text edits

_quarto.yml

@@ -3,7 +3,7 @@ project:
 
 book:
   title: "Lab notebook"
-  subtitle: "The effect of competition and climate on the dynamics of North American forest trees: from individuals to population"
+  subtitle: "The role of climate and competition on tree range distribution: a multi-scale approach from individuals to metapopulation dynamics"
   author:
     - name: Willian Vieira
       orcid: 0000-0003-0283-4570

conditional_lambda.qmd

@@ -1,14 +1,14 @@
 # Conditional effect of covariates {#sec-cond-lambda}
 
-In this chapter, we assessed the conditional effects of each covariate on the population growth rate ($\lambda$) for each individual species.
+In this chapter, we assessed the conditional effects of each covariate on the population growth rate ($\lambda$) for each species.
 Specifically, we quantified how $\lambda$ varies with changes in competition intensity for both conspecific and heterospecific individuals.
 Furthermore, we examined how $\lambda$ changes in response to variations in mean annual temperature and mean annual precipitation, spanning the range from the minimum to maximum observed values in the dataset.
-This analysis is similar with the sensitivity analysis discussed in @sec-sensAnalysis.
-However, due to the larger number of conditions for each covariate, we performed this analysis with a reduced number of replicates, using only 50 replicates from the posterior distribution of the parameters.
+This analysis is similar to the sensitivity analysis discussed in @sec-sensAnalysis.
+However, due to the larger number of conditions for each covariate, we performed this analysis using only 50 replicates from the posterior distribution of the parameters.
 
 For the competition effect analysis, we maintained temperature and precipitation at the optimal conditions defined by the average of the optimal climate conditions among the growth, survival, and recruitment models.
 When assessing the effect of conspecific competition, heterospecific competition was set to null.
-Conversely, when evaluating the effect of heterospecific competition, conspecific competition was defined to a small population size of $N = 0.1$.
+Conversely, when evaluating the effect of heterospecific competition, the conspecific competition was defined as a small population size of $N = 0.1$.
 
 We evaluated the climate effect under two competition conditions: low competition, where conspecific population size was set to $N = 0.1$, and high conspecific competition, where population size was established at the 99th percentile distribution of plot basal area experienced by the species in the dataset.
 When analyzing temperature, precipitation was held at its optimal condition, and vice versa.
@@ -83,7 +83,7 @@ unscaleClim <- function(
 #| label: fig-lambdaComp
 #| fig-width: 8
 #| fig-height: 4.5
-#| fig-cap: "The Average and 90% confidence intervals values for the population growth rate ($\\lambda$) as a function of conspecific (left panel) and heterospecific (right panel) competition intensity."
+#| fig-cap: "The Average and 90% confidence interval values for the population growth rate ($\\lambda$) as a function of conspecific (left panel) and heterospecific (right panel) competition intensity."
 
 lambdas |>
   filter(sim == 'competition') |>
@@ -179,7 +179,7 @@ clim_dt
 #| label: fig-lambdaTempplot
 #| fig-width: 8
 #| fig-height: 4.5
-#| fig-cap: "The Average and 90% confidence intervals values for the population growth rate ($\\lambda$) as a function of mean annual temperature for low (left panel) and high (right panel) competition intensity."
+#| fig-cap: "The Average and 90% confidence interval values for the population growth rate ($\\lambda$) as a function of mean annual temperature for low (left panel) and high (right panel) competition intensity."
 
 clim_dt |>
   filter(var == 'Temperature') |>
@@ -220,7 +220,7 @@ girafe(
 #| label: fig-lambdaPrec
 #| fig-width: 8
 #| fig-height: 4.5
-#| fig-cap: "The Average and 90% confidence intervals values for the population growth rate ($\\lambda$) as a function of mean annual precipitation for low (left panel) and high (right panel) competition intensity."
+#| fig-cap: "The Average and 90% confidence interval values for the population growth rate ($\\lambda$) as a function of mean annual precipitation for low (left panel) and high (right panel) competition intensity."
 
