Publications – Sebastian Schreiber

@article{b,
title = {Persistence and extinction for stochastic ecological difference equations with internal and external variables},
author = {M Benaïm and S J Schreiber},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2021/01/JMB2019.pdf},
year = {2019},
date = {2019-05-03},
journal = {Journal of Mathematical Biology},
volume = {79},
pages = {393–431},
abstract = {The dynamics of species’ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. To understand this interplay, we prove theorems for stochastic persistence and exclu- sion for stochastic ecological difference equations accounting for internal and external variables. Specifically, we use a stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for (i) all population densities spending little time at low densities i.e. stochastic persistence, and (ii) population trajectories asymptotically approaching the extinction set with positive probability. For (i) and (ii), respectively, we provide quantitative estimates on the fraction of time that the system is near the extinction set, and the probability of asymptotic extinction as a function of the initial state of the system. Furthermore, in the case of persistence, we provide lower bounds for the expected time to escape neighborhoods of the extinction set. To illustrate the applicability of our results, we analyze stochastic models of evolution- ary games, Lotka–Volterra dynamics, trait evolution, and spatially structured disease dynamics. Our analysis of these models demonstrates environmental stochasticity facilitates coexistence of strategies in the hawk–dove game, but inhibits coexis- tence in the rock–paper–scissors game and a Lotka–Volterra predator–prey model. Furthermore, environmental fluctuations with positive auto-correlations can promote persistence of evolving populations and persistence of diseases in patchy landscapes. While our results help close the gap between the persistence theories for deterministic and stochastic systems, we highlight several challenges for future research.},
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pubstate = {published},
tppubtype = {article}
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The dynamics of species’ densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. The interplay between these variables and species densities can determine whether a particular population persists or goes extinct. To understand this interplay, we prove theorems for stochastic persistence and exclu- sion for stochastic ecological difference equations accounting for internal and external variables. Specifically, we use a stochastic analog of average Lyapunov functions to develop sufficient and necessary conditions for (i) all population densities spending little time at low densities i.e. stochastic persistence, and (ii) population trajectories asymptotically approaching the extinction set with positive probability. For (i) and (ii), respectively, we provide quantitative estimates on the fraction of time that the system is near the extinction set, and the probability of asymptotic extinction as a function of the initial state of the system. Furthermore, in the case of persistence, we provide lower bounds for the expected time to escape neighborhoods of the extinction set. To illustrate the applicability of our results, we analyze stochastic models of evolution- ary games, Lotka–Volterra dynamics, trait evolution, and spatially structured disease dynamics. Our analysis of these models demonstrates environmental stochasticity facilitates coexistence of strategies in the hawk–dove game, but inhibits coexis- tence in the rock–paper–scissors game and a Lotka–Volterra predator–prey model. Furthermore, environmental fluctuations with positive auto-correlations can promote persistence of evolving populations and persistence of diseases in patchy landscapes. While our results help close the gap between the persistence theories for deterministic and stochastic systems, we highlight several challenges for future research.

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Rebecca S Snell Noelle G Beckman, Evan Fricke Bette Loiselle Carolina Carvalho Landon Jones Nathanael Lichti Nicky Lustenhouwer Sebastian Schreiber Christopher Strickland Lauren Sullivan Brittany Cavazos Itamar Giladi Alan Hastings Kimberly Holbrook Eelke Jongejans Oleg Kogan Flavia Montaño-Centellas Javiera Rudolph Haldre Rogers Rafal Zwolak Eugene Schupp A S R I L R S

Consequences of intraspecific variation in seed dispersal for plant demography, communities, evolution, and global change (Journal Article)

AoB Plants, 11 (4), pp. plz016, 2019.

(Abstract | Links | BibTeX)

@article{AoB-19,
title = {Consequences of intraspecific variation in seed dispersal for plant demography, communities, evolution, and global change},
author = {Rebecca S Snell, Noelle G Beckman, Evan Fricke, Bette A Loiselle, Carolina S Carvalho, Landon R Jones, Nathanael I Lichti, Nicky Lustenhouwer, Sebastian Schreiber, Christopher Strickland, Lauren L Sullivan, Brittany R Cavazos, Itamar Giladi, Alan Hastings, Kimberly Holbrook, Eelke Jongejans, Oleg Kogan, Flavia Montaño-Centellas, Javiera Rudolph, Haldre S Rogers, Rafal Zwolak, Eugene Schupp},
url = {https://academic.oup.com/aobpla/advance-article/doi/10.1093/aobpla/plz016/5416163},
doi = {10.1093/aobpla/plz016},
year = {2019},
date = {2019-03-21},
journal = {AoB Plants},
volume = {11},
number = {4},
pages = {plz016},
abstract = {As the single opportunity for plants to move, seed dispersal has an important impact on plant fitness, species distributions and patterns of biodiversity. However, models that predict dynamics such as risk of extinction, range shifts and biodiversity loss tend to rely on the mean value of parameters and rarely incorporate realistic dispersal mechanisms. By focusing on the mean population value, variation among individuals or variability caused by complex spatial and temporal dynamics is ignored. This calls for increased efforts to understand individual variation in dispersal and integrate it more explicitly into population and community models involving dispersal. However, the sources, magnitude and outcomes of intraspecific variation in dispersal are poorly characterized, limiting our understanding of the role of dispersal in mediating the dynamics of communities and their response to global change. In this manuscript, we synthesize recent research that examines the sources of individual variation in dispersal and emphasize its implications for plant fitness, populations and communities. We argue that this intraspecific variation in seed dispersal does not simply add noise to systems, but, in fact, alters dispersal processes and patterns with consequences for demography, communities, evolution and response to anthropogenic changes. We conclude with recommendations for moving this field of research forward.},
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pubstate = {published},
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}

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Schreiber, S J; Yamamichi, M; Strauss, S

When rarity has costs: coexistence under positive frequency-dependence and environmental stochasticity (Journal Article)

Ecology, 100 (7), pp. e02664, 2019.

(Links | BibTeX)

Clare Aslan Noelle G Beckman, Haldre Rogers Judie Bronstein Damaris Zurell Florian Hartig Katriona Shea Liba Pejchar Mike Neubert John Poulsen Janneke HilleRisLambers Maria Miriti Bette Loiselle Edu Effiom Jenny Zambrano Geno Schupp Gesine Pufal Jeremy Johnson James Bullock Jedediah Brodie Emilio Bruna Robert Stephen Cantrell Robin Decker Evan Fricke Katie Gurski Alan Hastings Oleg Kogan Onja Razafindratsima Manette Sandor Sebastian Schreiber Rebecca Snell Christopher Strickland Ying Zhou S M

Employing plant functional groups to advance seed dispersal ecology and conservation (Journal Article)

AoB Plants, 11 (2), pp. plz006, 2019.

