Spatial population dynamics of small mammals: some methodological and practical issues

Small mammals have been widely used to further our understanding of spatial and temporal population dynamical patterns, because their dynamics exhibit large variations, both in time (multi-annual cycles vs. seasonal variation only) and space (regional synchrony, travelling waves). Small mammals have therefore been the focus of a large number of empirical and statistical (analysis of time-series) studies, mostly based on trapping indices. These studies did not take into account sampling variability associated with the use of counts or estimates of population size. In this paper, we use our field study focusing on population dynamics and demography of small mammals in North Norway at three spatial scales (0.1, 10 and 100 km) to illustrate some methodological and practical issues. We first investigate the empirical patterns of spatial population dynamics, focusing on correlation among time-series of population abundance at increasing spatial scales. We then assess using simulated data the bias of estimates of spatial correlation induced by using either population indices such as the number of individuals captured (i.e., raw counts) or estimates of population size derived from statistical modeling of capture-recapture data. The problems encountered are similar to those described when assessing density-dependence in time-series -a special case of the consequence of measurement error for estimates of regression coefficients- but are to our knowledge ignored in the ecological literature. We suggest some empirical solutions as well as more rigorous approaches

Dinámica poblacional espacial de pequeños mamíferos: algunas cuestiones metodológicas y prácticas

Small mammals have been widely used to further our understanding of spatial and temporal population dynamical patterns, because their dynamics exhibit large variations, both in time (multi–annual cycles vs. seasonal variation only) and space (regional synchrony, travelling waves). Small mammals have therefore been the focus of a large number of empirical and statistical (analysis of time–series) studies, mostly based on trapping indices. These studies did not take into account sampling variability associated with the use of counts or estimates of population size. In this paper, we use our field study focusing on population dynamics and demography of small mammals in North Norway at three spatial scales (0.1, 10 and 100 km) to illustrate some methodological and practical issues. We first investigate the empirical patterns of spatial population dynamics, focusing on correlation among time–series of population abundance at increasing spatial scales. We then assess using simulated data the bias of estimates of spatial correlation induced by using either population indices such as the number of individuals captured (i.e., raw counts) or estimates of population size derived from statistical modeling of capture–recapture data. The problems encountered are similar to those described when assessing density–dependence in time-series —a special case of the consequence of measurement error for estimates of regression coefficients— but are to our knowledge ignored in the ecological literature. We suggest some empirical solutions as well as more rigorous approaches.Los pequeños mamíferos se han utilizado ampliamente para ayudarnos a comprender mejor las pautas dinámicas espaciales y temporales de las poblaciones. Ello obedece a que sus dinámicas presentan importantes variaciones, tanto por lo que respecta al tiempo (ciclos multianuales frente a una única variación estacional) como al espacio (sincronía regional, ondas progresivas). Por consiguiente, los pequeños mamíferos han sido objeto de gran número de estudios empíricos y estadísticos (análisis de series temporales), basados principalmente en índices de capturas por trampa. Dichos estudios no tomaban en consideración la variabilidad del muestreo asociada al empleo de recuentos o de estimaciones del tamaño poblacional. En el presente artículo utilizamos nuestro estudio de campo para analizar la dinámica poblacional y la demografía de los pequeños mamíferos del norte de Noruega en tres escalas espaciales (0,1, 10 y 100 km), además de ilustrar algunas cuestiones prácticas y metodológicas. En primer lugar, investigamos las pautas empíricas de la dinámica poblacional espacial, centrándonos en la correlación existente entre las series temporales de la abundancia poblacional en escalas espaciales cada vez mayores. Seguidamente, utilizamos datos simulados para evaluar el sesgo de las estimaciones de la correlación espacial inducida mediante el empleo, bien de índices poblacionales como el número de individuos capturados (es decir, recuentos brutos) o estimaciones del tamaño oblacional derivadas de la modelación estadística de los datos de captura–recaptura. Los problemas encontrados son similares a los descritos cuando se evalúa la dependencia de la densidad en las series temporales —un caso especial de la consecuencia del error de medición con respecto a las estimaciones de coeficientes de regresión—, pese a que, según parece, se han ignorado en la literatura ecológica. Por último, sugerimos algunas soluciones empíricas, así como planteamientos más rigurosos

Genetic diversity-fitness correlation revealed by microsatellite analyses in European alpine marmots (Marmota marmota). Conserv. Genet

