introduction.qmd

# Introduction {#sec-introduction}

Climate warming poses a pressing challenge for several species, particularly for trees that are failing to follow temperature warming [@Sittaro2017].
Understanding the mechanisms governing species distribution is crucial for comprehending how they will respond to novel conditions arising from climate change.
The niche theory predicts that a species thrives within a specific set of environmental conditions that allows it to have a positive growth rate [@Hutchinson1957].
Assuming geographic distribution is a manifestation of individual performance, bottom-up demographic range models incorporate environmental factors influencing growth, survival, and recruitment and allow one to predict species distribution [@maguire1973niche; @holt2009; @Schurr2012].
And this thing is what I tried to build during my thesis.

Here, I use this book as a lab notebook to share all the details related to the model construction so it can be easily replicated and extended to others.
The initial chapter covers the dataset description, the selected tree species, variables, and their computation methods.

This book unfolds in three separate parts.
The first one describes the growth, survival, and recruitment demographic models.
In the first chapter of this section (@sec-demo_model_description), we elucidate the ecological rationale behind each demographic model and its mathematical formulation.
The following chapter (@sec-mixed_cov) details how we improved the base models by partitioning the variance between random and fixed effects.
Here, we describe the ecological meaning behind the non-linear functions linking the climate and competition covariates to each demographic model.
To finish this section, we describe the technical details of the model fit in @sec-model-fit, the comparison between the models in @sec-model_comparison, and the practical information of how and where the model parameters are stored in @sec-parameters.

The second section evaluates the fit of these models for 31 forest tree species using the selected model in @sec-model_comparison.
It begins by discussing the model parameters and their goodness of fit by comparing posterior distributions with trait observations from the literature.
We evaluate the intercept parameters (@sec-parsIntercept) and the spatial random effects applied at the plot level (@sec-parsRandomEffects).
We then discuss the effect of competition (@sec-parsComp) and climate (@sec-parsClimate) covariates.
Subsequently, we employ two approaches to gauge the effect size of each covariate.
Specifically, we first compute the conditional effect of each covariate at the lower (1% quantile) and upper (99% quantile) distribution of the covariate (@sec-effectSize).
This metric allows one to quantify the range of the intensity effect a species experienced from the covariate.
Finally, we computed the average marginal effect of each covariate across the dataset (@sec-averageMarginalEffect).
This approach uses perturbation analysis to quantify the effect of each covariate on each observed measurement.
It allows one to compare the marginal effect among species and demographic models.

The final section details the integration of growth, survival, and recruitment models into an Integral Projection Model (IPM).
We start by describing the mathematical formulation of the IPM and its numerical approximation (@sec-ipm_description).
The second chapter (@sec-ipm_guide) is a practical guide detailing the use of the IPM code.
The following chapter describes the sensitivity analysis for the IPM to the demographic model parameters (@sec-sensAnalysis).
There, we use a random forest algorithm to rank the relative importance of each parameter in changing the intrinsic population growth rate.
The following two chapters describe each covariate's conditional (@sec-cond-lambda) and marginal (@sec-margin-lambda) effects.
Finally, we discuss the concept of suitable probability derived from the uncertainty around the population growth rate (@sec-suitableProbability).