Predation is one of the basic mechanisms of population growth control. Using a mathematical model, we explore the impact of predation in a prey population structured into two age classes, juveniles and adults, assuming a generalist predator. The specific predation pressure is represented for each of the two age classes by either no predation or Holling type II or Holling type III functional responses in various combinations. We distinguish two scenarios. In the first one, we seek for potential Allee effects or multiple stable states in the prey population, and explore the conditions at which the predation is more effective on juveniles than adults and vice versa. The most interesting finding here is the occurrence of bistability, or a predator-pit-like behaviour, when predators consume only juvenile prey, via a Holling type II functional response, an observation not described previously. In case only adults or both age classes are killed by predators exhibiting a type II functional response, the Allee effect occurs frequently. Multiple positive stable states are commonly observed if one of the age classes is exploited via a type III functional response. In the second scenario, we assume that the prey feeds on a resource and that the resource together with the prey undergoes outbreak dynamics, and we examine possibilities of control of such outbreaks using age-specific predation. Predation was proven to be able to suppress the prey population successfully. In some cases, an oscillation-free resource-prey-predator coexistence was detected.

Density-dependence is considered one of the most important regulators of population growth, and it has been documented across a wide variety of species. Typically, population growth rate and components thereof decline with increasing density (i.e., negative density-dependence); however, in species that exhibit high population densities and social behavior, positive density-dependence (i.e., Allee effect) may occur at low density. June sucker, a federally endangered lake sucker endemic to Utah Lake, Utah, USA, occurred historically at high density, and it exhibits coordinated feeding behavior. These characteristics indicate a potential for the existence of an Allee effect at current low population densities. To determine effects of density on growth, survival, and diet, I experimentally manipulated density of young June sucker in replicated enclosures in a natural environment. Larval June sucker were placed in enclosures at four different densities, and growth, survival, and diet of fish, and availability of prey (to determine selectivity) were measured at two time intervals. Both individual growth and survival were significantly lower at the lowest density compared to higher densities, indicative of a component Allee effect. Diets of individuals at low densities were more selective than diets of individuals at intermediate and high densities, suggesting a change in feeding strategy with density. Reduced growth and survival at low density suggests that corresponding, highly selective, feeding strategies may be less efficient than feeding strategies employed at higher densities. Allee effects appear to be an important consideration for recovery of this endangered species, and such effects may be common in historically abundant, but currently rare species.

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Mosquitoes are vectors for many diseases that cause significant mortality and morbidity across the globe such as malaria, dengue fever and Zika. As mosquito populations expand their range into new areas, they may undergo mate-finding Allee effects such that their ability to successfully reproduce becomes difficult at low population densities. With new technology, creating target specific gene modification may now be a viable method for mosquito population control. We develop a mathematical model to investigate the effects of releasing transgenic mosquitoes into newly established low-density mosquito populations. Our model consists of two life stages (aquatic and adult), which are further divided into three genetically distinct groups: heterogeneous and homogeneous transgenic alleles that cause female infertility and a homogeneous wild type. We perform analytical and numerical analyses on the equilibria to determine the level of saturation needed to eliminate mosquitoes in a given area. This model demonstrates the potential for a gene drive system to reduce the spread of invading mosquito populations. / Master of Science