Abstract The relationship between individual genetic diversity and fitness-related traits are poorly understood in the wild. The availability of highly polymorphic molecular markers, such as microsatellites, has made research on this subject more feasible. We used three microsatellite-based measures of genetic diversity, individual heterozygosity H, mean d 2 and mean d 2 outbreeding to test for a relationship between individual genetic diversity and important fitness trait, juvenile survival, in a population of alpine marmots (Marmota marmota), after controlling for the effects of ecological, social and physiological parameters that potentially influence juvenile survival in marmots. Analyses were conducted on 158 juveniles, and revealed a positive association between juvenile survival and genetic diversity measured by mean H. No association was found with mean d 2 and with mean d 2 outbreeding . This suggests a fitness disadvantage to less heterozygous juveniles. The genetic diversity-fitness correlation (GDFC) was somewhat stronger during years with poor environmental conditions (i.e. wet summers). The stressful environmental conditions of this high mountain population might enhance inbreeding depression and make this association between genetic diversity and fitness detectable. Moreover the mating system, allowing extra pair copulation by occasional immigrants, as well as close inbreeding, favours a wide range of individual genetic diversity (mean H ranges from 0.125 to 1), which also may have facilitated the detection of the GDFC. The results further suggest that the observed GDFC is likely to be explained by the ''local effect'' hypothesis rather than by the ''general effect'' hypothesis

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure

Post-critical set and non existence of preserved meromorphic two-forms

We present a family of birational transformations in $CP_2$ depending on two, or three, parameters which does not, generically, preserve meromorphic two-forms. With the introduction of the orbit of the critical set (vanishing condition of the Jacobian), also called ``post-critical set'', we get some new structures, some "non-analytic" two-form which reduce to meromorphic two-forms for particular subvarieties in the parameter space. On these subvarieties, the iterates of the critical set have a polynomial growth in the \emph{degrees of the parameters}, while one has an exponential growth out of these subspaces. The analysis of our birational transformation in $CP_2$ is first carried out using Diller-Favre criterion in order to find the complexity reduction of the mapping. The integrable cases are found. The identification between the complexity growth and the topological entropy is, one more time, verified. We perform plots of the post-critical set, as well as calculations of Lyapunov exponents for many orbits, confirming that generically no meromorphic two-form can be preserved for this mapping. These birational transformations in $CP_2$, which, generically, do not preserve any meromorphic two-form, are extremely similar to other birational transformations we previously studied, which do preserve meromorphic two-forms. We note that these two sets of birational transformations exhibit totally similar results as far as topological complexity is concerned, but drastically different results as far as a more ``probabilistic'' approach of dynamical systems is concerned (Lyapunov exponents). With these examples we see that the existence of a preserved meromorphic two-form explains most of the (numerical) discrepancy between the topological and probabilistic approach of dynamical systems.Comment: 34 pages, 7 figure

Scaling law in the Standard Map critical function. Interpolating hamiltonian and frequency map analysis

We study the behaviour of the Standard map critical function in a neighbourhood of a fixed resonance, that is the scaling law at the fixed resonance. We prove that for the fundamental resonance the scaling law is linear. We show numerical evidence that for the other resonances $p/q$, $q \geq 2$, $p \neq 0$ and $p$ and $q$ relatively prime, the scaling law follows a power--law with exponent $1/q$.Comment: AMS-LaTeX2e, 29 pages with 8 figures, submitted to Nonlinearit

Scaling of the Critical Function for the Standard Map: Some Numerical Results

The behavior of the critical function for the breakdown of the homotopically non-trivial invariant (KAM) curves for the standard map, as the rotation number tends to a rational number, is investigated using a version of Greene's residue criterion. The results are compared to the analogous ones for the radius of convergence of the Lindstedt series, in which case rigorous theorems have been proved. The conjectured interpolation of the critical function in terms of the Bryuno function is discussed.Comment: 26 pages, 3 figures, 13 table

Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Y

A stochastic model of Echinococcus multilocularis transmission in Hokkaido, Japan, focusing on the infection process

Echinococcus multilocularis causes human alveolar echinococcus. In Japan, high prevalence of E. multilocularis among the fox population has been reported throughout Hokkaido. Accordingly, control measures, such as fox hunting and the distribution of bait containing Praziquantel, have been conducted. This study developed a transmission model for individuals in the fox population and included a stochastic infection process to assess the prevalence of E. multilocularis. To make our model realistic, we used the worm burden for each individual in the fox population. We assumed that the worm burden depends on the number of protoscoleces in a predated vole and the number of infection experiences. We carried out stochastic simulations with 1,000 trials for the situations of Koshimizu and Sapporo, Hokkaido, Japan. The distribution of the worm burden among foxes obtained using the model agreed with dissection data. The simulation indicates that a careful choice of season is necessary for an effective distribution of Praziquantel-containing bait. A stochastic model for E. multilocularis, which can assess the range of the prevalence in the fox population, would be helpful in analyzing their complex life-cycle and also in designing control strategies.</p