Pollination and other ecosystem services produced by mobile organisms: a conceptual framework for the effects of land-use change.

Many ecosystem services are delivered by organisms that depend on habitats that are segregated spatially or temporally from the location where services are provided. Management of mobile organisms contributing to ecosystem services requires consideration not only of the local scale where services are delivered, but also the distribution of resources at the landscape scale, and the foraging ranges and dispersal movements of the mobile agents. We develop a conceptual model for exploring how one such mobile-agent-based ecosystem service (MABES), pollination, is affected by land-use change, and then generalize the model to other MABES. The model includes interactions and feedbacks among policies affecting land use, market forces and the biology of the organisms involved. Animal-mediated pollination contributes to the production of goods of value to humans such as crops; it also bolsters reproduction of wild plants on which other services or service-providing organisms depend. About one-third of crop production depends on animal pollinators, while 60-90% of plant species require an animal pollinator. The sensitivity of mobile organisms to ecological factors that operate across spatial scales makes the services provided by a given community of mobile agents highly contextual. Services vary, depending on the spatial and temporal distribution of resources surrounding the site, and on biotic interactions occurring locally, such as competition among pollinators for resources, and among plants for pollinators. The value of the resulting goods or services may feed back via market-based forces to influence land-use policies, which in turn influence land management practices that alter local habitat conditions and landscape structure. Developing conceptual models for MABES aids in identifying knowledge gaps, determining research priorities, and targeting interventions that can be applied in an adaptive management context.

[1]  Martin Burd,et al.  Bateman’s principle and plant reproduction: The role of pollen limitation in fruit and seed set , 2008, The Botanical Review.

[2]  A. Klein,et al.  Linking deforestation scenarios to pollination services and economic returns in coffee agroforestry systems. , 2007, Ecological applications : a publication of the Ecological Society of America.

[3]  C. Kremen,et al.  Effect of Human Disturbance on Bee Communities in a Forested Ecosystem , 2007, Conservation biology : the journal of the Society for Conservation Biology.

[4]  Teja Tscharntke,et al.  Habitat modification alters the structure of tropical host–parasitoid food webs , 2007, Nature.

[5]  R. Chaplin-Kramer,et al.  Insects as providers of ecosystem services: crop pollination and pest control. , 2007 .

[6]  P. Kevan,et al.  ASSESSMENT OF THE CAPACITY OF CANADIAN FEDERAL AND PROVINCIAL LEGISLATION TO CONSERVE NATIVE AND MANAGED POLLINATORS , 2007 .

[7]  Estacidn Bioldgica de Doiiana.  Variation in mutualisms : the spatio-temporal mosaic of a pollinator assemblage , 2007 .

[8]  A. Klein,et al.  Importance of pollinators in changing landscapes for world crops , 2007, Proceedings of the Royal Society B: Biological Sciences.

[9]  Sarah S. Greenleaf,et al.  Wild bee species increase tomato production and respond differently to surrounding land use in Northern California , 2006 .

[10]  N. Williams,et al.  Effects of Cultivation and Proximity to Natural Habitat on Ground-nesting Native Bees in California Sunflower Fields , 2006 .

[11]  Sarah S. Greenleaf,et al.  Wild bees enhance honey bees’ pollination of hybrid sunflower , 2006, Proceedings of the National Academy of Sciences.

[12]  S. Potts,et al.  The effects of cattle grazing on plant-pollinator communities in a fragmented Mediterranean landscape , 2006 .

[13]  Mark L. Winston,et al.  Pollinators provide economic incentive to preserve natural land in agroecosystems , 2006 .

[14]  M. Aizen,et al.  Plant reproductive susceptibility to habitat fragmentation: review and synthesis through a meta-analysis. , 2006, Ecology letters.

[15]  Ç. Şekercioğlu.  Increasing awareness of avian ecological function. , 2006, Trends in ecology & evolution.

[16]  A. P. Schaffers,et al.  Parallel Declines in Pollinators and Insect-Pollinated Plants in Britain and the Netherlands , 2006, Science.

[17]  R. Gegear,et al.  Plight of the bumble bee: Pathogen spillover from commercial to wild populations , 2006 .

