Analysis of business demography using markov chains : an application to Belgian data

This paper applies the theory of finite Markov chains to analyse the demographic evolution of Belgian enterprises. While other methodologies concentrate on the entry and exit of firms, the Markov approach also analyses migrations between economic sectors. Besides helping to provide a fuller picture of the evolution of the population, Markov chains also enable forecasts of its future composition to be made, as well as the computation of average lifetimes of companies by branch of activity. The method is applied to Belgian data from the Crossroads Bank for Enterprises (CBE). To ensure compliance with Eurostat-OECD definitions, only 'active' enterprises, i.e. enterprises with a positive turnover and/or at least one employee, are considered. The forecasting method is applied to simulate the demographic evolution of the CBE population between 2000 and 2006. This simulation seems to match well the observed changes. Taking migrations into account yields better forecasts than if they are not considered. Moreover, several off-diagonal percentages in the transition matrix are sigificantly different from zero. A case study shows that these migrations are changes in main activity and not the consequence of corrections of wrongly classified firms. Next, the average remaining lifetime and the average age of enterprises in a particular branch of activity is computed and analysed. These lifetimes and ages differ considerably across branches. As expected the life-times of public services are longer than average. Shorter lifetimes combined with an increasing number of enterprises is an indication of renewal inside the branch. A low average age is a sign of relatively new branches. Comparing age to total expected lifetime yields an indicator of closeness to extinction. This might be an indicator of the maturity of the branch. The method is more generally applicable in the sense that it can be used to analyse other populations than those from the CBE and other partitions of the populationBusiness demography, Markov chains, Transition matrix

Lifetime and reproduction of a marked individual in a two-species competition process

The interest is in a stochastic model for the competition of two species, which was first introduced by Reuter [18] and Iglehart [11], and then analyzed by Ridler-Rowe [19]. The model is related to the two-species autonomous competitive model (Zeeman [24]), where individuals compete either directly or indirectly for a limited food supply and, consequently, birth and death rates depend on the population size of one or both of the species. The aim is to complement the treatment of the model we started in [8,9] by focusing here on probabilistic descriptors that are inherently linked to an individual: its residual lifetime and the number of direct descendants. We present an approximating model based on the maximum size distribution, and we discuss on various models defined in terms of the underlying killing and reproductive strategies. Numerical examples are presented to show the effects of the killing and reproductive strategies on the behavior of an individual, and how the impact of these strategies on the descriptors vanishes in highly competitive ecosystems

Financialization of The United States Economy and the Effect on Small Firms and the Consumer

The recent trend of financialization affects small firms and the consumer. It follows the rise of the financial sector and what was in place for the rapid growth of it. The rapid growth of it also creates instability in the economy and the instability is studied to determine where it arose and how it can be reformed. The reform of the financial sector is aimed at suppressing corporate interests to satisfy that of the consumer and protect the small firm. The protection of consumer interest is rationalized in the need for small firms to satisfy consumer demand most efficiently

Mathematical models for investigating the long-term impact of Gyrodactylus salaris infections on Atlantic salmon populations

Gyrodactylus salaris Malmberg, 1957, is a notifiable freshwater ecto-parasite that infects both wild and farmed populations of Atlantic salmon (Salmo salar, L.). It has caused catastrophic damage to wild salmon stocks in Norway since its accidental introduction in 1975, reducing salmon density in some rivers by 98% over a period of five years. It is estimated that G. salaris has cost the Norwegian salmon industry more than 500 million EUR. Currently the UK has G. salaris free status under EU law, however, it is believed that if G. salaris emerged in the UK the impact would be similar to that witnessed in Norway. The aim of this thesis is to develop mathematical models that describe the salmon-G. salaris system in order to gain a greater understanding of the possible long-term impact the parasite may have on wild populations of Atlantic salmon in G. salaris-free territories such as the UK. Mathematical models, including deterministic, Leslie matrix and individual based models, were used to investigate the impact of G. salaris on Atlantic salmon at the individual and population level. It is known that the Atlantic strain of Atlantic salmon, examples of which occur naturally in Norway and the UK, does not have any resistance to G. salaris infections and the parasite population is able to quickly grow to epidemic levels. In contrast, the Baltic strain of Atlantic salmon, examples of which occur naturally in Sweden and Russia, exhibits some form of resistance and the parasite is unable to persist. Thus, baseline models were extended to include immunity to infection, a trade-off on salmon reproductive rate, and finally, to consider interactions between populations of G. salaris and multiple strains of salmon exhibiting varying levels of immunity from fully susceptible to resistant. The models proposed predict that in the absence of host resistance or an immune response infections by G. salaris will result in an epidemic followed by the extinction of the salmon host population. Models also predict that if salmon are able to increase their resistance to G. salaris infections through mutations, salmon population recovery after the epidemic is indeed possible within 10-15 years post introduction with low level parasite coexistence. Finally, models also highlight areas where additional information is needed in order to improve predictions and enable the estimation of important parameter values. Model predictions will ultimately be used to assist in future contingency planning against G. salaris outbreaks in the UK and possibly as a basis for future models describing other fish/ecto-parasite systems

The role of dispersal in range change in birds

Eurasian reed warbler Acrocephalus scirpaceus expanded its range in Great Britain in the late 20th and early 21st centuries. The role of dispersal in this range expansion was investigated. Inference of the mechanisms underlying the range dynamics drew on fieldwork, analysis of large observational datasets, and a simulation model; this model was run in a reedbed map of Britain, generated from satellite data using machine learning. Breeding season temperature sets up reed warbler’s range limit in Britain directly, by influencing occupancy in the current year, perhaps mediated through reed Phragmites australis phenology. Although components of productivity were positively related to temperature, these and adult survival did not decline to the range edge. There was therefore no evidence that demography plays a role in limiting reed warbler’s range in Britain; however, not all aspects of demography were investigated. Survival was negatively related to temperature, and simulations suggested that this may allow reed warbler to maintain a more northerly range limit than without such a relationship. Reed warbler’s range expansion can be explained by a gradual equilibration with climate space, enabled by long-distance dispersal: only rare long-distance dispersing individuals matched the rate of range expansion. Reed warbler’s range edge tracked climate change, but the bulk of the population lagged behind. This could be due to dispersal-limitation, or perhaps newly established populations grow too slowly to generate sufficient emigrants. Simulations suggested that reed warbler’s range size is more sensitive to demography than to dispersal. The number of fledglings per breeding attempt increased over time, probably due to climate warming, and could have increased emigration; if so, this may be the cause of a more rapid movement in the range centroid later in the study period. Emigration, transition and immigration may therefore play different roles in reed warbler’s range dynamics in space and time

Why Not the Best? How Science Failed the Florida Panther

The US Fish and Wildlife Service is charged with using the "best available science" to manage endangered species. But a scientific review panel found "fatal flaws" in agency models used to regulate development in the habitat of the critically endangered Florida panther. What happened