Mixing times towards demographic equilibrium in insect populations with temperature variable age structures

2016

BMC Ecol

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BackgroundThis work combines multivariate time series analysis and graph theory to detect synchronization and causality among certain ecological variables and to represent significant correlations via network projections. Four different statistical tools (cross-correlations, partial cross-correlations, Granger causality and partial Granger causality) utilized to quantify correlation strength and causality among biological entities. These indices correspond to different ways to estimate the relationships between different variables and to construct ecological networks using the variables as nodes and the indices as edges. Specifically, correlations and Granger causality indices introduce rules that define the associations (links) between the ecological variables (nodes). This approach is used for the first time to analyze time series of moth populations as well as temperature and relative humidity in order to detect spatiotemporal synchronization over an agricultural study area and to illustrate significant correlations and causality interactions via graphical models.ResultsThe networks resulting from the different approaches are trimmed and show how the network configurations are affected by each construction technique. The Granger statistical rules provide a simple test to determine whether one series (population) is caused by another series (i.e. environmental variable or other population) even when they are not correlated. In most cases, the statistical analysis and the related graphical models, revealed intra-specific links, a fact that may be linked to similarities in pest population life cycles and synchronizations. Graph theoretic landscape projections reveal that significant associations in the populations are not subject to landscape characteristics. Populations may be linked over great distances through physical features such as rivers and not only at adjacent locations in which significant interactions are more likely to appear. In some cases, incidental connections, with no ecological explanation, were also observed; however, this was expected because some of the statistical methods used to define non trivial associations show connections that cannot be interpreted phenomenologically.ConclusionsIncorporating multivariate causal interactions in a probabilistic sense comes closer to reality than doing per se binary theoretic constructs because the former conceptually incorporate the dynamics of all kinds of ecological variables within the network. The advantage of Granger rules over correlations is that Granger rules have dynamic features and provide an easy way to examine the dynamic causal relations of multiple time-series variables. The constructed networks may provide an intuitive, advantageous representation of multiple populations’ associations that can be realized within an agro-ecosystem. These relationships may be due to life cycle synchronizations, exposure to a shared climate or even more complicated ecological interactions such as moving behavior, dispersal patterns and host allocation. More...

Section: Resultsmentioning

confidence: 99%

Using multivariate cross correlations, Granger causality and graphical models to quantify spatiotemporal synchronization and causality between pest populations

2016

BMC Ecol

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“…Secondly, the asymptotic distribution properties of the theoretical and the empirical intensity transition matrices were compared using an entropy-based divergence distance measure [54]. In this case, the mosquito population stochastic process was considered as homogenous, and thus starting from an initial distribution of population states a limiting probability, Π i , exist: lim…”

Section: Markov Chain Model Validation and Equilibrium Distributionmentioning

confidence: 99%

“…H i represents the average amount of uncertainty of the population system for moving one step ahead being initially in state Si. We are now interested in estimating the average uncertainty of the chain for moving one step ahead of any other initial state, which is [54]:…”

Section: Markov Chain Model Validation and Equilibrium Distributionmentioning

confidence: 99%

“…Most of the age-structured matrix projection models have been used in demographic studies as a central tool to quantify the asymptotic growth rates (i.e., the dominant eigenvalue) and the reproductive values (dominant right and left eigenvalues). They have been also used in the context of MCs to estimate the stable age distribution and how it is affected under certain environments [53,54].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Temperature Conditioned Markov Chain Model for Predicting the Dynamics of Mosquito Vectors of Disease

Dorrestijn

Thomidis

et al. 2021

Insects

Understanding and predicting mosquito population dynamics is crucial for gaining insight into the abundance of arthropod disease vectors and for the design of effective vector control strategies. In this work, a climate-conditioned Markov chain (CMC) model was developed and applied for the first time to predict the dynamics of vectors of important medical diseases. Temporal changes in mosquito population profiles were generated to simulate the probabilities of a high population impact. The simulated transition probabilities of the mosquito populations achieved from the trained model are very near to the observed data transitions that have been used to parameterize and validate the model. Thus, the CMC model satisfactorily describes the temporal evolution of the mosquito population process. In general, our numerical results, when temperature is considered as the driver of change, indicate that it is more likely for the population system to move into a state of high population level when the former is a state of a lower population level than the opposite. Field data on frequencies of successive mosquito population levels, which were not used for the data inferred MC modeling, were assembled to obtain an empirical intensity transition matrix and the frequencies observed. Our findings match to a certain degree the empirical results in which the probabilities follow analogous patterns while no significant differences were observed between the transition matrices of the CMC model and the validation data (ChiSq = 14.58013, df = 24, p = 0.9324451). The proposed modeling approach is a valuable eco-epidemiological study. Moreover, compared to traditional Markov chains, the benefit of the current CMC model is that it takes into account the stochastic conditional properties of ecological-related climate variables. The current modeling approach could save costs and time in establishing vector eradication programs and mosquito surveillance programs.

“…In brief, the concept invokes the fundamental attributes of demographic entropy, as a measure of Darwinian fitness of age structured populations, to study the changes in genotypic and phenotypic composition as generated by the mutation-selection regime [4].Furthermore, established along the Leslie model Tuljapulkar [5], proposed a shift of the Leslie population model, to be patterned as a Markov chain in discrete time, in parliamentary procedure to quantify population converges to its stable age distribution [5,6]. By such a context demographic entropy has been used by Damos [7] as a highly qualitative predictor of the species survivorship budged and net reproductive success of insect populations reared in different temperature conditions towards the stable age distribution. The later approach includes the use of entropy (i.e.…”

Section: Introductionmentioning

confidence: 99%

Bio demographic aspects of population entropy in quantifying population heterogeneity and its consequences for population fitness and species adaptation

Proceedings of 2nd International Electronic Conference on Entropy and Its Applications

2015

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Entropy is a well-established measure of population variability and already used in contingency in life table analysis to capture the trends of population heterogeneity. However, entropy has been also utilized as a more general dynamic measure of species fitness and adaptation to varying ecological conditions. In this study we are concerned with a brief account of the latter. In principle, such demographic-population entropy is an analogue of the Gibbs-Boltzmann entropy in statistical mechanics, H=-Σpilnpi. Here, pi represents the probability density function of the age of reproducing individuals and therefore maximization of entropy is equivalent to maximization of the uncertainty of age reproduction. Moreover, considering that demographic dynamics are formally equivalent to the dynamics of a Markov chain, demographic entropy may be used to estimate the convergence rate of insect population transitions to the stable age distributions and demographic equilibriums under certain conditions. By interpreting population entropy as a distance measure between the variability of the mortality distribution where no outside forces interfere and the conditional entropy estimated given the known unperturbed reference mortality we may quantify species adaptive value. Through this operation, populations with the favored demographic properties gradually develop fitness advantages in the presence of the artificial selection factor.