Mathematics inspired by Darwin. Adaptive dynamics of dispersal and cooperation

In 1859, Charles Darwin published his theory of evolution by natural selection, the process occurring based on fitness benefits and fitness costs at the individual level. Traditionally, evolution has been investigated by biologists, but it has induced mathematical approaches, too. For example, adaptive dynamics has proven to be a very applicable framework to the purpose. Its core concept is the invasion fitness, the sign of which tells whether a mutant phenotype can invade the prevalent phenotype. In this thesis, four real-world applications on evolutionary questions are provided. Inspiration for the first two studies arose from a cold-adapted species, American pika. First, it is studied how the global climate change may affect the evolution of dispersal and viability of pika metapopulations. Based on the results gained here, it is shown that the evolution of dispersal can result in extinction and indeed, evolution of dispersalshould be incorporated into the viability analysis of species living in fragmented habitats. The second study is focused on the evolution of densitydependent dispersal in metapopulations with small habitat patches. It resulted a very surprising unintuitive evolutionary phenomenon, how a non-monotone density-dependent dispersal may evolve. Cooperation is surprisingly common in many levels of life, despite of its obvious vulnerability to selfish cheating. This motivated two applications. First, it is shown that density-dependent cooperative investment can evolve to have a qualitatively different, monotone or non-monotone, form depending on modelling details. The last study investigates the evolution of investing into two public-goods resources. The results suggest one general path by which labour division can arise via evolutionary branching. In addition to applications, two novel methodological derivations of fitness measures in structured metapopulations are given.

Phenology, fruit set and dispersal of Cordia multispicata Cham., an important weed shrub of abandoned pastures in eastern Amazonia

ABSTRACT - (Phenology, fruit set and dispersal of Cordia multispicata Cham., an important weed shrub of abandoned pastures in eastern Amazonia). The reproductive ecology of the distylous tropical shrub Cordia multispicata was studied in an abandoned pasture in Paragominas County , Pará state, Brazil. It is a common species in the Amazon basin where it occurs as a weed in open and disturbed habitats. C. multispicata has many flowers per inflorescence (85 ± 12) but 84% abort before fertilization. Flowering occurs throughout the year. Fruits are small, with a red fleshy pericarp (skin-pulp) attractive to birds. Fruit set is lower during the dry season (less than 30%) and higher during the rainy season when there are many visits of insects to the flowers. Fruiting has a peak between the end of the dry season and the middle of the rainy season. Nineteen bird species were observed foraging for the fruits of C. multispicata, and 79% of those species can be considered as potential dispersal agents. The efficient seed dispersal and aggregated spatial distribution associated with some characteristics of the dispersors greatly contributed to the success of this species in abandoned pastures of eastern Amazonia.

Seed characteristics and dispersal of dimorphic fruit segments of Cakile maritima Scopoli (Brassicaceae) population of southern Brazilian coastal dunes

Cakile maritima occurs sporadically along the southern Brazilian coast, where it is restricted to more protected sites at the base of foredunes. Somatic dimorphism in C. maritima is manifested as morphologically distinct upper and lower fruit segments (silicules). The two morphs were tested for differences in size, number of seeds, dispersal ability and natural establishment. In the C. maritima population of southern Brazil, the lower silicule has more seeds than upper silicule, and lower seeds are more likely to abort than the upper ones. Seeds from upper segments were significantly larger than those from lower ones; however, their mass ranges overlap. The mean silicule mass was not significantly different from both segments, but the silicule/seed mass ratio from upper and lower segments was significantly different. Both segments had high ability to float in sea water, more than 50% were still afloat after 70 days. Nevertheless, dispersal occurs mainly to landward due to dominant wind action. Most of the seedlings were restricted to within a one-metre radius of the mother plant, and were principally derived from lower fruit segments.

Reproductive phenology, pollination and seed dispersal syndromes on sandstone outcrop vegetation in the "Chapada Diamantina", northeastern Brazil: population and community analyses

Vegetation on rock outcrops in the "Chapada Diamantina" (soil islands) is often aggregated and surrounded by nude rock surfaces, thus creating natural units with well defined limits. The flowering and fruiting cycles of plants on 58 soil islands at altitudes between 1,100 and 1,140 meters above sea leavel were analyzed at Mãe Inácia Peak (12°27' S and 41°28' W) in the "Chapada Diamantina", Bahia, Brazil. The presence/absence of flowering and fruiting species on each soil island, and their respective cover areas were analyzed at both the population and community levels, and the phenophases of flowering and fruiting were observed during 24 successive months. The analyses of pollination and seed dispersal syndromes indicated that animals are more important in pollination than in seed dispersal (which is predominantly by anemochory and autochory). The flowering and fruiting of plants with animal pollination syndromes were correlated with rainfall and temperature. The flowering season varied during the year according to the pollination syndrome involved: entomophily was predominant from summer through autumn, ornithophily was predominant during winter, and anemophily in the spring. The staggered timing of flowering and fruiting among different species provides a nearly continuous supply of resources for the local fauna.

