The results suggest that the set of models are logical, and may provide reasonable estimates of post-fire mortality over long-term planning horizons. The logistic modeling approach used in this study has been used earlier for predicting tree-mortality as a consequence of regular mortality (mortality due to competition between trees) and irregular mortality, i.e., mortality due to wind damage [61
], prescribed fire [63
] and wildfire [17
]. In addition, the modeling approach using different steps has been used to model natural tree mortality [55
]. Here we use the Portuguese Forest Inventory and Project ForFireS dataset to parameterize, for a total of 16 common Portuguese tree species, a logistic regression model that assigns post-fire mortality.
Post-fire mortality has been studied using a variety of direct and indirect methods (e.g., [12
]). In the literature we can find two main types of models, the ones based on variables reflecting fire injury indicators and those based on biometric information. Here, while the proposed approach employs some concepts that featured in earlier work (e.g., [17
]) on the whole, the selected post-fire mortality models tend to differ significantly from other well-known classic approaches for fire-induced mortality (e.g., [34
]). However, the use of the latter methods in long-term forest management planning is constrained by the difficulty to predict accurately the fire injury/severity variables they use (e.g., crown-kill, bole-kill or fire intensity are information rarely available to forest beforehand).
As stressed above, the set of three models does not use fire-related variables, but information on species composition and forest structure. In this sense, the models provide: (i) a quantitative framework to address long-term planning periods; (ii) insight into different behavior or post-fire mortality between pure and mixed stands, helping to understand the performance of any forest structure; and (iii) information for making pre-fire management decisions over a wide range of tree sizes and species and in a variety of stand conditions in Portugal, which has been lacking in previous discussions.
4.1. Forest Composition, Heterogeneity and Structure
The models show that forest cover composition has an impact on the proportion of dead trees after a wildfire. The post-fire mortality models developed indicate that the conifers are the most prone to suffer mortality after wildfire, whereas the broadleaves are more resistant to fire (Figure 5
). This confirms the generally low fire susceptibility observed in most broadleaved trees compared with other forest types, probably explained by differences in fuel load composition, moisture content, flammability, and broadleaves resprouting ability (e.g., [3
]). Previous studies argued that the conifers have higher flammability because their contents in resins and oils [32
]. Other authors attribute the difference between broadleaves and conifers to the fact that the forest management regimens applied to both of the forest tree types is different, being broadleaves more resistant to the fire occurrence (e.g., [36
]). For instance, in Portugal, eucalyptus and maritime pine stands are usually industrial plantations with high stand densities, and highly prone to fire [22
]. In fact, commercial eucalypt plantations are very flammable due to the nature and accumulation of their litter and bark fuels with high levels of biomass, and thus prone to intense wildfires [20
]. In the case of mixed eucalyptus and pine stands, fire hazard may be even higher, when compared with pure stands of eucalyptus or pines [72
]. On the other hand, many of the oak stands (i.e., Q. Suber
and Q. rotundifolia
) are classified as “montado”, which is an agroforestry management regime, with low tree stocking, which reduces considerably the fire occurrence and propagation [4
] (proportion of dead trees, Table 7
). One explanation may be the high resprouting capability of some Mediterranean Quercus species such as Q. rotundifolia
, Q. suber
and Q. coccifera
], which can lead to Quercus dominated forest in places with high fire recurrence. Thus, understanding the relationships between composition of the forest cover and burn severity is important for developing management guidelines leading to fire-resilient forests.
Forest heterogeneity (mixed stands) was shown to be associated with low proportion of dead trees in the stand (Figure 4
). This is in accordance with results from [10
] who explored the relationship between forest heterogeneity and burn severity at the stand-level concluding that pure conifer stands present more severe fires than mixed stands. Thus, forest managers may consider enhancing the heterogeneity of forests when implementing fuel treatment schemes giving more importance to mixed stands. In fact, higher mortality is expected in coniferous stands rather than in broadleaved species, because most species from the former group are not able to resprout when the entire canopy is burned [34
In general, biometric variables that impacted post-fire mortality included tree diameter (dbh
of the tree, average dbh
of the stand and variability of tree diameters Sd
), and indicators of density such as basal area (G) and competition index (dbh
). The coefficients of biometric variables regarding stand structure are in concordance with findings from international studies (e.g., [17
]) and studies focused on Portuguese conditions [18
]. The stand-level model indicates that even-aged stands with higher tree diameters have lower probabilities of mortality after a fire than irregular stands with smaller-sized trees (model PsDead
). These small and dominated trees will be more exposed to a given intensity fire than larger trees, especially for low to moderate severity fires [21
Further, eucalyptus stands with a reduced variability of tree diameters (Sd
) results in lower probability of mortality than conifers stands (Figure 3
). Mortality in stands with higher densities is expected to be higher (PdMort
). These results agree with findings of [22
] who stated that the level of injury and mortality for a given species is a combined outcome of fire behavior, tree size and stand structure. Extensive model testing led to the rejection of other biometric variables as predictors of stand-level damage after a wildfire.
