Sigfrid Lundberg

Population Dynamics with Sequential Density-Dependencies

We analyse the importance of sequential density-dependent processes to population dynamics of single species. We divide a year into several processes of density-dependent reproduction and/or mortality. A sequence of n processes can be arranged in n ! different sequences. However, only (n - 1) ! of these represent unique relative orderings that have different stability properties and dynamics. Models with several sequential density-dependent processes have a much wider repertoire of dynamics than, e.g., ordinary models based on the logistic equation. Stable equilibrium density and the maximum density of cycles and unstable dynamics do not necessarily increase with increasing b (maximum per capita birth rate). The maps of density at time t + 1 (x t+1 ) versus density at time t (x t ) can have more than one hump, i.e., be bi- or multimodal, with multiple equilibria. In this type of system, chaos is not the only inevitable outcome of increased b. Instead stable equilibrium and/or periodic solutions may occur beyond the chaotic region as b increases. It is suggested that this type of model may apply to many kinds of organisms in seasonal environments. The explicit consideration of sequential density-dependence may be of critical importance for resource and conservation managers, to avoid switches between multiple equilibria or extinction due to poorly timed harvest or pest control.

Bird migration patterns: Conditions for stable geographical population segregation

Migration costs, increasing with increasing distance, and asymmetric competition between stationary and migratory individuals, and between individuals arriving early and late at the same destination, lead to latitudinal as well as longitudinal segregation between migratory bird populations. The evolution of leapfrog migration (winter quarters of different populations situated in reverse latitudinal sequence to the breeding sites) is promoted by asymmetric competition, particularly if such competition occurs for both breeding and wintering resources, and if migration costs are important as well. Asymmetric competition may also lead to a chain migration pattern (winter and breeding ranges in the same latitudinal sequence), if breeding and/or wintering suitability increases markedly towards the latitudinal extremes. Furthermore, chain migration also develops if there are migration costs but no asymmetric competition. Transition patterns between leapfrog and chain migration are stable under a narrow range of intermediary conditions. Strong asymmetric competition is expected to be associated with adaptive strategies used by the migrating birds to minimize the total time for the migratory journey, whereas high migration costs are expected to be associated with adaptations for minimizing risks and energy expenditure during migration.

A regional distributed WWW search and indexing service - the DESIRE way

In an attempt to implement a regional search engine we have created an open, metadata aware system for distributed, collaborative WWW-indexing. The system has three main components: a harvester (for collecting information), a database (for making the collection searchable), and a user interface (for making the information available). All components can be distributed across networked computers, thus supporting scalability. The system is metadata aware and thus allows searches on several fields including title, document author, and URL. Nordic Web Index (NWI) is an application using this system to create a regional Nordic Web-indexing service. NWI is built using five collaborating service points within the Nordic countries. The NWI databases can be used to build additional services. Services today include special metadata databases, multimedia databases, and statistics about the Nordic Web.

Pollinator functional response and plant population dynamics: Pollinators as a limiting resource

SummaryDuring recent years, much work has focused on which factors limit the reproductive success in plants. Several studies show a strong influence of either resource limitation, pollen limitation or a combined effect of both. The theoretical arguments for resource limitation are abundant, but there has been very little work done concerning the effect of pollinator availability. In this paper we construct a model to study how the reproductive success in plants is influenced by the foraging behaviour of the pollinators. The pollinator population is assumed to have a constant population density. A functional response function for the pollinators is derived. It is similar to a Holling type II functional response. It is shown that, since the pollinators are regulated by factors not included in the model and their capability to pollinate is limited by the functional response, this is sufficient for regulating the plant population. There also exists a threshold condition for the persistence of the plant population that depended on the search rate of the pollinators and the demographic parameters of the plant population. If this threshold condition is not satisfied the plant population cannot persist and will become extinct. If the condition is satisfied the plant population grows until it is limited at the equilibrium mentioned above.

Coevolution of competing species: ecological character displacement.

Character displacement of competing species is studied. A model, originally developed by MacArthur and Levins (Proc. Natl. Acad. Sci. USA 51 (1964), 1207-1210) and further analyzed by Lawlor and Maynard Smith (Amer. Nat. 110 (1976), 70-99), has been reanalyzed. In the present paper, a more formally correct analysis of the MacArthur-Levins model is provided. A standard population genetics approach to sexually reproducing populations is adopted. The same conclusion as proposed by Lawlor and Maynard Smith emerges; competition can lead only to character divergence. In our analysis we either require that allopatrically evolved consumer populations must be able to coexist at an ecologically stable equilibrium (hence, we require mutual invasibility), or consider the feasibility of allopatric equilibria.

The Effect of a Vector-Borne Disease on the Dynamics of Natural Plant Populations: A Model for Ustilago Violacea Infection of Lychnis Viscaria

A mathematical model was used to study how a parasitic castrating fungus affects the population dynamics of its host plant. The model is based on the interactions between the smut fungus Ustilago violacea and its host plant Lychnis viscaria. The model also includes the pollination process as this plays a central role in the transmission of the fungal spores between plants. Analysis of the model, with the disease absent, revealed that the pollinators have a limiting effect on the growth rate of the population. The model did not include any other density-dependent processes. A condition was calculated which had to be satisfied to enable the disease to invade the host population and it is shown that the disease must possess a minimum transmission potential to be able to invade the host population (...)

Intra-specific competition in the sex communication channel: a selective force in the evolution of moth pheromones?

A model for mate competition in moths sexually signalling with pheromones is presented. The model has four variables. N is the number of individuals of each sex per area unit. r is the length of the female odour plume as detected by a responding male. e is a parameter increasing with male ability to discriminate between concentrations. r-e becomes the competitive part of the female pheromone plume, i.e. the distance at which an upwind female is able to distract males from downwind plumes. Assuming a random distribution of males and females the number of matings in a generation can be calculated. Introducing a fourth parameter, B = surviving offspring of each sex from a mating, the population dynamics of the population can be described. Two special cases are analysed; (1) e = r, and (2) e = 0. In case (1) mating success increases with population density towards unity. In case (2) interference between the pheromone plumes of different females will lower the mating success at higher population densities. The stability of the communicating population decreases with increasing e and B. We conclude that there should be a strong selection pressure for male ability to discriminate between odour plumes under natural circumstances and for individually distinguishable pheromone plumes.

Evolution of increased susceptibility to infectious diseases in age structured populations.

Current theory on the epidemiology of infectious diseases in genetically heterogeneous host populations ignores age structure. Thus, the possibility that microparasites might have negative effects on fitness in different ways during different phases of the lives of their hosts is not accounted for. For example, infections causing mortality and morbidity among juveniles might also have an impairing effect on reproduction among adults, as is the case in many so called childhood diseases. I demonstrate that when this is the case there may be a selective pressure for the host to evolve a higher level of susceptibility to an infection, provided it has the following properties: it should (i) provide life-long immunity, (ii) have a negative effect on reproduction and (iii) not cause too many mortalities.