Clonal growth and dispersal potential of Leiothrix flagellaris Ruhland (Eriocaulaceae) in the rocky grasslands of Southeastern Brazil

Leiothrix flagellaris is a small clonal plant that grows in sandy/rocky, nutrient poor soils in the rocky grasslands ("campos rupestres") of southeastern Brazil. In the rainy season most of their flower heads differentiate into small rosettes, produced by pseudovivipary, and connected to the mother-plant by flexible, elongated stalks that can reach up to 90cm. Most of these rosettes remain suspended over rocks or over the sparse herbaceous surrounding vegetation, while a few arch low enough to come into contact with the surrounding soil and take root. These suspended rosettes can reach diameters comparable to currently rooted and reproductively active rosettes produced during previous reproductive periods. As the rooted rosettes grow up, their potential to generate and disperse new pseudoviviparous rosettes increase rapidly. This unusual guerrilla strategy of L. flagellaris seems to congregate a suit of traits that promote a fast increase in photosynthetic area and improve recruitment, thereby helping to circumvent dispersal and establishment failures in its severe environment.

Drift dispersal in central Southern Ontario /

Two tills are readily identi-f i able in central Southern Ontario, a very stony, loose deposit o-f variable matrix (Dummer till) and a moderately stony, fissile and compact deposit that is more homogeneous (drumlinized till). The quantity o-f Precambr i an, Paleozoic and Shadow Lake Formation (Paleozoic) rock types were determined and corresponding isopleth maps drawn. The changes in lithology content occurred in the direction o-f transport, there-fore, compositional isopleths o-f till may be considered equipotential lines for the reconstruction of glacier flow paths. Areal gradations of drift lithology indicated that the prime agents of dispersal were ice and glacial meltwaters. The down-ice abundance trend of till components indicated a dispersal pattern showing the concentration of a given lithology type peaking within a few kilometres of the source followed by a rapid decline and thereafter, a more gradual decrease with increasing distance. Within the esker deposits, igneous rocks may form the major component and can extend further onto the limestone plain than in the adjacent till. Evidence is presented that indicates the "style" of dispersal was one in which glacial ice may have been strongly influenced by local bedrock topography and the regional structural trends. The ice tended to follow pre-existing valleys and lows, depositing till composed mainly of local bedrock. Gradations in Paleozoic clast content showed that the local bedrock lithology became the primary till component within 3 km of down-ice transport. Evidence is presented that indicated the last glaciation may have occurred as a relatively thin ice mass, followed by stagnation and recession. No evidence of a lateglacial re-advance was found within the study area. Because of the lack of a contact between the Dummer and drumlinized till, and because of results showing gradation of the Dummer till into the drumlinized till (as indicated by lithology content and grain size), it is suggested that no re-advance occurred.

Methodische Grundlagen zur Bewahrung und Wiederherstellung großräumig funktionsfähiger ökologischer Beziehungen in der räumlichen Umweltplanung