(Links | BibTeX)

Cuello, W S; Gremer, J R; Trimmer, P C; Sih, A; Schreiber, S J

Predicting Evolutionarily Stable Strategies from Physiological Traits of Sonoran Desert Annuals (Journal Article)

Proceeding of the Royal Society B, in press, 286 , pp. 20182613, 2019.

(Links | BibTeX)

Gil, M A; Baskett, M L; Schreiber, S J

Social information drives ecological outcomes among competing species (Journal Article)

Ecology, 100 (11), pp. e02835, 2019.

(Links | BibTeX)

Schreiber, S J; Moore, J

The structured demography of open populations in fluctuating environments (Journal Article)

Methods in Ecology and Evolution, 9 , pp. 1569-1580, 2018.

(Links | BibTeX)

Schreiber, S J; Patel, S; terHorst, C

Evolution as a coexistence mechanism: Does genetic architecture matter? (Journal Article)

American Naturalist, 191 , pp. 407–420, 2018.

(Links | BibTeX)

terHorst, C; P, Zee; Heath, K; Miller, T; Pastore, A; Patel, S; S.J., Schreiber; Wade, M; Walsh, M

Evolution in a community context: trait responses to multiple species interaction (Journal Article)

American Naturalist, 191 , pp. 368–380, 2018.

(Links | BibTeX)

Moore, J; Puckett, B; Schreiber, S J

Restoration of Eastern oyster populations with positive density dependence (Journal Article)

Ecological Applications, 28 , pp. 897-909, 2018.

(Links | BibTeX)

Patel, S; Cortez, M H; Schreiber, S J

Partitioning the effects of eco-evolutionary feedbacks on community stability (Journal Article)

American Naturalist, 191 , pp. 381–394, 2018.

(Links | BibTeX)

Patel, S; Schreiber, S J

Robust permanence for ecological equations with internal and external feedbacks (Journal Article)

Journal of Mathematical Biology, 77 , pp. 79–105, 2018.

(Links | BibTeX)

Schreiber, S J

A dynamical trichotomy for structured populations experiencing positive density-dependence in stochastic environments (Incollection)

Hamaya, Matsunaga Elyadi H S Y; Pötzsche, C (Ed.): Advances in Difference Equations and Discrete Dynamical Systems, 212 , pp. 55–66, Springer, 2017.

(Links | BibTeX)

Cantrell, R S; Cosner, C; Lou, Y; Schreiber, S J

Evolution of natal dispersal in spatially heterogenous environments (Journal Article)

Mathematical Biosciences, 283 , 2017.

(Links | BibTeX)

Roth, G; Salceanu, P L; Schreiber, S J

Robust permanence for ecological maps (Journal Article)

SIAM Journal of Mathematical Analysis, 49 , pp. 3527-3549, 2017.

(Links | BibTeX)

Schreiber, S J

Coexistence in the face of uncertainty (Incollection)

Roderick, Makarov Roman Belair Jacques Melnik (Ed.): Recent Progress and Modern Challenges in Applied Mathematics, Modeling and Computational Science, pp. 349-384, Springer Verlag, 2017.

(Links | BibTeX)

Schreiber, S J; Ross, N

Individual-based Integral Projection Models: The role of size-structure on extinction risk and establishment success (Journal Article)

Methods in Ecology and Evolution, 7 , pp. 867–874, 2016.

(Links | BibTeX)

Hart, S P; Schreiber, S J; Levine, J M

How variation between individuals affects species coexistence (Journal Article)

Ecology Letters, 19 , pp. 825–838, 2016.

(Links | BibTeX)

Moore, J L; Lipcius, R N; Puckett, B; Schreiber, S J

The demographic consequences of growing older and bigger in oyster populations (Journal Article)

Ecological Applications, 26 , pp. 2206–2217, 2016.

(Links | BibTeX)

Rosenheim, J A; Schreiber, S J; Williams, N M

Does an `oversupply'of ovules cause pollen limitation? (Journal Article)

New Phytologist, 210 , pp. 324–332, 2016.

(Links | BibTeX)

Rosenheim, J A; Williams, N W; Schreiber, S J; Rapp, J

Modest pollen limitation of whole-plant seed production is in good agreement with modest uncertainty in whole-plant pollen receipt (Journal Article)

American Naturalist, 187 , pp. 397-404, 2016.

(Links | BibTeX)

Schreiber, S J

Unifying within- and between-generation bet-hedging theories: An ode to J.H Gillespie (Journal Article)

American Naturalist, 186 , pp. 792-796, 2015.

(Links | BibTeX)

Schreiber, S J; Patel, S

Evolutionarily induced alternative states and coexistence in systems with apparent competition (Journal Article)

Natural Resource Modelling, 28 , pp. 475-496, 2015.

(Links | BibTeX)

Schreiber, S J; Rosenheim, J A; Williams, N W; Harder, L

Evolutionary and Ecological Consequences of Multiscale Variation in Pollen Receipt for Seed Production (Journal Article)

American Naturalist, 185 , pp. 14–29, 2015.

(Links | BibTeX)

Evans, S; Hening, A; Schreiber, S J

Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments (Journal Article)

Journal of Mathematical Biology, 71 , pp. 325-359, 2015.

(Links | BibTeX)

Faure, M; Schreiber, S J

Convergence of evolutionary urn processes to non-equilibrium attractors (Journal Article)

Stochastic Processes and their Applications, 125 , pp. 3053-3074, 2015.

(Links | BibTeX)

Gaylord, B; Kroeker, K; Sunday, J; Anderson, K; Barry, J; Brown, N; Connell, S; Dupont, S; Fabricius, K; Hall-Spencer, J; Klinger, T; Milazzo, M; Munday, P; Russell, B; Sanford, E; Schreiber, S; Thiyagarahan, V; Vaughan, M; Widdicombe, S; Harley, C

Ocean acidification through the lens of ecological theory (Journal Article)

Ecology, 96 , pp. 3–15, 2015.

(Links | BibTeX)

Lipcius, R N; Burke, R P; McCulloch, D N; Schreiber, S J; Schulte, D M; Seitz, R D; Shen, J

Overcoming restoration paradigms: value of the historical record and metapopulation dynamics in native oyster restoration (Journal Article)

Frontiers in Marine Science, 2 , pp. Article 65 (1-15), 2015.

