Chapter 18 Forest dynamics model
This chapter provides an overview of a forest dynamics model, which builds on the previous models and allows simulating the recruitment, growth, mortality and management of woody plant cohorts in a forest stand. The model was described in De Cáceres et al. (2023) and is run using function fordyn() for a set of years.
18.1 Design principles
The design of the forest dynamics model is, to a large degree, inherited from the energy/water balance and growth models it builds on. Readers should refer to former sections to learn the design of the basic water balance (see 3.1), advanced water/energy balance (see 7.2) or growth/mortality processes (see 15.1). Regeneration, from either seed germination and establishment or via resprouting, and forest management are explicitly simulated at the level of fordyn() and hence their design will be the focus of this chapter, with implementation details described in chapter 19.
18.1.1 Recruitment from seeds
Recruitment of saplings involves a number of processes (flowering and pollination, fruit/seed production, dispersal, storage, seed predation, germination, seedling establishment and survival until the sapling stage). All these processes have their own biotic and abiotic drivers (Price et al. 2001), so that modelling becomes a challenging task. Processes leading to sapling recruitment are frequently extremely simplified or their mechanisms ignored in many forest models (Price et al. 2001). The design of the forest dynamics model with respect to recruitment follows that of many gap models. Local seed production is considered in a binary way, where plants are considered fertile and able to produce viable seeds if they reach a given height (different for shrubs and trees). Alternatively, the user can specify a set of species whose seeds arrive to the target stand via simulation control parameters or dispersal processes (see chapter 21). A seed bank exists in the forest stand, where seed levels are relative (up to 100%) and result from the interplay between seed rain and seed mortality. Germination is scheduled once a year (assumed to be in winter), and results in age cohorts entering a seedling bank. A constant probability of germination determines is used as a statistical surrogate of processes affecting germination success. Once successfully germinated, the germinant enters the most vulnerable life-stage of a tree, characterized by the highest mortality of the whole plant life-cycle. During the years between germination and recruitment the amount of seedlings decreases due to environmental filtering, depending on a set of regeneration thresholds. Typically, regeneration thresholds concern environmental conditions, although some models also consider ungulate browsing (Wehrli et al. 2007). In our case we focus on three environmental drivers limiting the transition from seedlings to saplings:
- Tolerance to low temperatures, indicated by the mean temperature of the coldest month.
- Drought tolerance, indicated by the annual moisture index or the daily water potential experienced by seedlings/saplings (Marañón et al. 2004; Lloret et al. 2009).
- Shade tolerance, indicated by the percentage of photosynthetic active radiation reaching the ground (Marañón et al. 2004).
While aging, seedling cohorts progressively increase their rooting depth, which influences their chances of survival in front of drought (Padilla & Pugnaire 2007). Aboveground growth is not explicitly modelled for cohorts in the seedling bank. When they reach a pre-specified age, seedling/saplings leave the seedling bank and recruitment as functional cohorts occurs. This entails ingrowth into a given diameter for trees, typically \(1\,cm\), or into a given height for shrubs. Maximum recruitment densities and plant size of recruited individuals are specified via species parameters. Importantly, trees recruited are subject to self-thinning processes before attaining the diameter of adult ingrowth (typically \(7.5\,cm\) diameter; see 17.4.1).
18.1.2 Resprouting
Resprouting is a common feature of Mediterranean species. Most, if not all, Mediterranean broadleaved species are able to resprout from buds protected in branches, subterranean structures (e.g. burl, taproot, lateral roots) or in the root collar after a disturbance destroys the aerial part. Yet, some differences in the resprouting ability (i.e. survival) exist regarding the type of disturbance and the species affected.
In medfate, resprouting is assumed happen from buds at the stump/stool level after a given disturbance has led to aboveground plant die-back. Resprouting can occur as a response to different disturbances. For example, resprouting occurs after clipping (e.g. if management is applied), after a fire, or after cavitation has led to dessication of above-ground plant organs.