 clim_dt |>
   filter(var == 'Precipitation') |>

covariates_description.qmd

@@ -12,37 +12,37 @@ library(ggpubr)
 library(MetBrewer)
 ```
 
-In this study, our main objective is to assess how climate and competition affect the demographic rates of tree species, and hence shape their range distribution.
-Climate, typically characterized by temperature and precipitation, is widely assumed as an important factor affecting vital rates and has been the focus of recent studies for tree species [@Csergo2017; @lesquin2021; @Kunstler2021; @Guyennon2023].
-Climate also exerts an indirect influence by shaping species composition, which in turn, impacts the variation in demographic rates through species interactions.
-indeed, competition for light has been shown as a principal driver in the demographic rates of forest trees [@Zhang2015; @lesquin2021].
-
-There are additional factors that influence the growth, survival, and recruitment of forest trees beyond the climate-competition dimensions.
-For instance, events like wildfire and insect outbreaks play crucial roles in changing demographic rates, particularly considering that these disturbances are sensitivite to climate change [@seidl2011].
-However, it's important to note that such disturbances are sporadic events, and our primary focus is on understanding responses to average conditions.
+In this study, our main objective is to assess how climate and competition affect the demographic rates of tree species and, hence, shape their range distribution.
+Climate, typically characterized by temperature and precipitation, is widely assumed to be an essential factor affecting vital rates and has been the focus of recent studies for tree species [@Csergo2017; @lesquin2021; @Kunstler2021; @Guyennon2023].
+Climate also exerts an indirect influence by shaping species composition, which impacts the variation in demographic rates through species interactions.
+Indeed, competition for light has been shown as a principal driver in the demographic rates of forest trees [@Zhang2015; @lesquin2021].
+
+Additional factors influence forest tree growth, survival, and recruitment beyond the climate-competition dimensions.
+For instance, events like wildfire and insect outbreaks play crucial roles in changing demographic rates, particularly considering these disturbances are sensitive to climate change [@seidl2011].
+However, it is important to note that such disturbances are sporadic, and our primary focus is understanding responses to average conditions.
 At the local scale, soil nitrogen can improve growth rate [@Ibanez2018] and facilitation can improve performance at range limits [@Ettinger2017].
 At a local scale, soil nitrogen content can enhance growth rates [@Ibanez2018], and facilitation can increase recruitment rates at range limits [@Ettinger2017].
-All these factors and other not cited here have the potential to affect the demographic rates of forest trees.
-However, our objective here is not to have the best and most complex model to achive the highest predicitive metric, but to do inference [@Tredennick2021].
+All these factors and others not cited here can potentially affect the demographic rates of forest trees.
+However, our objective here is not to have the best and most complex model to achieve the highest predictive metric but to make inferences [@Tredennick2021].
 Specifically, we aim to test the relative effect of climate and competition while controlling for other influential factors.
-Therefore, our modeling approach is guided by biological mechanisms, which tend to provide more robust extrapolation [@Briscoe2019], rather than being solely dictated by specific statistical metrics.
+Therefore, our modeling approach is guided by biological mechanisms, which tend to provide more robust extrapolation [@Briscoe2019] rather than being solely dictated by specific statistical metrics.
 
 In the following sections, we describe the inclusion of covariates into each demographic model.
 We start by incrementing the intercept growth, survival, and recruitment models, as described in the previous section, with plot random effects to account for the spatial heterogeneity among plots.
-Then, building on the intercept model with plot random effects, we introduce the competition for light component using individual basal area information.
-Finally, we complete the model by incorporating the climate component, wherein we include the effects of mean annual temperature (MAT) and mean annual precipitation (MAP).
+Then, building on the intercept model with plot random effects, we introduce the competition for light components using individual basal area information.
+Finally, we complete the model by incorporating the climate component, including the effects of mean annual temperature (MAT) and mean annual precipitation (MAP).
 
-It's worth noting that, due to the use of structured population models, the demographic models should vary as a function of the size trait.
+It is worth noting that, due to the use of structured population models, the demographic models should vary as a function of the size trait.
 The von Bertalanffy growth model implicitly incorporates the size effect within the model.
-For survival, we initially included individual size as a covariate, following a lognormal distribution to capture the potential higher mortality rates for small individuals (due to competition) and very large individuals (due to senescence).
-However, all models incorporating the size covariate performed worse compared to the baseline model (we discuss the details in @sec-model_comparison).
+For survival, we initially included individual size as a covariate, following a lognormal distribution to capture the potential higher mortality rates for small individuals (due to competition) and large individuals (due to senescence).
+However, all models incorporating the size covariate performed worse than the baseline model (we discuss the details in @sec-model_comparison).
 Therefore, we chose not to include the size covariate in the survival model.
-Additionally, due to the unavailability of data for the regeneration process, we used an ingrowth rate model that is independent of size.
+Additionally, due to the unavailability of data for the regeneration process, we used an ingrowth rate model independent of size.
 Consequently, only the growth model varies as a function of individual size.
 
 ## Plot random effects
 
-We account for the shared variance among individuals within the same plot in each demographic model using random effects.
+We use random effects to account for the shared variance among individuals within the same plot in each demographic model.
 In the context of each species-demographic model combination, we draw plot random effects ($\alpha_j$) from a normal distribution with a mean of zero, defined as:
 
 $$
@@ -61,7 +61,7 @@ Where $I$ can assume one of three forms: $\Gamma$ for the growth, $\psi$ for the
 
 ## Size effect
 
-For the growth model, the size effect is implicit incorporated in the model.
+For the growth model, the size effect is implicitly incorporated in the model.
 Specifically, following the von Bertalanffy model's definition, an individual's growth rate decreases exponentially with size, eventually reaching a zero growth rate as size approaches $\zeta_{\infty}$ (@fig-sizeEffect).
 