(Abstract | Links | BibTeX)

@article{fms-15,
title = {Overcoming restoration paradigms: value of the historical record and metapopulation dynamics in native oyster restoration},
author = {R N Lipcius and R P Burke and D N McCulloch and S J Schreiber and D M Schulte and R D Seitz and J Shen},
url = {http://journal.frontiersin.org/article/10.3389/fmars.2015.00065/abstract},
year = {2015},
date = {2015-01-01},
journal = {Frontiers in Marine Science},
volume = {2},
pages = {Article 65 (1-15)},
abstract = {Restoration strategies for native oyster populations rely on multiple sources of information, which often conflict due to time- and space-varying patterns in abundance and distribution. For instance, strategies based on population connectivity and disease resistance can differ, and extant and historical records of abundance and distribution are often at odds, such that the optimal strategy is unclear and valuable restoration sites may be excluded from consideration. This was the case for the Lynnhaven River subestuary of lower Chesapeake Bay, which was deemed unsuitable for Eastern Oyster restoration based on physical conditions, disease challenge, and extant oyster abundance. Consequently, we (i) evaluated previously unknown historical data from the 1800s, (ii) quantified extant oyster recruitment and abundance, physical conditions, and disease presence on constructed restoration reefs and alternative substrates, and (iii) assessed simulations from biophysical models to identify potential restoration sites in the metapopulation. The collective data distinguished numerous restoration sites (i) in the polyhaline zone (salinity 18.4-22.2) where disease resistance is evolving, (ii) where oysters were abundant in the late 1800s-early 1900s, (iii) of recent high recruitment, abundance and survival, despite consistent and elevated disease challenge, and (iv) interconnected as a metapopulation via larval dispersal. Moreover, a network of constructed restoration reefs met size structure, abundance and biomass standards of restoration success. These findings demonstrate that assumptions about the suitability of sites for oyster restoration based on individual processes can be severely flawed, and that in-depth examination of multiple processes and sources of information are required for oyster reef restoration plans to maximize success. We use these findings and previous information to recommend a strategy for successful restoration of subtidal oyster reefs throughout the range of the Eastern Oyster.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Restoration strategies for native oyster populations rely on multiple sources of information, which often conflict due to time- and space-varying patterns in abundance and distribution. For instance, strategies based on population connectivity and disease resistance can differ, and extant and historical records of abundance and distribution are often at odds, such that the optimal strategy is unclear and valuable restoration sites may be excluded from consideration. This was the case for the Lynnhaven River subestuary of lower Chesapeake Bay, which was deemed unsuitable for Eastern Oyster restoration based on physical conditions, disease challenge, and extant oyster abundance. Consequently, we (i) evaluated previously unknown historical data from the 1800s, (ii) quantified extant oyster recruitment and abundance, physical conditions, and disease presence on constructed restoration reefs and alternative substrates, and (iii) assessed simulations from biophysical models to identify potential restoration sites in the metapopulation. The collective data distinguished numerous restoration sites (i) in the polyhaline zone (salinity 18.4-22.2) where disease resistance is evolving, (ii) where oysters were abundant in the late 1800s-early 1900s, (iii) of recent high recruitment, abundance and survival, despite consistent and elevated disease challenge, and (iv) interconnected as a metapopulation via larval dispersal. Moreover, a network of constructed restoration reefs met size structure, abundance and biomass standards of restoration success. These findings demonstrate that assumptions about the suitability of sites for oyster restoration based on individual processes can be severely flawed, and that in-depth examination of multiple processes and sources of information are required for oyster reef restoration plans to maximize success. We use these findings and previous information to recommend a strategy for successful restoration of subtidal oyster reefs throughout the range of the Eastern Oyster.

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Patel, S; Schreiber, S J

Evolutionary driven regime shifts in ecological systems with intraguild predation (Journal Article)

American Naturalist, 186 , pp. E98–E110, 2015.

(Links | BibTeX)

Reigeda, C; Schreiber, S J; Altermatt, F; Holyoak, M

Metapopulation dynamics on ephemeral patches (Journal Article)

American Naturalist, 185 , pp. 183–195, 2015.

(Links | BibTeX)

Schreiber, S; Smith, K; Getz, W

Calculus for the Life Sciences (Book)

John Wiley & Sons, 2014.

(Links | BibTeX)

Faure, M; Schreiber, S J

Quasi-stationary distributions for randomly perturbed dynamical systems (Journal Article)

Annals of Applied Probability, 24 , pp. 553-598, 2014.

(Links | BibTeX)

Rosenheim, J A; Williams, N W; Schreiber, S J

Parental optimism versus parental pessimism in plants: how common should we expect pollen limitation to be? (Journal Article)

American Naturalist, 184 , pp. 75–90, 2014.

(Links | BibTeX)

Roth, G; Schreiber, S J

Pushed beyond the brink: Allee effects, environmental stochasticity, and extinction (Journal Article)

Journal of Biological Dynamics, 8 , pp. 187–205, 2014.

(Links | BibTeX)

Roth, G; Schreiber, S J

Persistence in fluctuating environments for interacting structured populations (Journal Article)

Journal of Mathematical Biology, 68 , pp. 1267–1317, 2014.

(Links | BibTeX)

Schreiber, S J

Motivating calculus with biology (Incollection)

Undergraduate Mathematics for the Life Sciences Processes and Models Assessment and Directions, pp. 177–188, Mathematical Association of America, 2013.

(Links | BibTeX)

Schreiber, S J; Killingback, T P

Cycling in space: Persistence of rock-paper-scissor metacommunities (Journal Article)

Theoretical Population Biology, 86 , pp. 1–11, 2013.

(Links | BibTeX)

Evans, S N; Ralph, P; Schreiber, S J; Sen, A

Stochastic growth rates in spatio-temporal heterogeneous environments (Journal Article)

Journal of Mathematical Biology, 66 , pp. 423-476, 2013.

(Links | BibTeX)

Park, M; Loverdo, C; Schreiber, S J; Lloyd-Smith, J O

Multiple scales of selection influence the evolutionary emergence of novel pathogens (Journal Article)

Philiosophical Transactions of the Royal Soceity. B, Vol. , pp. 368, 2013.

(Links | BibTeX)

Schreiber, S J

Evolution of patch selection in stochastic environments (Journal Article)

American Naturalist, 180 , pp. 17–34, 2012.

(Links | BibTeX)

Schreiber, S J

Persistence for stochastic difference equations: a mini-review (Journal Article)

Journal of Difference Equations and Applications, 18 , pp. 1381–1403, 2012.

(Links | BibTeX)

Ellner, S P; Schreiber, S J

Temporally variable dispersal and demography can accelerate the spread of invading species (Journal Article)

Theoretical Population Biology, 82 , pp. 283-298, 2012.

(Links | BibTeX)

Loverdo, C; Park, M; Schreiber, S J; Lloyd-Smtih, J

Influence of viral replication mechanisms on within-host evolutionary dynamics (Journal Article)

Evolution, 66 , pp. 3462–3471, 2012.

(Links | BibTeX)

Schaiber, J G; Silverstein, R; Kaczmarczyk, A N; Rutaganira, R U; Aggarwal, T; Schwemmer, M; Hom, C L; Grossberg, R K; Schreiber, S J

Constraints on the use of lifespan shortening Wolbachia to control dengue fever (Journal Article)

Journal of Theoretical Biology, 297 , pp. 26-32, 2012.

(Links | BibTeX)

Schreiber, S J

Mathematical Dances with Wolves (Journal Article)

Science, 334 , pp. 1214-1215, 2011.

