Importance of correlations among matrix entries in stochastic models in relation to number of transition matrices

Ramula, Satu; Lehtilä, Kari

doi:10.1111/j.0030-1299.2005.13940.x

Cited by 16 publications

(8 citation statements)

References 32 publications

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“…We used the Bayesian approach for inference and Markov chain Monte Carlo (MCMC) simulation for parameter estimation. We spec- were conducted in JAGS (Plummer, 2003) via the R package jagsUI (Kellner, 2016). Posterior summaries from three Markov chain Monte Carlo (MCMC) chains were based on 50,000 iterations after a burnin of 20,000 and a thinning interval of 10.…”

Section: Model Implementationmentioning

confidence: 99%

“…Covariation among and autocorrelation within vital rates affect the stochastic population growth rate (Caswell, ; Tuljapurkar, ). Positive covariation and autocorrelation tend to decrease the stochastic growth rate and to increase the variability in population size while negative covariation and autocorrelation results in opposite patterns buffering population dynamics (Ramula & Lehtilä, ; Tuljapurkar, Gaillard, & Coulson, ). However, it is difficult to make generalization because the life‐history strategy and regime of density dependence may affect the population consequences of covariation and autocorrelation (Colchero et al, ; Heino & Sabadell, ; Paniw, Ozgul, & Salguero‐Gómez, ; Ruokolainen et al, ; Tuljapurkar et al, ).…”

Section: Introductionmentioning

confidence: 99%

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Can temporal covariation and autocorrelation in demographic rates affect population dynamics in a raptor species?

Fay

Michler

Laesser

et al. 2020

Ecology and Evolution

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Theoretical studies suggest that temporal covariation among and temporal autocorrelation within demographic rates are important features of population dynamics. Yet, empirical studies have rarely focused on temporal covariation and autocorrelation limiting our understanding of these patterns in natural populations. This lack of knowledge restrains our ability to fully understand population dynamics and to make reliable population forecasts. In order to fill this gap, we used a long‐term monitoring (15 years) of a kestrel Falco tinnunculus population to investigate covariation and autocorrelation in survival and reproduction at the population level and their impact on population dynamics. Using Bayesian joint analyses, we found support for positive covariation between survival and reproduction, but weak autocorrelation through time. This positive covariation was stronger in juveniles compared with adults. As expected for a specialized predator, we found that the reproductive performance was strongly related to an index of vole abundance explaining 86% of the temporal variation. This very strong relationship suggests that the temporally variable prey abundance may drive the positive covariation between survival and reproduction in this kestrel population. Simulations suggested that the observed effect size of covariation could be strong enough to affect population dynamics. More generally, positive covariation and autocorrelation have a destabilizing effect increasing substantially the temporal variability of population size.

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Section: Model Implementationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Can temporal covariation and autocorrelation in demographic rates affect population dynamics in a raptor species?

Fay

Michler

Laesser

et al. 2020

Ecology and Evolution

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show abstract

“…To include stochasticity in vital rates several stochastic models have been developed (reviewed by Caswell 2001). These different models may produce divergent estimates of probability of and time to recovery since they produce different population growth rate estimates (Ramula and Lehtila 2005). Adult survival and breeding success of emperor penguins are nearly independent of each other (correlation r 0 (0.004).…”

Section: The Important Role Of Variance and Covariance In Vital Ratesmentioning

confidence: 99%

Limitation of population recovery: a stochastic approach to the case of the emperor penguin

Jenouvrier¹,

Barbraud²,

Weimerskirch³

et al. 2009

Oikos

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Major population crashes due to natural or human‐induced environmental changes may be followed by recoveries. There is a growing interest in the factors governing recovery, in hopes that they might guide population conservation and management, as well as population recovery following a re‐introduction program. The emperor penguin Aptenodytes forsteri population in Terre Adélie, Antarctica, declined by 50% during a regime shift in the mid‐1970s, when abrupt changes in climate and ocean environment regimes affected the entire Southern Ocean ecosystem. Since then the population has remained stable and has not recovered. To determine the factors limiting recovery, we examined the consequences of changes in survival and breeding success after the regime shift. Adult survival recovered to its pre‐regime shift level, but the mean breeding success declined and the variance in breeding success increased after the regime shift. Using stochastic matrix population models, we found that if the distribution of breeding success observed prior to the regime shift had been retained, the emperor penguin population would have recovered, with a median time to recovery of 36 years. The observed distribution of breeding success after the regime shift makes recovery very unlikely. This indicates that the pattern of breeding success is sufficient to have prevented emperor penguin population recovery. The population trajectory predicted on the basis of breeding success agrees with the observed trajectory. This suggests that the net effect of any facors other than breeding success must be small. We found that the probability of recovery and the time to recovery depend on both the mean and variance of breeding success. Increased variance in breeding success increases the probability of recovery when mean success is low, but has the opposite effect when the mean is high. This study shows the important role of breeding success in determining population recovery for a long‐lived species and demonstrates that demographic mechanisms causing population crash can be different from those preventing population recovery.

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“…The strong positive correlation present in our model is probably too strong since other factors will probably affect vital rates differently. Our estimates of the stochastic growth rate might therefore be biased low compared to natural populations (Ramula & Lehtilä 2005).…”

Section: E T H O D O L O G I C a L C O N S I D E R A T I O N S : M mentioning

confidence: 92%

Impacts of differential prey dynamics on the potential recovery of endangered arctic fox populations

Henden

Bardsen

Yoccoz

et al. 2008

Journal of Applied Ecology

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Summary 1.The arctic fox Vulpes lagopus in Fennoscandia was heavily decimated in the early 20th century and has failed to recover despite full protection during the last 70 years. On the contrary, since the 1970s the population has declined even further and the species is now on the verge of regional extinction. 2.The most recent population decline of the arctic fox in Fennoscandia has coincided with some distinct changes in the cyclic population dynamics of its key prey, lemmings and voles. Although this coincidence of events and the tight trophic connection between foxes and rodents suggest that the two phenomena are causally linked, the effects of spatio-temporal small rodent dynamics on the viability of arctic fox populations have not been fully explored. 3. Here we address how the mean, temporal variance and the periodicity of small rodent population density cycles impact long-term stochastic growth rate of arctic fox populations. We do this in a modelling framework where the vital rates of the fox are linked to realistic, quantitative realizations of small rodent density dynamics. 4. Arctic fox population growth rate was found to be highly sensitive to the temporal mean and to some extent to the variance in small rodent density cycles, whereas cycle period in the observed range of 3-to 5-year cycles was surprisingly of minor importance. 5. Synthesis and applications . Our analysis shows that small rodent population dynamics characterized by low-amplitude density cycles (irrespective of their average cycle period), provide little scope for positive population growth, and thus recovery, of the arctic fox. Thus, we advise that management actions such as re-introductions and red fox Vulpes vulpes control should be conducted in mountain tundra regions where regular, high-amplitude cycles, of any period, with recurrent high spring densities of rodents still prevail. In order to properly identify geographic areas with the highest potential for arctic fox recovery, the emphasis of current monitoring programmes of small rodent dynamics needs to consider more quantitative metrics than they currently employ.

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Importance of correlations among matrix entries in stochastic models in relation to number of transition matrices

Cited by 16 publications

References 32 publications

Can temporal covariation and autocorrelation in demographic rates affect population dynamics in a raptor species?

Can temporal covariation and autocorrelation in demographic rates affect population dynamics in a raptor species?

Limitation of population recovery: a stochastic approach to the case of the emperor penguin

Impacts of differential prey dynamics on the potential recovery of endangered arctic fox populations

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