Orientador: Wilson Castro Ferreira Junior / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T08:00:18Z (GMT). No. of bitstreams: 1 LouVega_Salvador_M.pdf: 1338284 bytes, checksum: f247d3dc13a783da27d224a3d32df47b (MD5) Previous issue date: 2008 / Resumo: Proponemos um modelo matemático para uma planta invasora, que acopla a dinâmica de reproduão com Efeito Allee e a dispersão de longa distância de uma planta invasora. Consideramos um efeito Allee devido à limitação de pólen, que reduz a produção de sementes. Introduzimos o efeito Allee através de uma função de probabilidade de encontro pólen-estigma que depende da densidade de plantas. Para a modelagem do processo de dispersão utilizamos equações íntegrorecursiva (IRE) tomando um núcleo de dispersão misto, que representa a dispesão local e a longa distância. Analisamos a dinâmica local do modelo determinando os pontos de equilíbrio e as suas estabilidades, para então analisar o processo de dispersão. Analisamos o modelo de dispersão por meio de simulação numérica, o que permitiu observar o deslocamento espacial da frente da invasão. Isto permitiu calcular a velocidade de expansão. Determinamos a inuência do efeito Allee, da capacidade reprodutiva e da dispersão de longa distância sobre a velocidade de expansão. Observamos que o efeito Allee torna velocidades aceleradas em velocidades constantes de expansão. A velocidade de expansão decresce com o aumento na intensidade do efeito Allee, mas aumenta com a capacidade reprodutiva. A dispersão de longa distância gera maiores velocidades de expansão, embora para fortes intensidades do efeito Allee o acréscimo na velocidade não é signifícativo em relação à velocidade gerada pela dispersão local. Os resultados mostram que apesar da dispersão contribuir ao aumento na velocidade de expansão, a dispersão também torna a população mais suscetável á extinção. / Abstract: We present a mathematical model which couples the reproductive dynamic with an Allee effect and a long distance diseprsal of an invasive plant. We consider an Allee effect due to pollen limitation, which reduces seed production. We introduce the Allee effect through a probability function that describes pollen-stigma encounters as function of the population density. To model the dispersal process we used integro-diference equations (IDE) and employed a mixed kernel which represents the local and long distance dispersal processes. We analyzed the local dynamic through the stability of their equilibrium points. For the spatial dynamic we used numerical simulations, that allowed us to observe the spatial displacement of the invasion front. This permitted us to compute the expansion speeds. We determined the inuence of the Allee effect, reproductive capacity and the long distance diseprsal on the invasion speeds. We observed than an Allee effect turns accelerating expansion speeds into constant speeds. Expansion speeds decreases with Allee effect intensity but increases with the reproductive capacity of the population. Long distance dispersal produces higher invasion speeds, but for strong intensities of the Allee effect, the increase is not significant in relation to the speeds generated by the local dispersal. Our results show that while dispersal contributes to expansion speeds, it also turns the population more susceptible to extinction. / Mestrado / Biomatematica / Mestre em Matemática Aplicada

Orientador: Wilson Castro Ferreira Junior / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação Científica / Made available in DSpace on 2018-08-22T04:48:33Z (GMT). No. of bitstreams: 1 LouVega_Salvador_D.pdf: 14692586 bytes, checksum: f745ca7fb3da3cfa09dfb8a8dd9f37bb (MD5) Previous issue date: 2013 / Resumo: Apresentamos um modelo integro - recursivo para a dispersão de uma planta que acopla uma dinâmica de reprodução, com efeito, Allee e uma dinâmica de dispersão em um meio heterogêneo. Propomos um modelo de difusão e sedimentação para derivar núcleos de dispersão teóricos, que representem o padrão de dispersão de sementes gerado por pássaros frugívoros em um meio heterogêneo. O núcleo gerado através do modelo _e capaz de reproduzir o padrão espacial de agregação de sementes gerado pelos pássaros frugívoros sob condições naturais. Enquanto _a dinâmica de reprodução, consideramos um efeito Allee devido à limitação de pólen, que reduz a produção de sementes. Introduzimos o efeito Allee através de uma função de probabilidade que depende da densidade local de plantas. Analisa-se o comportamento da expansão da planta, e estima-se a velocidade média de expansão. O modelo mostra uma invasão através de pulsos, que atribuímos ao efeito Allee e ao comportamento de dispersão da planta / Abstract: We present an integro-difference model for a plant dispersal, which couples a reproductive dynamic with Allee effect and dispersal dynamic in a heterogeneous environment. We propose diffusion and settling model to derive theoretical dispersal kernels that represent the seed dispersal pattern generated by frugivores birds in a heterogeneous environment. The dispersal kernel derived through the model is able to reproduce the aggregate seed dispersal pattern generated by the frugivores birds under field conditions. As for the reproductive dynamic, we consider an Allee effect due to pollen limitation, which reduces seed production. We introduce the Allee effect through a probability function, which depends on the local plant density. The plant expansion behavior is analyzed, and the average expansion speed is estimated. The model shows a pulsed invasion, which we attribute to the Allee effect and the plant dispersal behavior / Doutorado / Matematica Aplicada / Doutor em Matemática Aplicada