(Links | BibTeX)

Schreiber, S J

Ordinary Differential equations (Incollection)

Sourcebook in Theoretical Ecology, California University of California Press, 2011.

(BibTeX)

Schreiber, S J; Benaïm, M; Atchadé, K A S

Persistence in fluctuating environments (Journal Article)

Journal of Mathematical Biology, 62 , pp. 655-683, 2011.

(Abstract | Links | BibTeX)

@article{jmb-11,
title = {Persistence in fluctuating environments},
author = {S J Schreiber and M Benaïm and K A S Atchadé},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2019/08/schreiber_benaim2011.pdf},
year = {2011},
date = {2011-01-01},
journal = {Journal of Mathematical Biology},
volume = {62},
pages = {655-683},
abstract = {Understanding under what conditions interacting populations, whether they be plants, animals, or viral particles, coexist is a question of theoretical and practical importance in population biology. Both biotic interactions and environmental fluctuations are key factors that can facilitate or disrupt coexistence. To better understand this interplay between these deterministic and stochastic forces, we develop a mathematical theory extending the nonlinear theory of permanence for deterministic systems to stochastic difference and differential equations. Our condition for coexistence requires that there is a fixed set of weights associated with the interacting populations and this weighted combination of populations' invasion rates is positive for any (ergodic) stationary distribution associated with a subcollection of populations. Here, an invasion rate corresponds to an average per-capita growth rate along a stationary distribution. When this condition holds and there is sufficient noise in the system (i.e. all population states are accessible), we show that the populations approach a unique positive stationary distribution. Moreover, we show that our coexistence criterion is robust to small perturbations of the model functions. Using this theory, we illustrate that (i) environmental noise enhances or inhibits coexistence in communities with rock-paper-scissor dynamics depending on correlations between interspecific demographic rates, (ii) stochastic variation in mortality rates has no effect on the coexistence criteria for discrete-time Lotka-Volterra communities, and (iii) random forcing can promote genetic diversity in the presence of exploitative interactions.!!},
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tppubtype = {article}
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Schreiber, S J; Bolnick, D; ü, R B

The community effects of phenotypic and genetic variation within a predator population (Journal Article)

Ecology, 92 , pp. 1582-1593, 2011.

(Links | BibTeX)

Schreiber, S J; Ryan, M E

Invasion speeds of structured populations in fluctuating environments (Journal Article)

Theoretical Ecology, 4 , pp. 423-434, 2011.

(Abstract | Links | BibTeX)

Schreiber, S J; Li, C K

Evolution of unconditional dispersal in periodic environments (Journal Article)

Journal of Biological Dynamics (special issue on Adaptive Dynamics), 5 , pp. 120-134, 2011.

(Links | BibTeX)

Altermatt, F; Schreiber, S J; Holyoak, M

Interactive effects of disturbance and directionality of dispersal on species richness and composition in metacommunities (Journal Article)

Ecology, 92 , pp. 859–870, 2011.

(Links | BibTeX)

Bolnick, D; Amarasekare, P; 'u, Ara M S; ü, R B; Levine, J; Novak, M; Rudolf, V H; Schreiber, S J; Urban, M; Vasseur, D

Why intraspecific trait variation matters in community ecology (Journal Article)

Trends in Ecology and Evolution, 26 , pp. 185-194, 2011.

(Links | BibTeX)

Schreiber, S J

Interactive effects of temporal correlations, spatial heterogeneity, and dispersal on population persistence (Journal Article)

Proceedings of the Royal Society: Biological Sciences, 277 , pp. 1907-1914, 2010.

(Abstract | Links | BibTeX)

Edwards, K F; Schreiber, S J

Preemption of space can lead to intransitive coexistence of competitors (Journal Article)

Oikos, 119 , pp. 1201–1209, 2010.

(Abstract | Links | BibTeX)

Hofbauer, J; Schreiber, S J

Robust permanence for interacting structured populations (Journal Article)

Journal of Differential Equations, 248 , pp. 1955-1971, 2010.

(Abstract | Links | BibTeX)

Schreiber, S J; Lloyd-Smith, J O

Invasion dynamics in spatially heterogenous environments (Journal Article)

American Naturalist, 174 , pp. 490–505, 2009.

(Abstract | Links | BibTeX)

Schreiber, S J; Saltzman, E

Evolution of predator and prey movement into sink habitats (Journal Article)

American Naturalist, 174 , pp. 68–81, 2009.

(Abstract | Links | BibTeX)

@article{amnat-09a,
title = {Evolution of predator and prey movement into sink habitats},
author = {S J Schreiber and E Saltzman},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2021/01/AmNat2009.pdf},
year = {2009},
date = {2009-01-01},
journal = {American Naturalist},
volume = {174},
pages = {68--81},
abstract = {Mathematical models of predator-prey interactions in a patchy landscape are used to explore the evolution of dispersal into sink habitats. When evolution is constrained to a single trophic level, three evolutionary outcomes are observed. If predator-prey dynamics are sufficiently stable in source habitats, then there is an evolutionarily stable strategy (ESS) corresponding to sedentary phenotypes that specialize on source habitats. However, if predator-prey dynamics are sufficiently unstable in source habitats, then either an ESS corresponding to dispersive phenotypes utilizing both source and sink habitats or an evolutionary stable coalition (ESC) between dispersive and sedentary phenotypes emerges. ESCs only occur if dispersal into sink habitats can stabilize the predator-prey interactions. When evolution of dispersal proceeds at both trophic levels, nine evolutionary outcomes corresponding to any combination of specialists and generalists at one or both trophic levels were observed. Coevolution is largely top-down driven. If the predator mortality rate in sink habitats is low, then selection pressure for predator movement into sink habitats can forestall the evolution of prey sink populations. Alternatively, if this mortality rate is high, then the predators ultimately play a sedentary ESS. Only at intermediate predator mortality rates is there selection for predator and prey movement into sink habitats. These results suggest that the instability of predator-prey interactions may foster speciation near species borders. Moreover, they illustrate an evolutionary paradox of enrichment in which enriching source habitats can result in a loss of phenotypic diversity. !!},
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tppubtype = {article}
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Benaïm, M; Schreiber, S J

Persistence of structured populations in random environments (Journal Article)

Theoretical Population Biology, 76 , pp. 19-34, 2009.

(Abstract | Links | BibTeX)

Kon, R; Schreiber, S J

Host and multiple parasitoid dynamics with egg limitation (Journal Article)

SIAM Journal of Applied Mathematics, 69 , pp. 959-976, 2009.

(Abstract | Links | BibTeX)

Schreiber, S J; Rudolf, V

Crossing habitat boundaries: Coupling dynamics of ecosystems through complex life cycles (Journal Article)

Ecology Letters, 11 , pp. 576-587, 2008.