[18]  Neal M Williams,et al.  Complex responses within a desert bee guild (Hymenoptera: Apiformes) to urban habitat fragmentation. , 2006, Ecological applications : a publication of the Ecological Society of America.

[19]  J. Losey,et al.  The Economic Value of Ecological Services Provided by Insects , 2006 .

[20]  F. Herzog,et al.  Mixed biodiversity benefits of agri-environment schemes in five European countries. , 2006, Ecology letters.

[21]  A. Klein,et al.  Rain forest promotes trophic interactions and diversity of trap-nesting Hymenoptera in adjacent agroforestry. , 2006, The Journal of animal ecology.

[22]  Teja Tscharntke,et al.  Economic Evaluation of Pollination Services Comparing Coffee Landscapes in Ecuador and Indonesia , 2006 .

[23]  Carolina L. Morales,et al.  Invasive mutualisms and the structure of plant–pollinator interactions in the temperate forests of north‐west Patagonia, Argentina , 2006 .

[24]  L. Packer,et al.  Increased genetic differentiation in a specialist versus a generalist bee: implications for conservation , 2006, Conservation Genetics.

[25]  M. Aizen,et al.  Edge effects on flower-visiting insects in grapefruit plantations bordering premontane subtropical forest. , 2005 .

[26]  A. Kolb.  Reduced reproductive success and offspring survival in fragmented populations of the forest herb Phyteuma spicatum , 2005 .

[27]  S. Potts,et al.  Pollinator diversity and crop pollination services are at risk. , 2005, Trends in ecology & evolution.

[28]  Jonathan M. Chase,et al.  Trophic cascades across ecosystems , 2005, Nature.

[29]  O. Gordo,et al.  Phenology and climate change: a long-term study in a Mediterranean locality , 2005, Oecologia.

[30]  Carsten Thies,et al.  REVIEWS AND SYNTHESES Landscape perspectives on agricultural intensification and biodiversity - ecosystem service management , 2005 .

[31]  S. Cunningham,et al.  Rain Forest Provides Pollinating Beetles for Atemoya Crops , 2005, Journal of economic entomology.

[32]  Robert R. Dunn,et al.  Modern Insect Extinctions, the Neglected Majority , 2005 .

[33]  J. Ghazoul.  Pollen and seed dispersal among dispersed plants , 2005, Biological reviews of the Cambridge Philosophical Society.

[34]  L. Packer,et al.  Complementary sex determination substantially increases extinction proneness of haplodiploid populations. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[35]  Michelle T. Franklin,et al.  Lethal and sub-lethal effects of spinosad on bumble bees (Bombus impatiens Cresson). , 2005, Pest management science.

[36]  M. Winston,et al.  WILD BEE ABUNDANCE AND SEED PRODUCTION IN CONVENTIONAL, ORGANIC, AND GENETICALLY MODIFIED CANOLA , 2005 .

[37]  T. Roulston,et al.  Farming Practices Influence Wild Pollinator Populations on Squash and Pumpkin , 2005, Journal of economic entomology.

[38]  N. Haddad,et al.  THE EFFECTS OF PATCH SHAPE ON INDIGO BUNTINGS: EVIDENCE FOR AN ECOLOGICAL TRAP , 2005 .

[39]  N. Williams,et al.  Extinction order and altered community structure rapidly disrupt ecosystem functioning. , 2005, Ecology letters.

[40]  David Freudenberger,et al.  Ecosystem wicks: Woodland trees enhance water infiltration in a fragmented agricultural landscape in eastern Australia , 2005 .

[41]  C. Kremen.  Managing ecosystem services: what do we need to know about their ecology? , 2005, Ecology letters.

[42]  Jeremy D. Wilson,et al.  Does organic farming benefit biodiversity , 2005 .

[43]  D. Goulson,et al.  Causes of rarity in bumblebees , 2005 .

[44]  T. Sparks,et al.  Providing foraging resources for bumblebees in intensively farmed landscapes , 2005 .

[45]  S. Potts,et al.  Role of nesting resources in organising diverse bee communities in a Mediterranean landscape , 2005 .

[46]  Carsten Thies,et al.  The landscape context of cereal aphid–parasitoid interactions , 2005, Proceedings of the Royal Society B: Biological Sciences.

