Zoology

Download An Introduction to Mathematical Models in Ecology and by Mike Gillman PDF

By Mike Gillman

ISBN-10: 140517515X

ISBN-13: 9781405175159

Scholars usually locate it tough to understand basic ecological and evolutionary innovations due to their inherently mathematical nature. Likewise, the applying of ecological and evolutionary concept frequently calls for a excessive measure of mathematical competence.

This e-book is a primary step to addressing those problems, offering a huge creation to the foremost equipment and underlying techniques of mathematical versions in ecology and evolution. The booklet is meant to serve the desires of undergraduate and postgraduate ecology and evolution scholars who have to entry the mathematical and statistical modelling literature necessary to their topics.

The publication assumes minimum arithmetic and information wisdom while protecting a wide selection of equipment, a lot of that are on the fore-front of ecological and evolutionary examine. The e-book additionally highlights the purposes of modelling to functional difficulties similar to sustainable harvesting and organic keep an eye on.

Key good points:

  • Written sincerely and succinctly, requiring minimum in-depth wisdom of arithmetic
  • Introduces scholars to using laptop versions in either fields of ecology and evolutionary biology
  • Market - senior undergraduate scholars and starting postgraduates in ecology and evolutionary biology

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Additional resources for An Introduction to Mathematical Models in Ecology and Evolution: Time and Space

Example text

In order to pursue these lines of enquiry we need to understand some key terms: stability, equilibrium and perturbation. A simple physical model will illustrate these terms. Imagine that a ball is placed in a centre of a cup (Fig. 2). The ball is at rest but is it stable? We can only know this if we move the ball; that is, we perturb it. Upon release the ball returns to the base of SIMPLE MOD EL S OF T E M P ORA L C H A N G E 23 the cup. Therefore we can say that the ball at the bottom of the cup is at a position of stable equilibrium, defined as the steady state to which the ball will return after perturbation.

8 Myr ago this is hypothesized to have branched into two lineages. 8 Myr ago one of the branches again split to yield a total of three lineages, and so on. Sometimes the split will produce three or more branches but generally phylogenies are SIMPLE MOD EL S OF T E M P ORA L C H A N G E 33 (a) 250 200 Permian 150 Triassic 100 Jurassic Early Cret. 50 Late Cret. 0 (Mya) Paleogene Epicrionops Rhinatrema Uraeotyphlus “Ichthyophis” Caudocaecilia Ichthyophis 58 Gymnophiona 47 39 46 Scolecomorphus Boulengerula Herpele Caecilia Typhlonectes Chthonerpeton Gegeneophis Hypogeophis Praslinia Geotrypetes Dermophis Schistometopum Microcaecilia Luetkenotyphlus Siphonops Andrias Batrachuperus Hynobius Siren Ambystoma Dicamptodon Salamandra Pleurodeles Tylototriton Taricha Calotriton Triturus Proteus Necturus Rhyacotriton Amphiuma Bolitoglossa Eurycea Pseudotriton Plethodon Desmognathus Ensatina Hydromantes Speleomantes Ascaphus 45 35 51 Caudata 43 52 48 41 29 36 60 34 30 33 31 12 61 Anura Leiopelma Alytes Discoglossus Bombina Rhinophrynus Pipa Hymenochirus Xenopus Silurana Scaphiopus Spea Pelodytes Pelobates Brachytarsophrys Leptobrachium Leptolalax Heleophryne Caudiverbera Rheobatrachus Limnodynastes Mixophyes Crinia Uperoleia Myobatrachus Rhinoderma Telmatobius Batrachyla Ceratophrys Lepidobatrachus Trachycephalus Acris Hyla 57 56 25 54 53 24 55 44 40 23 32 18 37 28 22 14 Neobatrachia 1 16 5 10 15 2 59 6 26 20 49 27 50 13 3 11 4 7 42 21 17 19 9 Neogene 8 38 Eleutherodactylus Syrrhophus Phyllomedusa Litoria Cochranella Centrolene Leptodactylus Pleurodema Engystomops Odontophrynus Epipedobates Dendrobates Phyllobates Melanophryniscus Mertensophryne Amietophrynus Nectophrynoides Duttaphrynus Adenomus Pedostibes Leptophryne Sooglossus Nasikabatrachus Indirana Ptychadena Phrynobatrachus Petropedetes Conraua Pyxicephalus Cacosternum Tomopterna Micrixalus Nyctibatrachus Lankanectes Occidozyga Nannophrys Limnonectes Platymantis Ceratobatrachus Sataurois Meristogenys Rana Buergeria Rhacophorus Philautus Laliostoma Mantidactylus Boophis Hemisus Breviceps Spelaeophryne Callulina Hyperolius Atrixalus Trichobatrachus Arthroleptis Leptopelis Phrynomantis Scaphiophryne Synapturanus Hoplophryne Dermatonotus Elachistocleis Gastrophryne Melanobatrachus Kalophrynus Dyscophus Metaphrynella Microhyla Calluela Glyphoglossus Oreophryne Barygenys Sphenophryne Xenorhina Cophixalus Hylophorbus Rhinatrematidae Ichthyophiidae Caeciliidae Cryptobranchidae Hynobiidae Sirenidae Ambystomatidae Salamandridae Proteidae Rhyacotritonidae Amphiumidae Plethodontidae Leiopelmatidae Alytidae Bombinatoridae Rhinophrynidae Pipidae Scaphiopodidae Pelodytidae Pelobatidae Megophryidae Heleophrynidae Batrachophrynidae Limnodynastidae + Myobatrachidae Cycloramphinae Ceratophryidae Hylidae Brachycephalidae Phyllomedusinae Pelodryadinae Centrolenidae Leptodactylidae Alsodinae Nobleobatrachia [hyloidea] 300 Dendrobatidae Bufonidae Sooglossidae Nasikabatrachidae Ranixalinae Ptychadenidae Phrynobatrachidae Petropedetidae Pyxicephalidae Micrixalidae Nyctibatrachidae Dicroglossidae Natatanura [ranidae] Carboniferous Ceratobatrachidae Ranidae Rhacophoridae Mantellidae Hemisotidae Brevicipitidae Hyperoliidae Arthroleptidae Microhylidae 350 Dev.

Differentiation, which is one branch of calculus, provides a way of finding the gradient at a given point on a curve produced by a known function. Differentiation therefore provides a means of determining the rate of change of one variable in response to another. Moreover, whereas drawing a tangent is only an approximate way of finding a rate of change at a particular point, differentiation provides a precise value. Differentiation essentially provides a method of quantifying 40 CHAPTER 2 Fig. 11 (a) Geometric or exponential growth in discrete time.

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