(Abstract | Links | BibTeX)

Lipcius, R ~N; Eggleston, D ~B; Schreiber, S ~J; Seitz, R ~D; J.~Shen, ; M.~Sisson, ; Stockhausen, W ~T; Wang, H ~V

Metapopulation connectivity and stock enhancement of marine species (Journal Article)

Reviews in Fishery Science, 16 , pp. 101–110, 2008.

(Abstract | BibTeX)

@article{rfs-08,
title = {Metapopulation connectivity and stock enhancement of marine species},
author = {R ~N Lipcius and D ~B Eggleston and S ~J Schreiber and R ~D Seitz and J.~Shen and M.~Sisson and W ~T Stockhausen and H ~V Wang},
year = {2008},
date = {2008-01-01},
journal = {Reviews in Fishery Science},
volume = {16},
pages = {101--110},
abstract = {Various biophysical systems exhibit characteristics of metapopulation and network structure. The specific type of metapopulation or network structure can have substantially different effects on metapopulation dynamics of marine species with open populations displaying varying degrees of connectivity between subpopulations, and thus can have major consequences on stock enhancement efforts. We investigate the role of connectivity in metapopulation dynamics of the blue crab, Callinectes sapidus, and the Eastern oyster, Crassostrea virginica, with three dimensional hydrodynamic models simulating advection and diffusion. In the case of the blue crab, we model a metapopulation comprised of primary (i.e. seagrass beds) and secondary (i.e. salt marsh fringed coves and shorelines) nursery habitats, and spatially distinct spawning grounds connected via migration corridors. In the model simulations, we distinguish nursery habitats that are recruitment limited, and therefore optimal candidates for stock enhancement through release of hatchery-reared or translocated juveniles. In the case of the Eastern oyster, we model connectivity between numerous oyster reefs (i.e., subpopulations) positioned according to historical observations. Model simulations produce estimates of the degree of connectivity between all pairs of oyster reefs, which subsequently permits assessment of the diversity of patterns in network connectivity. From these results we distinguish the major characteristic types of connectivity patterns among oyster reefs, we identify those reefs most suitable for broodstock enhancement, and we discuss the means by which oyster reef networks, such as those occurring throughout Chesapeake Bay, may be enhanced successfully.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Schreiber, S J

On persistence and extinction of randomly perturbed dynamical systems (Journal Article)

Discrete and Continous Dynamical Systems B, 7 , pp. 457–463, 2007.

(Links | BibTeX)

Schreiber, S J

Periodicity, persistence, and collapse in host-parasitoid systems with egg limitation (Journal Article)

Journal of Biological Dynamics, 1 , pp. 273 - 287, 2007.

(Abstract | Links | BibTeX)

@article{jbd-07,
title = {Periodicity, persistence, and collapse in host-parasitoid systems with egg limitation},
author = {S J Schreiber},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2022/09/Periodicity-persistence-and-collapse-in-host-parasitoid-systems-with-egg-limitation.pdf},
year = {2007},
date = {2007-01-01},
journal = {Journal of Biological Dynamics},
volume = {1},
pages = {273 - 287},
abstract = {There is an emerging consensus that parasitoids are limited by the number of eggs which they can lay as well as the amount of time they can search for their hosts. Since egg limitation tends to destabilize host-parasitoid dynamics, successful control of insect pests by parasitoids requires additional stabilizing mechanisms such as heterogeneity in the distribution of parasitoid attacks and host density-dependence. To better understand how egg limitation, search limitation, heterogeneity in parasitoid attacks, and host density-dependence influence host-parasitoid dynamics, discrete time models accounting for these factors are analyzed. When parasitoids are purely egg-limited, a complete anaylsis of the host-parasitoid dynamics are possible. The analysis implies that the parasitoid can invade the host system only if the parasitoid's intrinsic fitness exceeds the host's intrinsic fitness. When the parasitoid can invade, there is a critical threshold, CV*>1, of the coefficient of variation (CV) of the distribution of parasitoid attacks that determines that outcome of the invasion. If parasitoid attacks sufficiently aggregated (i.e., CV>CV*), then the host and parasitoid coexist. Typically (in a topological sense), this coexistence is shown to occur about a periodic attractor or a stable equilibrium. If the parasitoid attacks are sufficiently random (i.e. CV1. When CV<1, the parasitoid exhibits highly oscillatory dynamics. Alternatively, when parasitoid attacks are sufficiently aggregated but not overly aggregated (i.e. CV>1 but close to 1), the host and parasitoid coexist about a stable equilibrium with low host densities. The implications of these results for classical biological control are discussed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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There is an emerging consensus that parasitoids are limited by the number of eggs which they can lay as well as the amount of time they can search for their hosts. Since egg limitation tends to destabilize host-parasitoid dynamics, successful control of insect pests by parasitoids requires additional stabilizing mechanisms such as heterogeneity in the distribution of parasitoid attacks and host density-dependence. To better understand how egg limitation, search limitation, heterogeneity in parasitoid attacks, and host density-dependence influence host-parasitoid dynamics, discrete time models accounting for these factors are analyzed. When parasitoids are purely egg-limited, a complete anaylsis of the host-parasitoid dynamics are possible. The analysis implies that the parasitoid can invade the host system only if the parasitoid's intrinsic fitness exceeds the host's intrinsic fitness. When the parasitoid can invade, there is a critical threshold, CV*>1, of the coefficient of variation (CV) of the distribution of parasitoid attacks that determines that outcome of the invasion. If parasitoid attacks sufficiently aggregated (i.e., CV>CV*), then the host and parasitoid coexist. Typically (in a topological sense), this coexistence is shown to occur about a periodic attractor or a stable equilibrium. If the parasitoid attacks are sufficiently random (i.e. CV<CV*), then the parasitoid drives the host to extinction. When parasitoids are weakly search-limited as well as egg-limited, coexistence about a global attractor occurs even if CV<CV*. However, numerical simulations suggest that the nature of this attractor depends critically on whether CV<1 or CV>1. When CV<1, the parasitoid exhibits highly oscillatory dynamics. Alternatively, when parasitoid attacks are sufficiently aggregated but not overly aggregated (i.e. CV>1 but close to 1), the host and parasitoid coexist about a stable equilibrium with low host densities. The implications of these results for classical biological control are discussed.

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Schreiber, S J; Vejdani, M

Handling time promotes the coevolution of aggregation in predator-prey systems (Journal Article)

Proceedings of the Royal Society: Biological Sciences, 273 , pp. 185-191, 2006.

(Abstract | Links | BibTeX)

Schreiber, S J

Host-parasitoid dynamics of a generalized Ŧhompson model (Journal Article)

Journal of Mathematical Biology, 52 , pp. 719–732, 2006.

(Abstract | Links | BibTeX)

Schreiber, S J

Persistence despite perturbations for interacting populations (Journal Article)

Journal of Theoretical Biology, 242 , pp. 844-52, 2006.