 ```{r,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
@@ -148,19 +148,19 @@ $$
 $$
 
 
-Here, $\upsilon$ determines the size at which survival is at its optimal and $\sigma_{\upsilon}$ quantifies the extent of survival decrease from the optimal size.
+Here, $\upsilon$ determines the size at which survival is optimal, and $\sigma_{\upsilon}$ quantifies the extent of survival decrease from the optimal size.
 A higher parameter value corresponds to a reduced effect of size on the survival probability (@fig-sizeEffect).
 
 ## Competition effect
 
 We use the basal area of larger individuals (BAL) as a metric for competition.
-Basal area is calculated as the sum of the cross-sectional areas of all trees within a plot, derived from their diameter at breast height (dbh) measurements, and its unit is square meters per hectare.
-For each focal individual, we calculate the competition intensity by summing the basal area of all individuals with a size greater than that of the focal individual. 
+We calculated basal area as the sum of the cross-sectional areas of all trees within a plot, derived from their diameter at breast height (dbh) measurements, and its unit is square meters per hectare.
+We calculate the competition intensity for each focal individual by summing the basal area of all individuals with a size greater than that of the focal individual. 
 We differentiate this sum of basal area between conspecific and heterospecific individuals.
 More details can be found in the @sec-dataset.
 
 Both the growth ($\Gamma$) and longevity ($\psi$) intercept parameters decrease exponentially with BAL.
-This negative effect of BAL on growth and longevity is driven by two parameters that describe the effect of conspecific ($\beta$) and heterospecfic ($\theta$) competition:
+This negative effect of BAL on growth and longevity is driven by two parameters that describe the effect of conspecific ($\beta$) and heterospecific ($\theta$) competition:
 
 $$
   \Gamma + \beta_{\Gamma} \times (BAL_{cons} + \theta_{\Gamma} \times BAL_{het})
@@ -171,8 +171,8 @@ $$
 $$
 
