present distribution of the butterfly suggests that hilly intervening terrain inhibits the colonization of distant habitat patches. These results shed additional light upon the dynamics of a metapopulation of the Bay checkerspot butterfly.

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Random Walks in Biology

Cited by 455 publications

References 0 publications

Megafauna extinction, tree species range reduction, and carbon storage in Amazonian forests

Megafauna extinction, tree species range reduction, and carbon storage in Amazonian forests

A Physically Based Model of Macroalgal Spore Dispersal in the Wave and Current-Dominated Nearshore

Long‐Distance Dispersal and Colonization in the Bay Checkerspot Butterfly, Euphydryas Editha Bayensis

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