(Abstract | Links | BibTeX)

Schreiber, S J; Lipcius, R; Seitz, R; Long, C

Dancing between the devil and the deep blue sea: The stabilizing effect of enemy-free sinks and victimless sinks (Journal Article)

Oikos, 113 , pp. 67–81, 2006.

(Abstract | Links | BibTeX)

@article{oikos-06,
title = {Dancing between the devil and the deep blue sea: The stabilizing effect of enemy-free sinks and victimless sinks},
author = {S J Schreiber and R Lipcius and R Seitz and C Long},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2022/09/Oikos-2006-Schreiber-Dancing-between-the-devil-and-deep-blue-sea-the-stabilizing-effect-of-enemyE28090free-and-victimless.pdf},
year = {2006},
date = {2006-01-01},
journal = {Oikos},
volume = {113},
pages = {67--81},
abstract = {Theoretical and empirical studies have shown that enemy-victim interactions in spatially homogenous environments can exhibit diverging oscillations which result in the extinction of one or both species. For enemy-victim models with overlapping generations, we investigate the dynamical implications of spatial heterogeneity created by enemy-free sinks or victimless sinks. An enemy-free sink is a behavioral, physiological or ecological state that reduces or eliminates the victim's vulnerability to the enemy but cannot sustain the victim population. For victims that move in an ideal-free manner, we prove that the inclusion of an enemy-free sink shifts the population dynamics from diverging oscillations to stable oscillations. During these stable oscillations, the victim disperses in an oscillatory manner between the enemy-free sink and the enemy-occupied patch. Enemy-free sinks with lower mortality rates exhibit oscillations with smaller amplitudes and longer periods. A victimless sink, on the other hand, is a behavioral, physiological or ecological state in which the enemy has limited (or no) access to its victims. For enemies that move in an ideal-free manner, we prove that victimless sinks also stabilize diverging oscillations. Simulations suggest that suboptimal behavior due to information gathering or learning limitations amplify oscillations for systems with enemy-free sinks and dampen oscillations for systems with victimless sinks. These results illustrate that the coupling of a sink created by unstable enemy-victim interactions and a sink created by unsuitable environmental conditions can result in population persistence at the landscape level.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Jacobs, F; Schreiber, S J

Random perturbations of dynamical systems with absorbing states (Journal Article)

SIAM Journal of Applied Dynamical Systems, 5 , pp. 293–312, 2006.

(Links | BibTeX)

Kirkland, S; Li, C K; Schreiber, S J

On the evolution of dispersal in patchy landscapes (Journal Article)

SIAM Journal on Applied Mathematics, 66 (4), pp. 1366-1382, 2006.

(Abstract | Links | BibTeX)

Li, C K; Schreiber, S J

On dispersal and population growth for multistate matrix models (Journal Article)

Linear Algebra Appl., 418 (2-3), pp. 900–912, 2006, ISSN: 0024-3795.

(Abstract | Links | BibTeX)

Lloyd-Smith, J O; Schreiber, S J; Getz, W M

Moving beyond averages: individual-level variation in disease transmission (Incollection)

Mathematical studies on human disease dynamics, 410 , pp. 235–258, Amer. Math. Soc., Providence, RI, 2006.

(Abstract | BibTeX)

@incollection{book-06,
title = {Moving beyond averages: individual-level variation in disease transmission},
author = {J O Lloyd-Smith and S J Schreiber and W M Getz},
year = {2006},
date = {2006-01-01},
booktitle = {Mathematical studies on human disease dynamics},
volume = {410},
pages = {235--258},
publisher = {Amer. Math. Soc.},
address = {Providence, RI},
series = {Contemp. Math.},
abstract = {It is common practice in disease modeling studies to characterize groups or subgroups using population-average parameters, most importantly the basic reproductive number, R0 . This approach overlooks variation at the individual level, which is caused by many factors. In this paper we show evidence of significant individual-level variation in transmission patterns for several diseases, and discuss how this can be incorporated into epidemiological models. We introduce a natural generalization of R0 : the `individual reproductive number', v, which is the expected number of secondary cases caused by a given infected individual. Individual reproductive numbers for a population are drawn from a continuous probability distribution with mean equal to R0 (or to the effective reproductive number, R, if the population is not wholly susceptible). In this framework, superspreading events correspond to extreme values from the right-hand tail of the distribution of v, and we propose a precise and generalizable definition of superspreading events based on probabilistic considerations. We analyze detailed transmission data for a range of directly-transmitted diseases, and find that conventional models assuming homogeneous transmission cannot account for observed patterns. Analysis of a branching process model incorporating individual-level heterogeneity reveals that observed levels of variation cause invasion dynamics to differ dramatically from predictions based on population averages. We explore the implications of these findings for outbreak control policies, demonstrating that individual-specific control measures are more likely to stop an outbreak than population-wide measures when both have the same effect on R0 . We also highlight the effectiveness of measures targeting highly infectious individuals, and discuss how our results relate to recently-proposed surveillance methods for emerging diseases. We conclude by discussing future challenges in empirical and theoretical studies.},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}

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It is common practice in disease modeling studies to characterize groups or subgroups using population-average parameters, most importantly the basic reproductive number, R0 . This approach overlooks variation at the individual level, which is caused by many factors. In this paper we show evidence of significant individual-level variation in transmission patterns for several diseases, and discuss how this can be incorporated into epidemiological models. We introduce a natural generalization of R0 : the `individual reproductive number', v, which is the expected number of secondary cases caused by a given infected individual. Individual reproductive numbers for a population are drawn from a continuous probability distribution with mean equal to R0 (or to the effective reproductive number, R, if the population is not wholly susceptible). In this framework, superspreading events correspond to extreme values from the right-hand tail of the distribution of v, and we propose a precise and generalizable definition of superspreading events based on probabilistic considerations. We analyze detailed transmission data for a range of directly-transmitted diseases, and find that conventional models assuming homogeneous transmission cannot account for observed patterns. Analysis of a branching process model incorporating individual-level heterogeneity reveals that observed levels of variation cause invasion dynamics to differ dramatically from predictions based on population averages. We explore the implications of these findings for outbreak control policies, demonstrating that individual-specific control measures are more likely to stop an outbreak than population-wide measures when both have the same effect on R0 . We also highlight the effectiveness of measures targeting highly infectious individuals, and discuss how our results relate to recently-proposed surveillance methods for emerging diseases. We conclude by discussing future challenges in empirical and theoretical studies.

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Schreiber, S J; Kelton, M

Sink habitats can alter ecological outcomes for competing species (Journal Article)

Journal of Animal Ecology, 74 (6), pp. 995-1004, 2005.