[47]  J. Blackmer,et al.  Abundance and Diversity of Euglossine Bees in the Fragmented Landscape of the Brazilian Atlantic Forest’ , 2005 .

[48]  D. Hodgson,et al.  How isolated is Antarctica? , 2005, Trends in ecology & evolution.

[49]  Millenium Ecosystem Assessment.  Ecosystems and human well-being: synthesis , 2005 .

[50]  Jane Memmott,et al.  Tolerance of pollination networks to species extinctions , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[51]  T. Ricketts,et al.  Confronting a biome crisis: global disparities of habitat loss and protection , 2004 .

[52]  D. A. Moeller.  Facilitative interactions among plants via shared pollinators , 2004 .

[53]  A. Nicotra,et al.  Plant isolation reduces outcross pollen receipt in a partially self‐compatible herb , 2004 .

[54]  C. Tingle.  Biodiversity and pest management in agroecosystems, 2nd edition , 2004 .

[55]  H. Samejima,et al.  The effects of human disturbance on a stingless bee community in a tropical rainforest , 2004 .

[56]  Michele R. Dudash,et al.  Pollination Syndromes and Floral Specialization , 2004 .

[57]  Miguel A. Altieri,et al.  Ecological Engineering for Pest Management: Advances in Habitat Manipulation for Arthropods , 2004 .

[58]  T. Ricketts.  Tropical Forest Fragments Enhance Pollinator Activity in Nearby Coffee Crops , 2004 .

[59]  R. Cartar.  RESOURCE TRACKING BY BUMBLE BEES: RESPONSES TO PLANT-LEVEL DIFFERENCES IN QUALITY , 2004 .

[60]  Michele R. Dudash,et al.  Pollen limitation of plant reproduction: Ecological and evolutionary causes and consequences , 2004 .

[61]  Gretchen C Daily,et al.  Economic value of tropical forest to coffee production. , 2004, Proceedings of the National Academy of Sciences of the United States of America.

[62]  W. Meek,et al.  The response of foraging bumblebees to successional change in newly created arable field margins , 2004 .

[63]  Diego P. Vázquez,et al.  ASYMMETRIC SPECIALIZATION: A PERVASIVE FEATURE OF PLANT-POLLINATOR INTERACTIONS , 2004 .

[64]  R. Frankl,et al.  Are forests potential landscape barriers for foraging bumblebees? Landscape scale experiments with Bombus terrestris agg. and Bombus pascuorum (Hymenoptera, Apidae) , 2004 .

[65]  G. Kudo,et al.  Does seed production of spring ephemerals decrease when spring comes early? , 2004, Ecological Research.

[66]  Bernd Blossey,et al.  Impact and management of purple loosestrife (Lythrum salicaria) in North America , 2001, Biodiversity & Conservation.

[67]  J. Thompson,et al.  Sources of variation in pollinator contribution within a guild: the effects of plant and pollinator factors , 1996, Oecologia.

[68]  I. Rasmussen,et al.  Gene flow inferred from seed dispersal and pollinator behaviour compared to DNA analysis of restriction site variation in a patchy population of Lotus corniculatus L. , 1992, Oecologia.

[69]  POLLEN TRANSFER BY HUMMINGBIRDS AND BUMBLEBEES, AND THE DIVERGENCE OF POLLINATION MODES IN PENSTEMON , 2003, Evolution; international journal of organic evolution.

[70]  D. Goulson.  Effects of introduced bees on native ecosystems , 2003 .

[71]  Teja Tscharntke,et al.  Mass flowering crops enhance pollinator densities at a landscape scale , 2003 .

[72]  Pat Willmer,et al.  LINKING BEES AND FLOWERS: HOW DO FLORAL COMMUNITIES STRUCTURE POLLINATOR COMMUNITIES? , 2003 .

[73]  M. Muth,et al.  The Fable of the Bees Revisited: Causes and Consequences of the U.S. Honey Program* , 2003, The Journal of Law and Economics.

[74]  Anthony R. Ives,et al.  Biodiversity and biocontrol: emergent impacts of a multi-enemy assemblage on pest suppression and crop yield in an agroecosystem , 2003 .

[75]  I. Steffan‐Dewenter.  Importance of Habitat Area and Landscape Context for Species Richness of Bees and Wasps in Fragmented Orchard Meadows , 2003 .