Regarding disturbance type, differences in survivorship through resprouting mostly depends on the intensity of the disturbance experienced, with an increasing occurrence of mortality after disturbances in the following order: browsing, cutting, drought and fire (Espelta et al. 1999). Fire is the disturbance that causes greatest mortality, probably because it may physically destroy part of the bud bank due to lethal temperatures or directly charring it (Pausas et al. 2016). Moreover, resprouting vigor also depends on the size of the plant (Moreira et al. 2012). According to different literature sources, the number of resprouts initially produced is approximately 2 per 1 cm2 of stump area (Retana et al. 1992; García‐Jiménez et al. 2017). Hence, in medfate the final density of resprouts depends on the disturbance that caused resprouting (via survivorship) and on the diameter of the parent plant, but in all cases the resprouts inherit the root system of their parent.
Like saplings originated from seeds, resprouts are subject to self-thinning processes before attaining the diameter of ingrowth (see 17.4.1).
18.1.3 Forest management
Forest management is an optional process in fordyn() simulations. Furthermore, management actions need to be defined in an external function to be supplied by the user. This design was chosen because there are multiple potential management strategies, and different traditions are followed in different countries. To work properly within fordyn() simulations, the supplied management function needs to accept a forest object as input, as well as a list of management parameters, and it has to return the reduction in tree density, the reduction in shrub cover and the management parameters to be applied in subsequent calls.
Although the former design allows users to tailor management functions to their simulation needs, the package includes defaultManagementFunction() to facilitate the simulation of these process in many situations, and which is briefly described here. The function implements two different management models:
- Irregular management: An uneven-aged stand is managed using thinning operations each time a threshold value of a chosen stand-level metric (such as basal area or Hart-Becking index) is trespassed. Thinning operations can focus on trees of specific diameter classes.
- Regular management: An even-aged (monospecific) stand is managed in cycles where thinning (preparatory) cuts are followed by final (regeneration) cuts. Thinning operations are similar as those of irregular management. One or several final cuts can be scheduled, the first starting whenever mean diameter surpasses a chosen threshold, and the following after a chosen number of years. Optionally, tree planting (of a chosen species) can be scheduled to occur after the last final cut.
The former models apply cuts on tree cohorts irrespective of their species. The default management function applies shrub clearing each time there is an operation on trees, resulting in removal of any shrub cover above a given maximum value.
18.2 State variables
The main state variables of the forest dynamic model are those conforming the structure and composition of the forest stand, i.e. the set of woody cohorts (either trees or shrubs) and their attributes (height, density, DBH, cover, etc.). Additionally, the seed species identity and relative abundance in the seed bank are also state variables of the model. Since the model performs calls to the growth() model, many other state variables are defined for intra-annual simulations (see 15.4). When including forest management action, additional state variables may be defined as management parameters.
18.3 Process scheduling
The fordyn() model divides the period to be simulated in years, which is the top-level time step of simulations. Given an input forest object, the function first initializes the input for function growth(). For each year to be simulated the model the performs the following steps:
- Calls function
growth()to simulate daily water/carbon balance, growth and mortality processes (sub-daily processes may also be involved intranspirationMode = "Sperry"ortranspirationMode = "Sureau"). See section 15.4 for details of growth scheduling. - If a management function is supplied, calls this function and apply the resulting reductions in tree density and shrub cover.
- If required, simulates seed production, seed bank mortality, seed rain, recruitment from seeds and/or resprouting (see chapter 19). In a spatial context, seed rain will include seeds dispersed from other forest stands 21.
- Removes tree (or shrub) cohorts whose remaining density (resp. cover) is lower than a specified threshold.
- Merges surviving cohorts with recruitment in the
forestobject and prepares the input of functiongrowth()for the next annual time step. - Store current status of the
forestobject and update output tables/summaries.
18.4 Inputs and outputs
An important difference between fordyn() and the previous simulation functions is that it does not require a specific input object, as in spwb()or growth() functions. In other words, soil, vegetation, meteorology and control inputs are directly introduced as parameters to the function call to fordyn().
18.4.1 Soil, vegetation and meteorology
Soil
Soil input requirements are the same as for the former models and were fully described in section 2.3.
Vegetation
Unlike the former models, vegetation input for fordyn are objects of the class forest, which were described in section 2.4.4.