 When $\theta < 1$, it means that conspecific competition is stronger than heterospecific competition.
-Conversely, when $\theta > 1$, heterospecific competition prevails, and when $\theta = 1$, there is no distinction between conspecific and heterospecific competition (@fig-CovCompEffectGrowthMort).
-Note that both $\beta$ and $\theta$ are unbounded parameters that can either converge towards negative values (indicating competition) or positive values (indivating facilitation).
+Conversely, heterospecific competition prevails when $\theta > 1$, and when $\theta = 1$, there is no distinction between conspecific and heterospecific competition (@fig-CovCompEffectGrowthMort).
+Note that both $\beta$ and $\theta$ are unbounded parameters that either converge towards negative (indicating competition) or positive (indicating facilitation) values.
 
 ```{r,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
 #| label: fig-CovCompEffectGrowthMort
@@ -221,21 +221,21 @@ tibble(
 ```
 
 For the recruitment model, conspecific and heterospecific BAL affect different components of the model.
-Conspecific BAL, or simply the total conspecific plot basal area (as recruitment is necessarily smaller than any adult individual), has a unimodal effect on the annual ingrowth rate ($\phi$).
+Conspecific BAL, or the total conspecific plot basal area (as recruitment is necessarily smaller than any adult individual), has an unimodal effect on the annual ingrowth rate ($\phi$).
 This effect is characterized by an optimal basal area for ingrowth at $\delta^{\phi}$ and an increased effect controlled by the parameter $\sigma^{\phi}$:
 
 $$
   \phi - \left(\frac{BAL_{cons} - \delta_{\phi}}{\sigma_{\phi}}\right)^2
 $$
 
-The underlying concept of this equation is that ingrowth rate should increase with conspecific density, but only up to a certain point determined by $\delta^{\phi}$.
-At higher densities, ingrowth rate is expected to decrease due to competition (@fig-CovCompEffectRec).
+The underlying concept of this equation is that the ingrowth rate should increase with conspecific density, but only up to a certain point determined by $\delta^{\phi}$.
+The ingrowth rate is expected to decrease at higher densities due to competition (@fig-CovCompEffectRec).
 
 ```{r,echo=Echo,eval=Eval,cache=Cache,warning=Warng,message=Msg}
 #| label: fig-CovCompEffectRec
 #| fig-width: 8.5
 #| fig-height: 4.5
-#| fig-cap: "Illustration of the impact of conspecific basal area on the ingrowth rate and the impact of total basal area on the survival rate of recruited individuals."
+#| fig-cap: "Illustration of the impact of the conspecific basal area on the ingrowth rate and the impact of the total basal area on the survival rate of recruited individuals."
 
 tibble(
     opt_BA = c(5, 40, 40),
@@ -317,8 +317,8 @@ $$
 
 ## Climate effect
 
-As our focus is on inference rather than prediction, we chose to not conduct model selection concerning the climate variables.
-Instead, we opted for the mean annual temperature (MAT) and mean annual precipitation (MAP) as our chosen bioclimatic variables, which are widely used for species distribution modeling.
+As we focus on inference rather than prediction, we chose not to conduct model selection concerning the climate variables.
+Instead, we opted for the mean annual temperature (MAT) and mean annual precipitation (MAP) as our chosen bioclimatic variables widely used for species distribution modeling.
 Each demographic function varies in function of a bell-shaped curve determined by an optimal climate condition ($\xi$) and a climate breadth parameter ($\sigma$) as follows:
 
 $$
@@ -334,7 +334,7 @@ $$
 $$
 
 The climate breadth parameter ($\sigma$) influences the strength of the specific climate variable's effect on each demographic model (@fig-CovClim).
-This unimodal function is flexible as it can assume various shapes to better accommodate the data.
+This unimodal function is flexible as it can assume various shapes to accommodate the data better.
 However, this flexibility also introduces the possibility of parameter degeneracy or redundancy, where different combinations of parameter values yield similar outcomes.
 To mitigate parameter degeneracy, we constrained the optimal climate condition parameter ($\xi$) within the observed climate range for the species, thereby assuming that the optimal climate condition falls within our data range.