The spread of invasive species poses a major ecological and economical threat. Consequently there are ongoing efforts to develop a generalizable mechanism to predict establishment success of non-native species. One proposed mechanism to predict establishment success is propagule pressure, which is defined as the number of individuals introduced at a given time. Although some studies have demonstrated a positive correlation between propagule pressure and establishment success, others have not, and the effect of propagule pressure on establishment success remains unclear. To address this challenge, a strain of bacteria engineered with an Allee effect, a growth dynamic that is often associated with establishing species, was used. The timing between successive introduction events that resulted in establishment success was measured. It was observed that if the time between two introduction events was sufficiently long, growth did not occur. By manipulating the growth rate of the bacteria, it was shown that that the minimal time between the two introduction events that resulted in growth was constrained as growth rate decreased. Moreover, it was concluded that asymmetry in the density of bacteria introduced in the introduction events increased the maximum time between introduction events that resulted in growth. These results help to remedy conflicting data in the literature by identifying conditions where propagule pressure has, and does not have, a positive impact on establishment success. These findings can have major implications in understanding and predicting the unique population dynamics of invasive species.

Many biological populations reside in increasingly fragmented landscapes, which arise from human activities and natural causes. Landscape characteristics may change abruptly in space and create sharp transitions (interfaces) in landscape quality. How the patchiness of landscapes affects ecosystem diversity and stability depends, among other things, on how individuals move through the landscape. Individuals adjust their movement behavior to local habitat quality and show preferences for some habitat types over others. In this thesis, we focus on how landscape composition and the movement behaviour of individuals at an interface between patches of different quality affect the steady state of a single species. We consider a model of reaction-diffusion equations for the temporal evolution of the density of the population in space. Individual movement is described by a diffusion process, e.g., an uncorrelated random walk. Population net growth is encapsulated in the growth function that considers birth and death of individuals, including nonlinear effects that arise from competition and/or facilitation within the species. We consider the simplest case of two adjacent one-dimensional patches, e.g., two intervals on the real line that share one boundary point. Conditions are homogeneous within a patch but differ between patches. The movement behaviour of individuals between the two patches is incorporated into matching conditions of population flux and density at the interface between patches, i.e., the boundary point that the intervals share. These matching conditions turn out to be continuous in the flux but discontinuous in the density. Several authors have studied similar models recently. Most of these studies consider monostable dynamics on both patches, i.e., logistic growth. Under logistic growth, the net population growth rate is a strictly decreasing function of population density. Logistic population dynamics are very simple: the population extinction state is unstable and a positive steady state is globally asymptotically stable. In this work, we also include bistable dynamics, i.e., an Allee effect. Biologically, an Allee effect occurs when individuals cooperate at some level so that the net population growth rate is increasing with population density for at least some low or intermediate densities. Models with Allee growth typically exhibit bistability: there are two locally stable steady states, one at low density (possibly zero) and one at high density. This bistability makes mathematical analysis more challenging, but leads to more interesting results in return. Mathematically, most existing work on related models is based on linear stability analysis of the extinction state. We focus on the nonlinear models and specifically on positive steady states. We establish the existence, uniqueness and - in some cases - global asymptotic stability of a positive steady state. We classify the shape of these states depending on movement behaviour. We clarify the role of movement in this context. In particular, we investigate the following prior observation: a randomly diffusing population at steady state in a continuously varying habitat can exceed its carrying capacity. Our results clarify when and under which conditions this effect can arise in our two-patch landscape. The analysis of the model with an Allee effect on one of the two patches yields a rich and interesting structure of steady states. Under certain parameter conditions, some of these states are amenable to explicit stability calculations. These yield insights into the possible bifurcations that can occur in our system. Finally, we indicate how the model and analysis here can be extended to systems of reaction-diffusion equations on graphs that represent natural habitats with different geometries, for example watersheds.