Metereological input
The minimum weather variables required to run the model are min/max temperatures (\(T_{min}\) and \(T_{max}\)), min/max relative humidity (\(RH_{min}\) and \(RH_{max}\)), precipitation (\(P\)) and solar radiation (\(Rad\)). Wind speed (\(u\)) is also needed, but the user may use missing values if not available (a default value will be used in this case). Wind speed is assumed to have been measured at a specific height above the canopy (by default at 2 m). Atmospheric \(CO_2\) concentration (\(C_{atm}\)) may also be specified, but if missing a default constant value is assumed, which is taken from the control parameters. Definitions and units of these variables were given in section 2.5.
18.4.2 Vegetation functional parameters
The forest dynamics model requires many functional parameters to be specified for plant cohorts. Some of them depend on whether the basic or advanced water balance is adopted, whereas others are inherited from the growth model. Here we report functional parameters needed in addition to those necessary for the growth model (see 15.5.2).
All of them concern the simulation of recruitment and are specified in the species parameter table (i.e. SpParams).
| Symbol | Units | R | Description |
|---|---|---|---|
| \(H_{seed}\) | \(cm\) | SeedProductionHeight |
Minimum height for seed production |
| \(SM\) | \(mg\) | SeedMass |
Seed dry mass |
| \(SL\) | \(yr\) | SeedLongevity |
Seedbank average longevity |
| \(Disp_{dist}\) | \(m\) | DispersalDistance |
Distance parameter for dispersal kernel |
| \(Disp_{shape}\) | DispersalShape |
Shape parameter for dispersal kernel | |
| \(P_{recr}\) | [0-1] | ProbRecr |
Probability of recruitment from seeds within the bioclimatic limits imposed by temperature, moisture and light thresholds |
| \(TCM_{recr}\) | \(^{\circ} \mathrm{C}\) | MinTempRecr |
Minimum average temperature (Celsius) of the coldest month for successful recruitment from seeds |
| \(MI_{recr}\) | MinMoistureRecr |
Minimum value of the moisture index (annual precipitation over annual PET) for successful recruitment from seeds | |
| \(FPAR_{recr}\) | % | MinFPARRecr |
Minimum percentage of PAR at the ground level for successful recruitment from seeds |
| \(N_{tree, recr}\) | \(ind \cdot ha^{-1}\) | RecrTreeDensity |
Density of tree recruits from seeds. |
| \(N_{tree, ingrowth}\) | \(ind \cdot ha^{-1}\) | IngrowthTreeDensity |
Density of trees reaching ingrowth DBH. |
| \(DBH_{tree,recr}\) | \(cm\) | RecrTreeDBH |
DBH for tree recruits from seeds or resprouting (e.g. 1 cm). |
| \(DBH_{tree,ingrowth}\) | \(cm\) | IngrowthTreeDBH |
Ingrowth DBH for trees (e.g. 7.5 cm). |
| \(H_{tree, recr}\) | \(cm\) | RecrTreeHeight |
Height for tree recruits from seeds or resprouting |
| \(Cover_{shrub, recr}\) | % | RecrShrubCover |
Recruitment cover for shrubs |
| \(H_{shrub, recr}\) | \(cm\) | RecrShrubHeight |
Recruitment height for shrubs |
| \(Resp_{fire}\) | RespFire |
Number of resprouts per stem after fire disturbance | |
| \(Resp_{dist}\) | RespDist |
Number of resprouts per stem after undefined disturbance (typically desiccation) | |
| \(Resp_{clip}\) | RespClip |
Number of resprouts per stem after clipping |
18.4.3 Control parameters
Control parameters modulate the overall behavior of fordyn simulations, which extend the parameters used for growth simulations (see section 15.5.3). First, there are parameters that regulate the application of seed production, seed bank dynamics, recruitment from seeds, resprouting and the removal of cohorts with few individuals:
applySeedBankDynamics [= TRUE]: Boolean flag to indicate that seed bank dynamics (seed production, seed bank mortality and seed rain) need to be simulated.applyRecruitment [= TRUE]: Boolean flag to indicate that recruitment from seeds is allowed.applyResprouting [= TRUE]: Boolean flag to indicate that resprouting is allowed.recruitmentMode [= "annual/stochastic"]: String describing how recruitment from seeds is applied. Current accepted values are “annual/deterministic”, “annual/stochastic”, “daily/deterministic” or “daily/stochastic”.removeEmptyCohorts [= FALSE]: Boolean flag to indicate the removal of cohorts whose density is too low.minimumTreeCohortDensity [= 1]: Threshold of tree density resulting in cohort removal.minimumShrubCohortCover [= 0.01]: Threshold of shrub cover resulting in cohort removal.dynamicallyMergeCohorts [= TRUE]: Boolean flag to indicate that cohorts should be merged when possible. This option speeds up calculations but results in a loss of cohort identity and reinitialization of many state variables.keepCohortsWithID [= TRUE]: Boolean flag to indicate that cohorts having a non-missing value in a columnObsID(if present) should not be merged or removed.
