Additional tables, figures, and methods from A framework for estimating the determinants of spatial and temporal variation in vital rates and inferring the occurrence of unobserved extreme events

We develop a general framework that combines long-term tag–recapture data and powerful statistical and modelling techniques to investigate how population, environmental and climate factors determine variation in vital rates and population dynamics in an animal species, using as a case study the population of brown trout living in Upper Volaja (Western Slovenia). This population has been monitored since 2004. Upper Volaja is a sink, receiving individuals from a source population living above a waterfall. We estimate the numerical contribution of the source population on the sink population and test the effects of temperature, population density and extreme events on variation in vital rates among 2647 individually tagged brown trout. We found that individuals dispersing downstream from the source population help maintain high population densities in the sink population despite poor recruitment. The best model of survival for individuals older than juveniles includes additive effects of birth cohort and sampling occasion. Fast growth of older cohorts and higher population densities in 2004–2005 suggest very low population densities in the late 1990s, which we hypothesize were caused by a flash flood that strongly reduced population size and created the habitat conditions for faster individual growth and transient higher population densities after the extreme event

Titles and legends from A framework for estimating the determinants of spatial and temporal variation in vital rates and inferring the occurrence of unobserved extreme events

We develop a general framework that combines long-term tag–recapture data and powerful statistical and modelling techniques to investigate how population, environmental and climate factors determine variation in vital rates and population dynamics in an animal species, using as a case study the population of brown trout living in Upper Volaja (Western Slovenia). This population has been monitored since 2004. Upper Volaja is a sink, receiving individuals from a source population living above a waterfall. We estimate the numerical contribution of the source population on the sink population and test the effects of temperature, population density and extreme events on variation in vital rates among 2647 individually tagged brown trout. We found that individuals dispersing downstream from the source population help maintain high population densities in the sink population despite poor recruitment. The best model of survival for individuals older than juveniles includes additive effects of birth cohort and sampling occasion. Fast growth of older cohorts and higher population densities in 2004–2005 suggest very low population densities in the late 1990s, which we hypothesize were caused by a flash flood that strongly reduced population size and created the habitat conditions for faster individual growth and transient higher population densities after the extreme event

Zak_Lipo_tag_recapture

Tag-recapture data for the marble trout populations of Zakojska and Lipovscek (two .csv files). Mark = fish ID; Year = year of sampling; Month = month of sampling;Run = first pass (1) or second pass (2); Sector = stream section in which the fish was sampled; Length = total length of fish (mm); Weight = weight of the fish (g); Age = age of fish - fish emerge in May/June, they are 0+ up to first winter, then 1+ and so on; Cohort: year of birth (format Cyy); Adc: 1 if adipose fin was cut - only for fish with no tag when sampled; Adip = additional tag associated with a piece of the adipose cut

Zak_Lipo_SNP_genotype

Genotype data for the marble trout populations of Zakojska and Lipovscek. LOCATION = name of the stream/population; SAMPLE_ID fish ID, corresponds to Mark in the tag-recapture dataset; SEX = sex of fish - ? and NA mean not available/uncertain;YOB = year of birth of fish. Additional columns are the bi-allelic SNPs (0 means not genotyped)

Prediction of mean cohort-specific growth with random-effects or non-linear least squares model.

<p>Prediction of mean cohort-specific growth trajectories (i.e. individual random effects <i>u</i> and <i>v</i> = 0) using the von Bertalanffy growth function model with cohort as a categorical predictor for both and <i>k</i> (solid line) and non-linear least-squares regression using the R function <i>nls</i> (dashed line) for the 2001 (a) and 2002 (b) cohorts for the population of Gacnik, and 2001 (c) and 1999 (d) cohorts for the population of Zakojska. Estimates of model parameters are reported in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003828#pcbi-1003828-t003" target="_blank">Table 3</a>.</p

Number of recaptures for fish and observed growth trajectories.

<p>Frequency of number of capture/recaptures for fish (left column) and observed individual growth trajectories (right column) for the populations of Gacnik (top row) and Zakojska (bottom row).</p

Parameters of the von Bertalanffy growth function model for two cohorts of Gacnik and Zakojska.

<p>Parameter estimates and 95% confidence intervals of the von Bertalanffy growth function model for two cohorts of Gacnik and Zakojska with individuals random effects and cohort as predictors for both and <i>k</i> (random-effects model) and non-linear least squares regression separately for each cohort using the R function <i>nls</i>. 95% confidence intervals of parameters estimates for the two models do not overlap for any of the von Bertalanffy growth function's parameters.</p><p>Parameters of the von Bertalanffy growth function model for two cohorts of Gacnik and Zakojska.</p

Cohort-specific growth trajectories.

<p>Cohort-specific growth trajectories for the marble trout populations of Zakojska (panel a) and Gacnik (b). The cohorts with the biggest and smallest body size at age 8 as predicted by the model were for Zakojska the 2006 and 2004 cohorts and for Gacnik the 2000 and 2003 cohorts.</p

Growth trajectories from simulated data with negative, positive and no correlation between <i>L</i>_∞ and <i>k</i>.

<p>Growth trajectories from simulated data according to <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003828#pcbi.1003828.e036" target="_blank">Eq. 7</a> (no predictors, only intercept and individual random effects) with strong negative (left panel, Pearson's <i>r</i> = −0.9), positive (middle panel, <i>r</i> = 0.6), and no correlation (right panel, <i>r</i> = 0) between <i>L</i>_∞ and <i>k</i> at the individual level. For all three panels, <i>L</i>_∞ = 330 mm, <i>k</i> = 0.37 y⁻¹, <i>t</i>₀ = −0.38 y, σ_v = 0.22, σ_u = 0.22.</p

Prediction of validation data using random-effects model or mean cohort-specific length-at-age empirical data.

<p>Example of prediction of validation data for the population of Gacnik using the model with cohort as predictor for both and <i>k</i> (panel a, <i>R</i>² = 0.76, MAE = 19 mm) and mean cohort-specific length-at-age empirical data (b, <i>R</i>² = 0.66, MAE = 22 mm). For the population of Zakojska, (c) model predictions (<i>R</i>² = 0.72, MAE = 24 mm), and (d) predictions using mean cohort-specific length-at-age empirical data (<i>R</i>² = 0.36, MAE = 37 mm).</p