Mit der Verwirklichung ,Ökologischer Netzwerke‘ werden Hoffnungen zum Stopp des Verlustes der biologischen Vielfalt verknüpft. Sowohl auf gesamteuropäischer Ebene (Pan-European Ecological Network - PEEN) als auch in den einzelnen Staaten entstehen Pläne zum Aufbau von Verbundsystemen. Im föderalen Deutschland werden kleinmaßstäbliche Biotopverbundplanungen auf Landesebene aufgestellt; zum nationalen Biotopverbund bestehen erste Konzepte. Die vorliegende Arbeit ist auf diese überörtlichen, strategisch vorbereitenden Planungsebenen ausgerichtet. Ziele des Verbunds sind der Erhalt von Populationen insbesondere der gefährdeten Arten sowie die Ermöglichung von Ausbreitung und Wanderung. Aufgrund fehlender Datengrundlagen zu den Arten und Populationen ist es nicht ohne weiteres möglich, die Konzepte und Modelle der Populationsökologie in die überörtlichen Planungsebenen zu übertragen. Gemäß der o.g. Zielstellungen sollte sich aber die Planung von Verbundsystemen an den Ansprüchen der auf Verbund angewiesenen Arten orientieren. Ziel der Arbeit war die Entwicklung einer praktikablen GIS-gestützten Planungshilfe zur größtmöglichen Integration ökologischen Wissens unter der Bedingung eingeschränkter Informationsverfügbarkeit. Als Grundlagen dazu werden in Übersichtsform zunächst die globalen, europäisch-internationalen und nationalen Rahmenbedingungen und Anforderungen bezüglich des Aufbaus von Verbundsystemen zusammengestellt. Hier sind die Strategien zum PEEN hervorzuheben, die eine Integration ökologischer Inhalte insbesondere durch die Berücksichtigung räumlich-funktionaler Beziehungen fordern. Eine umfassende Analyse der landesweiten Biotopverbundplanungen der BRD zeigte die teilweise erheblichen Unterschiede zwischen den Länderplanungen auf, die es aktuell nicht ermöglichen, ein schlüssiges nationales Konzept zusammenzufügen. Nicht alle Länder haben landesweite Biotopverbundplanungen und Landeskonzepte, bei denen dem geplanten Verbund die Ansprüche von Arten zugrunde gelegt werden, gibt es nur ansatzweise. Weiterhin wurde eine zielgerichtete Eignungsprüfung bestehender GIS-basierter Modelle und Konzepte zum Verbund unter Berücksichtigung der regelmäßig in Deutschland verfügbaren Datengrundlagen durchgeführt. Da keine integrativen regelorientierten Ansätze vorhanden waren, wurde der vektorbasierte Algorithmus HABITAT-NET entwickelt. Er arbeitet mit ,Anspruchstypen‘ hinsichtlich des Habitatverbunds, die stellvertretend für unterschiedliche ökologische Gruppen von (Ziel-) Arten mit terrestrischer Ausbreitung stehen. Kombiniert wird die Fähigkeit zur Ausbreitung mit einer Grobtypisierung der Biotopbindung. Die wichtigsten Grundlagendaten bilden die jeweiligen (potenziellen) Habitate von Arten eines Anspruchstyps sowie die umgebende Landnutzung. Bei der Bildung von ,Lebensraumnetzwerken‘ (Teil I) werden gestufte ,Funktions- und Verbindungsräume‘ generiert, die zu einem räumlichen System verknüpft sind. Anschließend kann die aktuelle Zerschneidung der Netzwerke durch Verkehrstrassen aufgezeigt werden, um darauf aufbauend prioritäre Abschnitte zur Wiedervernetzung zu ermitteln (Teil II). Begleitend wird das Konzept der unzerschnittenen Funktionsräume (UFR) entworfen, mit dem die Indikation von Habitatzerschneidung auf Landschaftsebene möglich ist. Diskutiert werden schließlich die Eignung der Ergebnisse als kleinmaßstäblicher Zielrahmen, Tests zur Validierung, Vergleiche mit Verbundplanungen und verschiedene Setzungen im GIS-Algorithmus. Erläuterungen zu den Einsatzmöglichkeiten erfolgen beispielsweise für die Bereiche Biotopverbund- und Landschaftsplanung, Raumordnung, Strategische Umweltprüfung, Verkehrswegeplanung, Unterstützung des Konzeptes der Lebensraumkorridore, Kohärenz im Schutzgebietssystem NATURA 2000 und Aufbau von Umweltinformationssystemen. Schließlich wird ein Rück- und Ausblick mit der Formulierung des weiteren Forschungsbedarfs verknüpft.

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Can salvage logging affect seed dispersal by birds into burned forests?

The recovery of vegetation in Mediterranean ecosystems after wildfire is mostly a result of direct regeneration, since the same species existing before the fire regenerate on-site by seeding or resprouting. However, the possibility of plant colonization by dispersal of seeds from unburned areas remains poorly studied. We addressed the role of the frugivorous, bird-dependent seed dispersal (seed rain) of fleshy-fruited plants in a burned and managed forest in the second winter after a fire, before on-site fruit production had begun. We also assessed the effect on seed rain of different microhabitats resulting from salvage logging (erosion barriers, standing snags, open areas), as well as the microhabitats of unlogged patches and an unburned control forest, taking account of the importance of perches as seed rain sites. We found considerable seed rain by birds in the burned area. Seeds, mostly from Olive trees Olea europaea and Evergreen pistaches Pistacia lentiscus, belonged to plants fruiting only in surrounding unburned areas. Seed rain was heterogeneous, and depended on microhabitat, with the highest seed density in the unburned control forest but closely followed by the wood piles of erosion barriers. In contrast, very low densities were found under perches of standing snags. Furthermore, frugivorous bird richness seemed to be higher in the erosion barriers than elsewhere. Our results highlight the importance of this specific post-fire management in bird-dependent seed rain and also may suggest a consequent heterogeneous distribution of fleshy-fruited plants in burned and managed areas. However, there needs to be more study of the establishment success of dispersed seeds before an accurate assessment can be made of the role of bird-mediated seed dispersal in post-fire regeneration