(Abstract | Links | BibTeX)

@article{jae-05,
title = {Sink habitats can alter ecological outcomes for competing species},
author = {S J Schreiber and M Kelton},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2022/09/Sink_Habitats_Can_Alter_Ecological_Outco.pdf},
year = {2005},
date = {2005-01-01},
journal = {Journal of Animal Ecology},
volume = {74},
number = {6},
pages = {995-1004},
abstract = {1. Species often compete for breeding sites in heterogeneous landscapes consisting of sources and sinks. To understand how the presence or absence of sink breeding sites influence ecological outcomes, we extend Pulliam's source--sink model to competing species.
2. In a homogeneous landscape consisting of source sites, we prove that one species, the 'superior' competitor, competitively excludes the other. Dominance is determined by a simple rule: the species that at equilibrium acquires new breeding sites at a faster rate dominates.
3. We prove that the inclusion of sink sites can alter this ecological outcome by either mediating coexistence, reversing competitive dominance, or facilitating a priority effect.
4. Sink-mediated coexistence requires the species to exhibit asymmetries in acquiring sink sites, the 'inferior' species to have a competitive advantage on sink sites and the ratio of sink to source sites be sufficiently low.
5. For example, if the sink breeding sites are competitive refuges for the 'inferior' competitor and not too low in quality, coexistence occurs if the number of sink sites lies below a threshold. Alternatively, when the number of sink sites exceeds this threshold, competitive dominance is reversed and the 'superior' competitor is displaced.
6. Counter-intuitively, despite being unable to support species in isolation, sink habitats embedded in a geographical mosaic of sources and sinks can enhance biodiversity by mediating coexistence or alter species composition by reversing competitive interactions.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Keagy, J; Schreiber, S J; Cristol, D A

Replacing Sources with Sinks: When Do Populations Go Down the Drain? (Journal Article)

Restoration Ecology, 13 (3), pp. 529-535, 2005.

(Links | BibTeX)

Lloyd-Smith, J; Schreiber, S J; Kopp, P E; Getz, W M

Superspreading and the impact of individual variation on disease emergence (Journal Article)

Nature, pp. 355–359, 2005.

(Abstract | Links | BibTeX)

@article{nature-05,
title = {Superspreading and the impact of individual variation on disease emergence},
author = {J Lloyd-Smith and S J Schreiber and P E Kopp and W M Getz},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2022/09/nature04153.pdf},
year = {2005},
date = {2005-01-01},
journal = {Nature},
pages = {355--359},
abstract = {Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R0, which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R0 can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous `superspreading events' in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R0 is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency. !!},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Ruggieri, E; Schreiber, S J

The dynamics of the Schoener-Polis-Ħolt model of intra-guild predation (Journal Article)

Mathematical Biosciences and Engineering, 2 (2), pp. 279–288, 2005, ISSN: 1547-1063.

(Abstract | Links | BibTeX)

Schreiber, S J

On Allee effects in structured populations (Journal Article)

Proceedings of the American Mathematical Society, 132 (10), pp. 3047–3053, 2004.

(Links | BibTeX)

Schreiber, S J

Coexistence for species sharing a predator (Journal Article)

Journal of Differential Equations, 196 , pp. 209–225, 2004.

(Links | BibTeX)

Schreiber, S J; Rittenhouse, S

From simple rules to cycling in community assembly (Journal Article)

Oikos, 105 , pp. 349–358, 2004.

(Abstract | Links | BibTeX)

Benaïm, M; Schreiber, S J; Tarrés, P

Generalized urn models of evolutionary processes (Journal Article)

Annals of Applied Probability, 14 , pp. 1455–1478, 2004.

(Abstract | Links | BibTeX)

Hofbauer, J; Schreiber, S J

To persist or not to persist? (Journal Article)

Nonlinearity, 17 , pp. 1393–1406, 2004.

(Links | BibTeX)

Schreiber, S J

Allee effects, chaotic transients, and unexpected extinctions (Journal Article)

Theoretical Population Biology, 2003.

(Abstract | Links | BibTeX)

Schreiber, S J; Tobiason, G A

The evolution of resource use (Journal Article)

Journal of Mathematical Biology, 47 , pp. 56–78, 2003.

(Abstract | Links | BibTeX)

Schreiber, S J

Permanence of weakly coupled vector fields (Journal Article)

SIAM Journal on Mathematical Analysis, 33 (5), pp. 1048–1057 (electronic), 2002, ISSN: 0036-1410.

(BibTeX)

Schreiber, S J; Fox, L R; Getz, W M

Parasitoid sex allocation affects coevolution of patch selection in host-parasitoid systems (Journal Article)

Evolutionary Ecology Research, 4 , pp. 701-718, 2002.

(Abstract | Links | BibTeX)

'n, Mierczy J; Schreiber, S J

Kolmogorov vector fields with robustly permanent subsystems (Journal Article)

Journal of Mathematical Analysis and Applications, 267 (1), pp. 329–337, 2002.

(Links | BibTeX)

Schreiber, S J; Mills, N J; Gutierrez, A P

Host-limited dynamics of autoparasitoids (Journal Article)

Journal of Theoretical Biology, 212 , pp. 141-153, 2001.

(Links | BibTeX)

Schreiber, S J

Chaos and Sudden Extinction in Simple Ecological Models (Journal Article)

Journal of Mathematical Biology, 42 , pp. 239–260, 2001.

(Abstract | Links | BibTeX)

Schreiber, S J

Urn models, replicator processes, and random genetic drift (Journal Article)

SIAM Journal of Applied Mathematics, 61 , pp. 2148–2167, 2001.

(Abstract | Links | BibTeX)

@article{siap-01,
title = {Urn models, replicator processes, and random genetic drift},
author = {S J Schreiber},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2022/09/s0036139999352857.pdf},
year = {2001},
date = {2001-01-01},
journal = {SIAM Journal of Applied Mathematics},
volume = {61},
pages = {2148--2167},
abstract = {To understand the relative importance of natural selection and random genetic drift in finite but growing populations, the asymptotic behavior of a class of generalized Polya urns is studied using the method of ordinary differential equation (ODE). Of particular interest is the replicator process: two balls (individuals) are chosen from an urn (the population) at random with replacement and balls of the same colors (strategies) are added or removed according to probabilities that depend only on the colors of the chosen balls. Under the assumption that the expected number of balls being added always exceeds the expected number of balls being removed whenever balls are in the urn, the probability of nonextinction is shown to be positive. On the event of nonextinction, three results are proven: (i) the number of balls increases asymptotically at a linear rate, (ii) the distribution x(n) of strategies at the nth update is a "noisy" Cauchy--Euler approximation to the mean limit ODE of the process, and (iii) the limit set of x(n) is almost surely a connected internally chain recurrent set for the mean limit ODE. Under a stronger set of assumptions, it is shown that for any attractor of the mean limit ODE there is a positive probability that the limit set for x(n) lies in this attractor. Theoretical and numerical estimates for the probabilities of nonextinction and convergence to an attractor suggest that random genetic drift is more likely to overcome natural selection in small populations for which pairwise interactions lead to highly variable outcomes, and is less likely to overcome natural selection in large populations with the potential for rapid growth.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Schreiber, S J; Fox, L R; Getz, W M

Coevolution of contrary choices in host-parasitoid systems (Journal Article)

American Naturalist, pp. 637–648, 2000.