[76]  Richard S. Ostfeld,et al.  COMMUNITY DISASSEMBLY, BIODIVERSITY LOSS, AND THE EROSION OF AN ECOSYSTEM SERVICE , 2003 .

[77]  J. Cronin.  MATRIX HETEROGENEITY AND HOST–PARASITOID INTERACTIONS IN SPACE , 2003 .

[78]  Teja Tscharntke,et al.  Fruit set of highland coffee increases with the diversity of pollinating bees , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[79]  S. Potts,et al.  Response of plant-pollinator communities to fire: changes in diversity, abundance and floral reward structure , 2003 .

[80]  Ingolf Steffan-Dewenter,et al.  Honeybee foraging in differentially structured landscapes , 2003, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[81]  Nick M. Haddad,et al.  CORRIDOR USE BY DIVERSE TAXA , 2003 .

[82]  R. Ostfeld,et al.  Effect of Forest Fragmentation on Lyme Disease Risk , 2003 .

[83]  William F. Morris,et al.  13. Which Mutualists Are Most Essential? Buffering of Plant Reproduction against the Extinction of Pollinators , 2003 .

[84]  B. Malmqvist,et al.  Mechanisms behind positive diversity effects on ecosystem functioning: testing the facilitation and interference hypotheses , 2003, Oecologia.

[85]  F. Moberg,et al.  Mobile Link Organisms and Ecosystem Functioning: Implications for Ecosystem Resilience and Management , 2003, Ecosystems.

[86]  B. Danforth,et al.  Gene Flow and Population Structure in an Oligolectic Desert Bee, Macrotera (Macroteropsis) portalis (Hymenoptera: Andrenidae) , 2003 .

[87]  Neal M. Williams,et al.  Crop pollination from native bees at risk from agricultural intensification , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[88]  M. Aizen,et al.  Reproductive success in fragmented habitats: do compatibility systems and pollination specialization matter? , 2002 .

[89]  E. Sanderson,et al.  The Human Footprint and the Last of the Wild , 2002 .

[90]  C. Zachariades,et al.  Effects of Habitat Fragmentation on Pollinator Diversity and Plant Reproductive Success in Renosterveld Shrublands of South Africa , 2002 .

[91]  G. S. Albuquerque,et al.  Abundance and Diversity of Euglossine Bees in the Fragmented Landscape of the Brazilian Atlantic Forest1 , 2002 .

[92]  Achim Gathmann,et al.  Foraging ranges of solitary bees , 2002 .

[93]  A. Klein,et al.  Effects of Land‐Use Intensity in Tropical Agroforestry Systems on Coffee Flower‐Visiting and Trap‐Nesting Bees and Wasps , 2002 .

[94]  D. Simberloff,et al.  Ecological Specialization and Susceptibility to Disturbance: Conjectures and Refutations , 2002, The American Naturalist.

[95]  A. Fitter,et al.  Rapid Changes in Flowering Time in British Plants , 2002, Science.

[96]  Teja Tscharntke,et al.  SCALE‐DEPENDENT EFFECTS OF LANDSCAPE CONTEXT ON THREE POLLINATOR GUILDS , 2002 .

[97]  D. H. Boshier,et al.  Increased pollen flow counteracts fragmentation in a tropical dry forest: An example from Swietenia humilis Zuccarini , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[98]  Kimberly A. With,et al.  THRESHOLD EFFECTS OF LANDSCAPE STRUCTURE ON BIOLOGICAL CONTROL IN AGROECOSYSTEMS , 2002 .

[99]  C. Brühl,et al.  Determinants of stingless bee nest density in lowland dipterocarp forests of Sabah, Malaysia , 2002, Oecologia.

[100]  J. Barthell,et al.  PROMOTION OF SEED SET IN YELLOW STAR‐THISTLE BY HONEY BEES: EVIDENCE OF AN INVASIVE MUTUALISM , 2001 .

[101]  C. Dick.  Genetic rescue of remnant tropical trees by an alien pollinator. , 2001, Proceedings. Biological sciences.

[102]  P. Reich,et al.  Diversity and Productivity in a Long-Term Grassland Experiment , 2001, Science.

