Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution

A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $\lambda_n$ and a particle dies with instantaneous rate $\mu_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make explicit an important derivation connecting transition probabilities and continued fractions. We then develop an efficient algorithm for computing these probabilities that analyzes the error associated with approximations in the method. We demonstrate that this error-controlled method agrees with known solutions and outperforms previous approaches to computing these probabilities. Finally, we apply our novel method to several important problems in ecology, evolution, and genetics

Stability and invariant manifold for a predator-prey model with Allee effect

Predator-prey models are similar to host-parasite and host-parasitoid models. We investigate the stability and invariant manifolds of a discrete predator-prey model by using center manifold theory which is not addressed in Celik and Duman (Chaos Solitons Fractals 40: 1956-1962, 2009), and Wang et al. (Ecol. Complex. 8: 81-85, 2011)

The Formation of Collective Silk Balls in the Spider Mite Tetranychus urticae Koch

Tetranychus urticae is a phytophagous mite that forms colonies of several thousand individuals. These mites construct a common web to protect the colony. When plants become overcrowded and food resources become scarce, individuals gather at the plant apex to form a ball composed of mites and their silk threads. This ball is a structure facilitating group dispersal by wind or animal transport. Until now, no quantitative study had been done on this collective form of migration. This is the first attempt to understand the mechanisms that underlie the emergence and growth of the ball. We studied this collective behaviour under laboratory conditions on standardized infested plants. Our results show that the collective displacement and the formation of balls result from a recruitment process: by depositing silk threads on their way up to the plant apex, mites favour and amplify the recruitment toward the balls. A critical threshold (quorum response) in the cumulative flow of mites must be reached to observe the emergence of a ball. At the beginning of the balls formation, mites form an aggregate. After 24 hours, the aggregated mites are trapped inside the silk balls by the complex network of silk threads and finally die, except for recently arrived individuals. The balls are mainly composed of immature stages. Our study reconstructs the key events that lead to the formation of silk balls. They suggest that the interplay between mites' density, plant morphology and plant density lead to different modes of dispersions (individual or collective) and under what conditions populations might adopt a collective strategy rather than one that is individually oriented. Moreover, our results lead to discuss two aspects of the cooperation and altruism: the importance of Allee effects during colonization of new plants and the importance of the size of a founding group

Self-Assemblage and Quorum in the Earthworm Eisenia fetida (Oligochaete, Lumbricidae)

Despite their ubiquity and ecological significance in temperate ecosystems, the behavioural ecology of earthworms is not well described. This study examines the mechanisms that govern aggregation behaviour specially the tendency of individuals to leave or join groups in the compost earthworm Eisenia fetida, a species with considerable economic importance, especially in waste management applications. Through behavioural assays combined with mathematical modelling, we provide the first evidence of self-assembled social structures in earthworms and describe key mechanisms involved in cluster formation. We found that the probability of an individual joining a group increased with group size, while the probability of leaving decreased. Moreover, attraction to groups located at a distance was observed, suggesting a role for volatile cues in cluster formation. The size of earthworm clusters appears to be a key factor determining the stability of the group. These findings enhance our understanding of intra-specific interactions in earthworms and have potential implications for extraction and collection of earthworms in vermicomposting processes

Life Cycle Replacement by Gene Introduction under an Allee Effect in Periodical Cicadas

Periodical cicadas (Magicicada spp.) in the USA are divided into three species groups (-decim, -cassini, -decula) of similar but distinct morphology and behavior. Each group contains at least one species with a 17-year life cycle and one with a 13-year cycle; each species is most closely related to one with the other cycle. One explanation for the apparent polyphyly of 13- and 17-year life cycles is that populations switch between the two cycles. Using a numerical model, we test the general feasibility of life cycle switching by the introduction of alleles for one cycle into populations of the other cycle. Our results suggest that fitness reductions at low population densities of mating individuals (the Allee effect) could play a role in life cycle switching. In our model, if the 13-year cycle is genetically dominant, a 17-year cycle population will switch to a 13-year cycle given the introduction of a few 13-year cycle alleles under a moderate Allee effect. We also show that under a weak Allee effect, different year-classes (“broods”) with 17-year life cycles can be generated. Remarkably, the outcomes of our models depend only on the dominance relationships of the cycle alleles, irrespective of any fitness advantages

Settling Decisions and Heterospecific Social Information Use in Shrikes

Animals often settle near competitors, a behavior known as social attraction, which belies standard habitat selection theory. Two hypotheses account for these observations: individuals obtain Allee benefits mediated by the physical presence of a competitor, or they use successfully settled individual as a source of information indicating the location of high quality habitat. We evaluated these hypotheses experimentally in two species of shrikes. These passerine birds with a raptor-like mode of life impale prey to create larders that serve as an indicator of male/habitat quality. Thus, two forms of indirect information are available in our system: a successfully settled shrike and its larder. Typically these two cues are associated with each other, however, our experimental treatment created an unnatural situation by disassociating them. We manipulated the presence of larders of great grey shrikes and examined the settling decisions of red-backed shrikes within and outside the great grey shrike territories. Male red-backed shrikes did not settle sooner on plots with great grey shrikes compared to plots that only contained artificial larders indicating that red-backed shrikes do not use the physical presence of a great grey shrike when making settling decisions which is inconsistent with the Allee effect hypothesis. In contrast, for all plots without great grey shrikes, red-backed shrikes settled, paired and laid clutches sooner on plots with larders compared to plots without larders. We conclude that red-backed shrikes use larders of great grey shrikes as a cue to rapidly assess habitat quality

Climate change, phenological shifts, eco-evolutionary responses and population viability: toward a unifying predictive approach

The debate on emission targets of greenhouse gasses designed to limit global climate change has to take into account the ecological consequences. One of the clearest ecological consequences is shifts in phenology. Linking these shifts to changes in population viability under various greenhouse gasses emission scenarios requires a unifying framework. We propose a box-in-a-box modeling approach that couples population models to phenological change. This approach unifies population modeling with both ecological responses to climate change as well as evolutionary processes. We advocate a mechanistic embedded correlative approach, where the link from genes to population is established using a periodic matrix population model. This periodic model has several major advantages: (1) it can include complex seasonal behaviors allowing an easy link with phenological shifts; (2) it provides the structure of the population at each phase, including the distribution of genotypes and phenotypes, allowing a link with evolutionary processes; and (3) it can incorporate the effect of climate at different time periods. We believe that the way climatologists have approached the problem, using atmosphere–ocean coupled circulation models in which components are gradually included and linked to each other, can provide a valuable example to ecologists. We hope that ecologists will take up this challenge and that our preliminary modeling framework will stimulate research toward a unifying predictive model of the ecological consequences of climate change

Genetic Structure, Nestmate Recognition and Behaviour of Two Cryptic Species of the Invasive Big-Headed Ant Pheidole megacephala

info:eu-repo/semantics/publishe