(Abstract | Links | BibTeX)

@article{amnat-00,
title = {Coevolution of contrary choices in host-parasitoid systems},
author = {S J Schreiber and L R Fox and W M Getz},
url = {https://schreiber.faculty.ucdavis.edu/wp-content/uploads/sites/568/2019/08/2000_schreiber_fox_getz_AmNat.pdf},
year = {2000},
date = {2000-01-01},
journal = {American Naturalist},
pages = {637--648},
abstract = {We investigate patch selection strategies of hosts and parasitoids in heterogeneous environments. Previous theoretical work showed that when host traits vary among patches, coevolved populations of hosts and parasitoids make congruent choices (i.e.,hosts and parasitoids preferentially select the same patches) and exhibit direct density dependence in the distribution of percent parasitism. However, host-parasitoid systems in the field show a range of patterns in percent parasitism, while behavioral studies indicate that hosts and parasitoids can exhibit contrary choices (i.e., hosts avoid parches favored by the parasitoid). We extend previous theory by permitting life-history traits of the parasitoid as well as the host to vary among patches. Our analysis implies that in coevolutionarily stable populations, hosts preferentially select patches that intrinsically support higher host equilibrium numbers (i.e., the equilibrium number achieved by hosts when both populations are confined toa single patch) and that parasitoids preferentially select patches that intrinsically support higher parasitoid equilibrium numbers (i.e., the equilibrium number achieved by the parasitoids when both populations are confined to a patch). Using this result, we show how variation in life-history traits among patches leads to contrary or congruent choices or leads to direct density dependence, inverse density dependence, or density independence in the distribution of percent parasitism. In addition, we determine when populations playing the coevolutionarily stable strategies are ecologically stable. Our analysis shows that heterogeneous environments containing patches where the intrinsic rate of growth of the host and the survivorship rate ofthe parasitoid are low result in the coevolved populations exhibiting contrary choices and, as a result, promote ecological stability.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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Schreiber, S J

Criteria for $C^r$ robust permanence (Journal Article)

Journal of Differential Equations, 162 , pp. 400–426, 2000.

(Abstract | Links | BibTeX)

Benaïm, M; Schreiber, S J

Ergodic properties of weak asymptotic pseudotrajectores for semiflows (Journal Article)

Journal of Dynamics and Differential Equations, 12 , pp. 579–598, 2000.

(Links | BibTeX)

Eisenberg, J N S; Washburn, J O; Schreiber, S J

The generalist feeding behaviors of empAedes sierrensis larvae and their effects on protozoan populations (Journal Article)

Ecology, 81 , pp. 921-935, 2000.

(Abstract | BibTeX)

@article{ecology-00,
title = {The generalist feeding behaviors of empAedes sierrensis larvae and their effects on protozoan populations},
author = {J N S Eisenberg and J O Washburn and S J Schreiber},
year = {2000},
date = {2000-01-01},
journal = {Ecology},
volume = {81},
pages = {921-935},
abstract = {The generalist feeding strategy of larvae of the western tree hole mosquito, Aedes sierrensis, is central to understanding the community-level effects of the tritrophic interactions among mosquito larvae, midsized organisms (such as protozoa), and lower-level organisms (such as bacteria and fungi) in west coast phytotelmata. Laboratory microcosm experiments were conducted to characterize the feeding strategies of Ae. sierrensis larvae in the presence of multiple resource types (free-swimming protozoa and substrate-bound particulate material). In our experiment, we quantified the effects of varying instar numbers and profile, resource type, and refuge size on predation of protozoa. Refugia were explicitly modeled in our microcosms, representing the interstitial spaces of leaf litter and the wood lining of natural tree holes. Results from these microcosm experiments suggested that: (1) Even in the absence of larvae, the majority of protozoa resided in the small-volume, resource-rich refugia. There was, however, a strong nonlinear and negative relationship between larval densities in the upper compartment and the protozoan densities in the refuge, suggesting that there was continual movement of protozoa between the two spaces. (2) Fourth instars harvested resources by filter-feeding at a higher rate than second instars. (3) As the level of substrate-bound particulate food was increased, the predation pressure by filter-feeding on the protozoa decreased. (4) As the refuge volume increased, the predation pressure on the protozoa decreased. We constructed a three-state-variable mathematical model describing the generalist feeding behavior of Ae. sierrensis larvae. The model system, with constant predator densities and two prey groups, exhibited full cooperativity; i.e., an increase in protozoa density resulted in a shift toward predation by filter feeding, while an increase in substrate-bound resources resulted in a shift toward predation by browsing. This indirect mutualism is mechanistically distinct from previously published systems and provides a potential mechanism for protozoan persistence in the presence of larval predation.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}

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The generalist feeding strategy of larvae of the western tree hole mosquito, Aedes sierrensis, is central to understanding the community-level effects of the tritrophic interactions among mosquito larvae, midsized organisms (such as protozoa), and lower-level organisms (such as bacteria and fungi) in west coast phytotelmata. Laboratory microcosm experiments were conducted to characterize the feeding strategies of Ae. sierrensis larvae in the presence of multiple resource types (free-swimming protozoa and substrate-bound particulate material). In our experiment, we quantified the effects of varying instar numbers and profile, resource type, and refuge size on predation of protozoa. Refugia were explicitly modeled in our microcosms, representing the interstitial spaces of leaf litter and the wood lining of natural tree holes. Results from these microcosm experiments suggested that: (1) Even in the absence of larvae, the majority of protozoa resided in the small-volume, resource-rich refugia. There was, however, a strong nonlinear and negative relationship between larval densities in the upper compartment and the protozoan densities in the refuge, suggesting that there was continual movement of protozoa between the two spaces. (2) Fourth instars harvested resources by filter-feeding at a higher rate than second instars. (3) As the level of substrate-bound particulate food was increased, the predation pressure by filter-feeding on the protozoa decreased. (4) As the refuge volume increased, the predation pressure on the protozoa decreased. We constructed a three-state-variable mathematical model describing the generalist feeding behavior of Ae. sierrensis larvae. The model system, with constant predator densities and two prey groups, exhibited full cooperativity; i.e., an increase in protozoa density resulted in a shift toward predation by filter feeding, while an increase in substrate-bound resources resulted in a shift toward predation by browsing. This indirect mutualism is mechanistically distinct from previously published systems and provides a potential mechanism for protozoan persistence in the presence of larval predation.

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Schreiber, S J

Successional stability of vector fields in dimension three (Journal Article)

Proceedings of the American Mathematical Soceity, 127 , pp. 993–1002, 1999.

(Links | BibTeX)