[103]  David Kleijn,et al.  Agri-environment schemes do not effectively protect biodiversity in Dutch agricultural landscapes , 2001, Nature.

[104]  T. Tscharntke,et al.  Pollination, seed set and seed predation on a landscape scale , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[105]  T. Ricketts.  The Matrix Matters: Effective Isolation in Fragmented Landscapes , 2001, The American Naturalist.

[106]  L. Chittka,et al.  Successful invasion of a floral market , 2001, Nature.

[107]  S. Harrison,et al.  Effects of Habitat Size and Patch Isolation on Reproductive Success of the Serpentine Morning Glory , 2001 .

[108]  T. Tscharntke,et al.  Succession of bee communities on fallows , 2001 .

[109]  R. Morse,et al.  The value of honey bees as pollinators of U.S. Crops in 2000. , 2001 .

[110]  John F. Mull,et al.  Harvester Ants (Pogonomyrmex spp.): Their Community and Ecosystem Influences , 2000 .

[111]  D. C. Paton.  Disruption of Bird‐Plant Pollination Systems in Southern Australia , 2000 .

[112]  S. Corbet.  Conserving Compartments in Pollination Webs , 2000 .

[113]  S. Cunningham,et al.  Depressed pollination in habitat fragments causes low fruit set , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[114]  C. Herrera.  FLOWER‐TO‐SEEDLING CONSEQUENCES OF DIFFERENT POLLINATION REGIMES IN AN INSECT‐POLLINATED SHRUB , 2000 .

[115]  B. Law,et al.  Common blossom bats (Syconycteris australis) as pollinators in fragmented Australian tropical rainforest , 1999 .

[116]  T. Tscharntke,et al.  Effects of habitat isolation on pollinator communities and seed set , 1999, Oecologia.

[117]  C. Parmesan,et al.  Poleward shifts in geographical ranges of butterfly species associated with regional warming , 1999, Nature.

[118]  David W. Inouye,et al.  ENDANGERED MUTUALISMS: The Conservation of Plant-Pollinator Interactions , 1998 .

[119]  T. Tscharntke,et al.  Bioindication using trap‐nesting bees and wasps and their natural enemies: community structure and interactions , 1998 .

[120]  R. Cowling,et al.  Ecosystem services, efficiency, sustainability and equity: South Africa's Working for Water programme. , 1998, Trends in ecology & evolution.

[121]  M. Groom,et al.  Allee Effects Limit Population Viability of an Annual Plant , 1998, The American Naturalist.

[122]  J C Stout,et al.  Foraging bumblebees avoid flowers already visited by conspecifics or by other bumblebee species , 1998, Animal Behaviour.

[123]  I. Hanski.  Metapopulation dynamics , 1998, Nature.

[124]  J. Nason,et al.  Reproductive and Genetic Consequences of Forest Fragmentation: Two Case Studies of Neotropical Canopy Trees , 1997 .

[125]  J. Dover.  Conservation headlands: effects on butterfly distribution and behaviour , 1997 .

[126]  R. O'Neill,et al.  The value of the world's ecosystem services and natural capital , 1997, Nature.

[127]  W. Kunin.  Population size and density effects in pollination : Pollinator foraging and plant reproductive success in experimental arrays of Brassica kaber , 1997 .

[128]  A. Brody,et al.  Effects of experimental manipulation of inflorescence size on pollination and pre-dispersal seed predation in the hummingbird-pollinated plant Ipomopsis aggregata , 1997, Oecologia.

[129]  G. Fry,et al.  Bumblebee movement in a fragmented agricultural landscape , 1997 .

[130]  J. Bosch,et al.  Flowering phenology, floral traits and pollinator composition in a herbaceous Mediterranean plant community , 1997, Oecologia.

[131]  J. Cane.  The potential consequences of pollinator declines on the conservation of biodiversity and stability of food crop yields , 1997 .

[132]  J. Cornuet,et al.  Genetic differentiation of continental and island populations of Bombus terrestris (Hymenoptera: Apidae) in Europe , 1996, Molecular ecology.

[133]  B. Husband,et al.  EVOLUTION OF THE MAGNITUDE AND TIMING OF INBREEDING DEPRESSION IN PLANTS , 1996, Evolution; international journal of organic evolution.