<p>Alternative stable states have been, based on theoretical findings, predicted to be common in ecological systems. Empirical data from a number of laboratory and natural studies strongly suggest that alternative stable states also occur in real populations, communities and ecosystems. Potential mechanisms involve population size-structure and food-dependent individual development. These features can lead to ontogenetic niche shifts, juvenile recruitment bottlenecks and emergent Allee effects; phenomena that establish destabilising positive feedbacks in a system and hence create alternative stable states.</p><p>I studied the consequences of population size-structure for community dynamics at different scales of system complexity. I performed laboratory and ecosystem experiments. Small poecilliid fishes and planktonic invertebrates with short generation times and life spans were used as model organisms. This allowed me to assess the long-term dynamics of the populations and communities investigated.</p><p>The main experimental results are: (a) An ontogenetic niche shift in individuals of the phantom midge <i>Chaoborus</i> made the population vulnerable to an indirect competitive recruitment bottleneck imposed by cladoceran mesozooplankton via rotifers. Consequentially the natural zooplankton food web exhibited two alternative attractors. (b) Body size determined the success of <i>Poecilia reticulata</i> invading resident population of <i>Heterandria formosa</i> and thus the type of alternative stable state that established. Small invaders were outcompeted by the residents, whereas large invaders excluded their competitor by predating on its recruits. (c) External juvenile and adult mortality altered the internal feedback structure that regulates a laboratory population of <i>H. formosa</i> in such a way that juvenile biomass increased with mortality. This biomass overcompensation in a prey population can establish alternative stable states with top-predators being either absent or present.</p><p>The major conclusion is that size-structure and individual growth can indeed lead to alternative stable states. The considerations of these ubiquitous features of populations offer hence new insights and deeper understanding of community dynamics. Alternative stable states can have tremendous consequences for human societies that utilise the ecological services provided by an ecological system. Understanding the effects of size-structure on alternative stability is thus crucial for sustainable exploitation or production of food resources.</p>

Alternative stable states have been, based on theoretical findings, predicted to be common in ecological systems. Empirical data from a number of laboratory and natural studies strongly suggest that alternative stable states also occur in real populations, communities and ecosystems. Potential mechanisms involve population size-structure and food-dependent individual development. These features can lead to ontogenetic niche shifts, juvenile recruitment bottlenecks and emergent Allee effects; phenomena that establish destabilising positive feedbacks in a system and hence create alternative stable states. I studied the consequences of population size-structure for community dynamics at different scales of system complexity. I performed laboratory and ecosystem experiments. Small poecilliid fishes and planktonic invertebrates with short generation times and life spans were used as model organisms. This allowed me to assess the long-term dynamics of the populations and communities investigated. The main experimental results are: (a) An ontogenetic niche shift in individuals of the phantom midge Chaoborus made the population vulnerable to an indirect competitive recruitment bottleneck imposed by cladoceran mesozooplankton via rotifers. Consequentially the natural zooplankton food web exhibited two alternative attractors. (b) Body size determined the success of Poecilia reticulata invading resident population of Heterandria formosa and thus the type of alternative stable state that established. Small invaders were outcompeted by the residents, whereas large invaders excluded their competitor by predating on its recruits. (c) External juvenile and adult mortality altered the internal feedback structure that regulates a laboratory population of H. formosa in such a way that juvenile biomass increased with mortality. This biomass overcompensation in a prey population can establish alternative stable states with top-predators being either absent or present. The major conclusion is that size-structure and individual growth can indeed lead to alternative stable states. The considerations of these ubiquitous features of populations offer hence new insights and deeper understanding of community dynamics. Alternative stable states can have tremendous consequences for human societies that utilise the ecological services provided by an ecological system. Understanding the effects of size-structure on alternative stability is thus crucial for sustainable exploitation or production of food resources.