Chebanov law and Vakar formula in mathematical models of complex systems

Ecological models written in a mathematical language L(M) or model language, with a given style or methodology can be considered as a text. It is possible to apply statistical linguistic laws and the experimental results demonstrate that the behaviour of a mathematical model is the same of any literary text of any natural language. A text has the following characteristics: (a) the variables, its transformed functions and parameters are the lexic units or LUN of ecological models; (b) the syllables are constituted by a LUN, or a chain of them, separated by operating or ordering LUNs; (c) the flow equations are words; and (d) the distribution of words (LUM and CLUN) according to their lengths is based on a Poisson distribution, the Chebanov's law. It is founded on Vakar's formula, that is calculated likewise the linguistic entropy for L(M). We will apply these ideas over practical examples using MARIOLA model. In this paper it will be studied the problem of the lengths of the simple lexic units composed lexic units and words of text models, expressing these lengths in number of the primitive symbols, and syllables. The use of these linguistic laws renders it possible to indicate the degree of information given by an ecological model.

Documentación de modelos y flujos de trabajo: el siguiente reto en el manejo de información ecológica

Los modelos ecológicos se han convertido en una pieza clave de esta ciencia. La generación de conocimiento se consigue en buena medida mediante procesos analíticos más o menos complejos aplicados sobre conjuntos de datos diversos. Pero buena parte del conocimiento necesario para diseñar e implementar esos modelos no está accesible a la comunidad científica. Proponemos la creación de herramientas informáticas para documentar, almacenar y ejecutar modelos ecológicos y flujos de trabajo. Estas herramientas (repositorios de modelos) están siendo desarrolladas por otras disciplinas como la biología molecular o las ciencias de la Tierra. Presentamos un repositorio de modelos (ModeleR) desarrollado en el contexto del Observatorio de seguimiento del cambio global de Sierra Nevada (Granada-Almería). Creemos que los repositorios de modelos fomentarán la cooperación entre científicos, mejorando la creación de conocimiento relevante que podría ser transferido a los tomadores de decisiones.

Importancia de la caracterización de la masa de raíces en la simulación de ecosistemas forestales

Los análisis de sensibilidad son una herramienta importante para comprender el funcionamiento de los modelos ecológicos, así como para identificar los parámetros más importantes en su funcionamiento. Además, los análisis de sensibilidad pueden utilizarse para diseñar de forma más efectiva planes de muestreo de campo dirigidos a calibrar los modelos ecológicos. En los estudios de ecosistemas forestales, el análisis cuantitativo de la parte subterránea es mucho más costoso y complicado que el estudio de la parte aérea, en especial el estudio de la dinámica de producción y descomposición de raíces gruesas y finas de los árboles. En este trabajo se muestra un ejemplo de análisis de sensibilidad del modelo forestal FORECAST a parámetros que definen la biomasa, longevidad y concentración de nitrógeno en las raíces de los árboles. El modelo se calibró para simular dos rodales de pino silvestre (Pinus sylvestris) en los Pirineos de Navarra. Los resultados indican que la tasa de renovación de raíces finas es el parámetro más influyente en las estimaciones del modelo de crecimiento de los árboles, seguida de la concentración de N en las mismas, siendo la relación biomasa subterránea/total el parámetro al cual el modelo es menos sensible. Además, el modelo es más sensible a los parámetros que definen el componente subterráneo de la biomasa arbórea cuando simula un sitio de menor capacidad productiva y mayor limitación por nutrientes.

Syntactic and Semantic Relationships in Models of Complex Systems: An Ecological Case

In this paper, the authors extend and generalize the methodology based on the dynamics of systems with the use of differential equations as equations of state, allowing that first order transformed functions not only apply to the primitive or original variables, but also doing so to more complex expressions derived from them, and extending the rules that determine the generation of transformed superior to zero order (variable or primitive). Also, it is demonstrated that for all models of complex reality, there exists a complex model from the syntactic and semantic point of view. The theory is exemplified with a concrete model: MARIOLA model.

No effect of unemployment on intimate partner-related femicide during the financial crisis: a longitudinal ecological study in Spain

Background: Spain’s financial crisis has been characterized by an increase in unemployment. This increase could have produced an increase in deaths of women due to intimate partner-related femicides (IPF). This study aims to determine whether the increase in unemployment among both sexes in different regions in Spain is related to an increase in the rates of IPF during the current financial crisis period. Methods: An ecological longitudinal study was carried out in Spain’s 17 regions. Two study periods were defined: pre-crisis period (2005–2007) and crisis period (2008–2013). IPF rates adjusted by age and unemployment rates for men and women were calculated. We fitted multilevel linear regression models in which observations at level 1 were nested within regions according to a repeated measurements design. Results: Rates of unemployment have progressively increased in Spain, rising above 20 % from 2008 to 2013 in some regions. IPF rates decreased in some regions during crisis period with respect to pre-crisis period. The multilevel analysis does not support the existence of a significant relationship between the increase in unemployment in men and women and the decrease in IPF since 2008. Discussion: The increase in unemployment in men and women in Spain does not appear to have an effect on IPF. The results of the multilevel analysis discard the hypothesis that the increase in the rates of unemployment in women and men are related to an increase in IPF rates. Conclusions: The decline in IPF since 2008 might be interpreted as the result of exposure to other factors such as the lower frequency of divorces in recent years or the medium term effects of the integral protection measures of the law on gender violence that began in 2005.

An Ecological Model for Predicting Behaviour of Mediterranean Shrublands

In order to build dynamic models for prediction and management of degraded Mediterranean forest areas was necessary to build MARIOLA model, which is a calculation computer program. This model includes the following subprograms. 1) bioshrub program, which calculates total, green and woody shrubs biomass and it establishes the time differences to calculate the growth. 2) selego program, which builds the flow equations from the experimental data. It is based on advanced procedures of statistical multiple regression. 3) VEGETATION program, which solves the state equations with Euler or Runge-Kutta integration methods. Each one of these subprograms can act as independent or as linked programs.