Analytical methodologies based on X-Ray Fluorescence Spectrometry (XRF) and Inductively Couple Plasma Spectroscopy (ICP) for the assessment of metal dispersal around mining environments

La investigació que es presenta en aquesta tesi es centra en l'aplicació i millora de metodologies analítiques existents i el desenvolupament de nous procediments que poden ser utilitzats per a l'estudi dels efectes ambientals de la dispersió dels metalls entorn a les zones mineres abandonades. En primer lloc, es van aplicar diferents procediments d'extracció simple i seqüencial per a estudiar la mobilitat, perillositat i bio-disponibilitat dels metalls continguts en residus miners de característiques diferents. Per altra banda, per a estudiar les fonts potencials de Pb en la vegetació de les zones mineres d'estudi, una metodologia basada en la utilització de les relacions isotòpiques de Pb determinades mitjançant ICP-MS va ser avaluada. Finalment, tenint en compte l'elevat nombre de mostres analitzades per a avaluar l'impacte de les activitats mineres, es va considerar apropiat el desenvolupament de mètodes analítics d'elevada productivitat. En aquest sentit la implementació d'estratègies quantitatives així com l'aplicació de les millores instrumentals en els equips de XRF han estat avaluades per a aconseguir resultats analítics fiables en l'anàlisi de plantes. A més, alguns paràmetres de qualitat com la precisió, l'exactitud i els límits de detecció han estat curosament determinats en les diverses configuracions de espectròmetres de XRF utilitzats en el decurs d'aquest treball (EDXRF, WDXRF i EDPXRF) per a establir la capacitat de la tècnica de XRF com a tècnica alternativa a les clàssiques comunament aplicades en la determinació d'elements en mostres vegetals.

Patterns of pollen and seed dispersal in a small, fragmented population of the wind-pollinated tree Araucaria angustifolia in southern Brazil

Paternity analysis based on eight microsatellite loci was used to investigate pollen and seed dispersal patterns of the dioecious wind- pollinated tree, Araucaria angustifolia. The study sites were a 5.4 ha isolated forest fragment and a small tree group situated 1.7 km away, located in Paran alpha State, Brazil. In the forest fragment, 121 males, 99 females, 66 seedlings and 92 juveniles were mapped and genotyped, together with 210 seeds. In the tree group, nine male and two female adults were mapped and genotyped, together with 20 seeds. Paternity analysis within the forest fragment indicated that at least 4% of the seeds, 3% of the seedlings and 7% of the juveniles were fertilized by pollen from trees in the adjacent group, and 6% of the seeds were fertilized by pollen from trees outside these stands. The average pollination distance within the forest fragment was 83 m; when the tree group was included the pollination distance was 2006m. The average number of effective pollen donors was estimated as 12.6. Mother- trees within the fragment could be assigned to all seedlings and juveniles, suggesting an absence of seed immigration. The distance of seedlings and juveniles from their assigned mother- trees ranged from 0.35 to 291m ( with an average of 83m). Significant spatial genetic structure among adult trees, seedlings, and juveniles was detected up to 50m, indicating seed dispersal over a short distance. The effective pollination neighborhood ranged from 0.4 to 3.3 ha. The results suggest that seed dispersal is restricted but that there is longdistance pollen dispersal between the forest fragment and the tree group; thus, the two stands of trees are not isolated.

Investigating early hominin dispersal patterns: developing a framework for climate data integration

An investigation using the Stepping Out model of early hominin dispersal out of Africa is presented here. The late arrival of early hominins into Europe, as deduced from the fossil record, is shown to be consistent with poor ability of these hominins to survive in the Eurasian landscape. The present study also extends the understanding of modelling results from the original study by Mithen and Reed (2002. Stepping out: a computer simulation of hominid dispersal from Africa. J. Hum. Evol. 43, 433-462). The representation of climate and vegetation patterns has been improved through the use of climate model output. This study demonstrates that interpretative confidence may be strengthened, and new insights gained when climate models and hominin dispersal models are integrated. (C) 2007 Elsevier Ltd. All rights reserved.