Regarding the individual tree mortality PdTree
the coefficients of biometric variables also confirmed the findings of previous studies. For tree-level mortality prediction of forest species in Portugal, best-fitting model PdTree1
indicates that stand basal area (G) and dbh
traits affected the mortality rate (basal area (G) was negatively related with tree mortality). This is in concordance with other studies [17
]. In addition, size (dbh)
has a greatest effect on mortality rate at the level of the individual tree, with larger trees size exhibiting mortality rates much lower than smaller trees, consistent with a decrease in mortality reported by several studies [18
]. These two variables are related, so for a fixed value of basal area (G) if the stand density increases, it means that average tree diameters are smaller. This means that fire would more likely be more intense and more trees are likely to die. Indeed, fire intensity varies and this could result in different probability curves depending on species and intensity [70
The results suggest that both slope and stand location (i.e., altitude) also impact mortality. In the stand-level model (PdMort
), steeper slopes increase the probability of death to occur in a stand and also the expected damage (Figure 4
). This is in concordance with other studies developed in Portugal [2
]. This effect may be explained as slope increases fire spread rate and consequently increases fire intensity [77
]. Additionally, altitude has a significant impact on fire behavior possibly due difference in fuel moisture present in a given stand, and weather conditions, in particular, with temperature and precipitation and the compounding effects of fuels [78
]. In our case, altitude correlates positively with the degree of mortality in burned areas. Thus, forest managers may want to consider avoiding severe topographic conditions (e.g., steeper slopes when planning new plantations), in order to increase resilience to fire and management of wildfire damage.
Validation of the models was done through studies of the performance of the functions. No specific validation datasets were set-aside and later used for that purpose. Two main reasons justify this decision. Firstly, the relatively small number of observations in the stand dataset used. Secondly, we were more interested in obtaining the best possible parameter estimates. There are advantages and disadvantages of splitting the dataset for model validation purposes as discussed by [60
]. However, they concluded that cross validation by data splitting and double cross validation may provide little, if any, additional information in the process of evaluating regression models.
4.2. Pre and Post-Fire Smart Management: Applicability
This research estimated a set of three models to predict mortality that present a real step forward for managing mixed stands under fire risk conditions, and identifying management options that reduce the expected losses due to fire. This may be critical to design prescriptions that may reduce ecological and economic wildfire damage through adequate planning, as a management objective in numerical planning calculations or easy integration of post-fire mortality in forest simulators and optimization systems, particularly in ecosystems where wildfires are a recurrent disturbance. It is useful to interpret the current study in the broader context of fuel management, whereas stand management strategies are widely accepted as effective means to establish less flammable and more resilient forests and landscapes in recently burned area.
In the framework of forest management planning, the stand-level models PsDead and PdMort are useful for planning when the growth and yield model used does not provide the dimensions of each of the trees. First, model PsDead may be used to predict whether mortality may occur in a stand after a wildfire (i.e., there is at least one dead tree in the stand). If the stand presents mortality, model PdMort gives the proportion of dead trees in the stand (i.e., the total number of trees that will die is provided). For this reason no threshold value is needed to convert the estimated probability into a dichotomous variable (e.g., death or survival). Because PdMort cannot be used for a specific tree, the model PdTree to predict the probability of a tree to die should be applied. Thus, the selected model at tree-level PdTree may be used to predict the probability of mortality of each tree in the stand and to build a list of all trees in the stand ordered according to this probability (which means that the trees should simply be sorted from higher to smaller mortality probability, trees with higher probability are ranked first in the list). The management planning model may then select the trees that will be assumed to die for planning purposes by going down the list and stopping when the number of trees that are estimated to die by model PdMort is reached.
Another way to use these set of models in forest management scheduling and scenarios analyses is in the framework of a full risk profile, especially when first generate fire occurrence with an earlier model for pure and mixed forest stands [44
], after which the degree of damage can be predicted with the second model PdMort
. Thus, the quality of the models is dependent on the quality of the equations used for that purpose. In a management planning context, the PdTree
post-fire mortality model is very important when the growth and yield simulation uses an individual tree model (which means that every tree may have different characteristics).