College of Letters & Science

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The College of Letters and Science, the largest center for learning, teaching and research at Montana State University, offers students an excellent liberal arts and sciences education in nearly 50 majors, 25 minors and over 25 graduate degrees within the four areas of the humanities, natural sciences, mathematics and social sciences.

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Quantifying fixed individual heterogeneity in demographic parameters: Performance of correlated random effects for Bernoulli variables
(Wiley, 2021-10) Fay, Rémi; Authier, Matthieu; Hamel, Sandra; Jenouvrier, Stéphanie; Pol, Martijn; Cam, Emmanuelle; Gaillard, Jean‐Michel; Yoccoz, Nigel G.; Acker, Paul; Allen, Andrew; Aubry, Lise M.; Bonenfant, Christophe; Caswell, Hal; Coste, Christophe F. D. Coste; Larue, Benjamin; Coeur, Christie Le; Gamelon, Marlène; Macdonald, Kaitlin R.; Moiron, Maria; Nicol‐Harpe, Alex; Pelletier, Fanie; Rotella, Jay J.; Teplitsky, Celine; Touzot, Laura; Wells, Caitlin P.; Sæther, Bernt‐Erik
An increasing number of empirical studies aim to quantify individual variation in demographic parameters because these patterns are key for evolutionary and ecological processes. Advanced approaches to estimate individual heterogeneity are now using a multivariate normal distribution with correlated individual random effects to account for the latent correlations among different demographic parameters occurring within individuals. Despite the frequent use of multivariate mixed models, we lack an assessment of their reliability when applied to Bernoulli variables. Using simulations, we estimated the reliability of multivariate mixed effect models for estimating correlated fixed individual heterogeneity in demographic parameters modeled with a Bernoulli distribution. We evaluated both bias and precision of the estimates across a range of scenarios that investigate the effects of life-history strategy, levels of individual heterogeneity and presence of temporal variation and state dependence. We also compared estimates across different sampling designs to assess the importance of study duration, number of individuals monitored and detection probability. In many simulated scenarios, the estimates for the correlated random effects were biased and imprecise, which highlight the challenge in estimating correlated random effects for Bernoulli variables. The amount of fixed among-individual heterogeneity was frequently overestimated, and the absolute value of the correlation between random effects was almost always underestimated. Simulations also showed contrasting performances of mixed models depending on the scenario considered. Generally, estimation bias decreases and precision increases with slower pace of life, large fixed individual heterogeneity and large sample size. We provide guidelines for the empirical investigation of individual heterogeneity using correlated random effects according to the life-history strategy of the species, as well as, the volume and structure of the data available to the researcher. Caution is warranted when interpreting results regarding correlated individual random effects in demographic parameters modeled with a Bernoulli distribution. Because bias varies with sampling design and life history, comparisons of individual heterogeneity among species is challenging. The issue addressed here is not specific to demography, making this warning relevant for all research areas, including behavioral and evolutionary studies.
Temporal correlations among demographic parameters are ubiquitous but highly variable across species
(Wiley, 2022-07) Fay, Rémi; Hamel, Sandra; van de Pol, Martijn; Gaillard, Jean‐Michel; Yoccoz, Nigel G.; Acker, Paul; Authier, Matthieu; Larue, Benjamin; Coeur, Christie Le; Macdonald, Kaitlin R.; Nicol‐Harper, Alex; Barbraud, Christophe; Bonenfant, Christophe; Van Vuren, Dirk H.; Cam, Emmanuelle; Delord, Karine; Gamelon, Marlène; Moiron, Maria; Pelletier, Fanie; Rotella, Jay; Teplitsky, Celine; Visser, Marcel E.; Wells, Caitlin P.; Wheelwright, Nathaniel T.; Jenouvrier, Stéphanie; Sæther, Bernt‐Erik
Temporal correlations among demographic parameters can strongly influence population dynamics. Our empirical knowledge, however, is very limited regarding the direction and the magnitude of these correlations and how they vary among demographic parameters and species’ life histories. Here, we use long-term demographic data from 15 bird and mammal species with contrasting pace of life to quantify correlation patterns among five key demographic parameters: juvenile and adult survival, reproductive probability, reproductive success and productivity. Correlations among demographic parameters were ubiquitous, more frequently positive than negative, but strongly differed across species. Correlations did not markedly change along the slow-fast continuum of life histories, suggesting that they were more strongly driven by ecological than evolutionary factors. As positive temporal demographic correlations decrease the mean of the long-run population growth rate, the common practice of ignoring temporal correlations in population models could lead to the underestimation of extinction risks in most species.