[134]  L. Harder,et al.  Ecology and evolution of plant mating. , 1996, Trends in ecology & evolution.

[135]  L. Harder,et al.  Pollen Dispersal and Mating Patterns in Animal-Pollinated Plants , 1996 .

[136]  R. Crozier,et al.  Sex determination and population biology in the hymenoptera. , 1995, Trends in ecology & evolution.

[137]  Michael H. Unsworth,et al.  Review and synthesis , 1995, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[138]  H. Dreisig.  Ideal free distributions of nectar foraging bumblebees , 1995 .

[139]  M. Muth,et al.  Why Support the Price of Honey , 1995 .

[140]  Miguel A. Altieri,et al.  Biodiversity And Pest Management In Agroecosystems , 1994 .

[141]  I. Washitani.  Patterns of female fertility in heterostylous Primula sieboldii under pollinater limitation , 1994 .

[142]  W. Wcislo,et al.  Behavior and Phenology of a Specialist Bee (Dieunomia) and Sunflower (Helianthus) Pollen Availability , 1994 .

[143]  M. Aizen,et al.  HABITAT FRAGMENTATION, NATIVE INSECT POLLINATORS, AND FERAL HONEY BEES IN ARGENTINE, "CHACO SERRANO"' , 1994 .

[144]  J. Gingras,et al.  Complementary Aspects of Strawberry Pollination by Honey and IndigenQus Bees (Hymenoptera) , 1993 .

[145]  E. Southwick,et al.  Estimating the Economic Value of Honey Bees (Hymenoptera: Apidae) as Agricultural Pollinators in the United States , 1992 .

[146]  P. Becker,et al.  More about euglossine bees in Amazonian forest fragments , 1991 .

[147]  D. Marshall.  Nonrandom mating in wild radish : variation in pollen donor success and effects of multiple paternity among one- to six-donor pollinations , 1991 .

[148]  A. Snow.  Effects of Pollen-Load Size and Number of Donors on Sporophyte Fitness in Wild Radish (Raphanus raphanistrum) , 1990, The American Naturalist.

[149]  Carl J. Walters,et al.  Large‐Scale Management Experiments and Learning by Doing , 1990 .

[150]  Kamaljit S. Bawa,et al.  Plant-Pollinator Interactions in Tropical Rain Forests , 1990 .

[151]  C. Johansen,et al.  Pollinator protection: a bee & pesticide handbook. , 1990 .

[152]  R. Morse,et al.  The value of honey bees as pollinators of U.S. crops. II , 1989 .

[153]  Ola Jennersten.  Pollination in Dianthus deltoides (Caryophyllaceae): effects of habitat fragmentation on visitation and seed set , 1988 .

[154]  C. Herrera.  Variation in mutualisms : the spatio temporal mosaic of a pollinator assemblage , 1988 .

[155]  P. Kareiva,et al.  Finding and Losing Host Plants by Phyllotreta: Patch Size and Surrounding Habitat , 1985 .

[156]  D. Campbell,et al.  The Mechanism of Competition for Pollination between Two Forest Herbs , 1985 .

[157]  J. Pleasants.  Bumblebee Response to Variation in Nectar Availability , 1981 .

[158]  D. Simberloff,et al.  Conservation Biology: An Evolutionary-Ecological Perspective , 1980 .

[159]  L. Real,et al.  Effective mutualism between sequentially flowering plant species , 1979, Nature.

[160]  N. Waser.  Competition for Hummingbird Pollination and Sequential Flowering in Two Colorado Wildflowers , 1978 .

[161]  Graham H. Pyke,et al.  Optimal Foraging: A Selective Review of Theory and Tests , 1977, The Quarterly Review of Biology.

[162]  C. Johansen.  Pesticides and Pollinators , 1977 .

[163]  A. Love.  The Evolution of Flowering Plants , 1975, The Quarterly Review of Biology.

[164]  J. Free.  Dandelion as a Competitor to Fruit Trees for Bee Visits , 1968 .

[165]  S. E. C R E S S W E L L,et al.  An Economic Model of the Limits to Foraging Range in Central Place Foragers with Numerical Solutions for Bumblebees , 2022 .