Next, a few parameters control the production/arrival of seeds:
seedRain [= NULL]: Vector of species names whose seed rain is to be added to seed bank, regardless of local seed production.seedProductionTreeHeight [= 300]: Default minimum tree height for producing seeds (when species parameterSeedProductionHeightis missing).seedProductionShrubHeight [= 30]: Default minimum shrub height for producing seeds (when species parameterSeedProductionHeightis missing).
Then we have default parameters determining whether recruitment occurs:
probRecr [= 0.05]: Default annual probability of germination (when species parameterProbRecris missing).minTempRecr [= 0]: Default threshold of minimum average temperature of the coldest month necessary for recruiting (when species parameterMinTempRecris missing).minMoistureRecr [= 0.3]: Default threshold of minimum moisture index (annual precipitation over annual ETP) necessary for recruiting (when species parameterMinMoistureRecris missing).minFPARRecr [= 10]: Default threshold of minimum fraction of PAR (in %) reaching the ground necessary for recruiting (when species parameterMinFPARRecris missing).
Finally, there are a set of parameters specifying default values for recruited cohort attributes:
recrTreeDBH [= 1]: Default DBH (cm) for recruited trees (when species parameterRecrTreeDBHis missing).recrTreeDensity [= 100]: Default maximum density (ind·ha-1) for recruited trees (when species parameterRecrTreeDensityis missing).recrTreeHeight [= 100]: Default height (cm) for recruited trees (when species parameterRecrTreeHeightis missing).recrShrubCover [= 1]: Default maximum cover (%) for recruited shrubs (when species parameterRecrShrubCoveris missing).recrShrubHeight [= 100]: Default height (cm) for recruited shrubs (when species parameterRecrShrubHeightis missing).
18.4.4 Model output
| Element | Description |
|---|---|
StandSummary |
A data frame with stand-level summaries (leaf area index, tree basal area, tree density, shrub cover, etc.) at the beginning of the simulation and after each simulated year. |
SpeciesSummary |
A data frame with species-level summaries (leaf area index, tree basal area, tree density, shrub cover, etc.) at the beginning of the simulation and after each simulated year. |
CohortSummary |
A data frame with cohort-level summaries (leaf area index, tree basal area, tree density, shrub cover, etc.) at the beginning of the simulation and after each simulated year. |
TreeTable |
A data frame with tree-cohort data (species, density, diameter, height, etc.) at the beginning of the simulation (if any) and after each simulated year. |
DeadTreeTable |
A data frame with dead tree-cohort data (species, density, diameter, height, etc.) at the beginning of the simulation and after each simulated year. |
CutTreeTable |
A data frame with cut tree-cohort data (species, density, diameter, height, etc.) per each simulated year. |
ShrubTable |
A data frame with shrub-cohort data (species, density, cover, height, etc.) at the beginning of the simulation and after each simulated year. |
DeadShrubTable |
A data frame with dead shrub-cohort data (species, density, cover, height, etc.) at the beginning of the simulation (if any) and after each simulated year. |
CutShrubTable |
A data frame with cut shrub-cohort data (species, density, cover, height, etc.) per each simulated year. |
ForestStructures |
A list with the forest object of the stand at the beginning of the simulation and after each simulated year. |
GrowthResults |
A list with the results of calling function growth (i.e., see 15.5.4) for each simulated year. |
ManagementArgs |
If management is considered, a list of management arguments to be used in another call to fordyn(). |
NextInputObject |
An object of class growthInput to be used in a subsequent simulation. |
NextForestObject |
An object of class forest to be used in a subsequent simulation. |