Evaluation of Species Invasiveness: A Case Study with Acacia dealbata Link. on the Slopes of Cabeça (Seia-Portugal)

: One of the main causes of biodiversity loss in the world is the uncontrolled expansion of invasive plants. According to the edaphoclimatic conditions of each region, plants acquire different invasion behaviors. Thus, to better understand the expansion of invasive plants with radial growth, it is proposed to use two equations, the Annual Linear Increment (ALI) and the Annual Invasiveness Rate (AIR). These equations are applied using spatiotemporal data obtained from the analysis of orthophotomaps referring populations of Acacia dealbata Link. in areas located in Serra da Estrela, Portugal. As a result, the area occupied by this species in the parish of Cabeça was evaluated and a 20-year projection was carried out. The data produced by these equations contributed to improving the knowledge about the invasion behavior of exotic species in a rigorous and detailed way according to local ecological conditions. This study may serve as the basis for the application of other similar situations concerning invasive species in other territories, to improve the efﬁciency of future projections for these species. Local technical and scientiﬁc knowledge will contribute to improving spatial and management planning, enabling a better adequacy and effectiveness of the control measures to be adopted.


Framework
The impact of invasive plants on ecosystems is a major cause of biodiversity loss in the world, especially in some large well identified hotspots [1][2][3][4]. Knowing its invasive potential is essential to create control strategies and prevent further invasions, mainly with the advent scenarios promoted by climate change [5]. In Portugal, according to Morais et al. [6], Acacia dealbata Link. is the species with the greatest invasive potential, mainly due to its high seed production capacity, which is associated with an effective germination rate above 70%, a rapid growth and allelopathic capacity [6][7][8]. According to the latest National Forest Inventory, from 1995 to 2015, the areas occupied by Acacia genus species increased by approximately 5.7 thousand hectares in the Portuguese territory, reaching 8.4 thousand hectares in 2015 [9][10][11].
This problem occurs in areas occupied with native forest species, more often within the habitats of the Natura 2000 Network (ecological network for the European Union's community space), such as the European dry heaths (code of habitat: 4030), pre-desert Mediterranean scrublands (code of habitat: 5330) and the Galician-Portuguese oak trees of Quercus robur and Quercus pyrenaica (code of habitat: 9230), among others [12], but also in recreation and leisure areas used by the population, such as urban parks or other public domain areas [13]. However, the most important economic impacts occur when acacia populations emerge alongside agricultural crops [14][15][16], impairing the germination and growth of important cultivated food species [10].
In this sense, invasion rate prediction, modeling and management of acacia-dominated ecosystems are challenging tasks that need further investigation and intervention [17,18]. Several studies present results on the prediction of the development of invasive species; however, the models available do not use a stain invasiveness rate, nor an annual linear increment [19][20][21]. Morphological, chorological and ecological characterization data for this species are well known, as are the most efficient control methods [22,23]. However, the annual invasiveness rates for A. dealbata are unknown in the largest majority of the Portuguese territory.
On the other hand, the economic valorization of A. dealbata wood and its ornamental value, associated with the exuberant yellow flowers that occur during winter, are factors that contributed to its dissemination [10,24]. In fact, A. dealbata, in the past, was promoted at a regional festival that took place in the Serra de Monchique, dedicated to silver wattle, which ended due to the persistent awareness of the botanist Malato Beliz [25,26]. However, in view of the high economic, social and environmental impacts of the rapid expansion of A. dealbata in Portugal, it is intended with this article to present the equations to calculate the Annual Linear Increment (ALI) and the Annual Invasiveness Rate (AIR) of invasive species with concentric dissemination; to evaluate, through the analysis of a case study, the expansion of A. dealbata on the slopes of Cabeça (Seia-Portugal); and to contribute to improving the knowledge on the invasive capacity of A. dealbata through more efficient planning of control actions.

Characteristics of Acacia Dealbata That Favor Invasion
A. dealbata is a tree of the Leguminosae family, originating from the south east of Australia and Tasmania, introduced in Europe (France, Spain, Italy, Turkey), South Africa, New Zealand, western USA (California), Asia (India, Sri Lanka), South America (Argentina, Chile) and Madagascar, where it presents an invasive behavior [23]. It was introduced in Portugal at the end of the 19th century and rapidly spread all over the mainland territory [27]. It is estimated that in 1975, A. dealbata occupied 2500 ha [11]. This tree can grow up to 15 m and its flowering occurs from January to March, presenting an exuberant yellow color. The pods are up to 8 cm in length and develop about 8 seeds with 4.5 × 2.5 mm [28].
Its invasiveness is associated with a high growth rate in poor and acidic soils due to its ability to fix atmospheric nitrogen through symbiosis with bacteria of the genus Rhizobium [29][30][31], in addition to factors such as the high production of attractive flowers for pollinators, self-pollinating capacity, vegetative reproduction and the production of a large amount of viable seeds for a long period of time [32][33][34]. The accumulation of seeds in the soil can reach more than 62,000 seeds per square meter in the territories of Serra da Estrela (Portugal) [35]. These seeds are often disseminated by ants, birds, water or simply by the force of gravity, and can remain in the soil for decades until they are disturbed, e.g., by fire [36]. In this context, the use of controlled fire can help to reduce the seed banks in the soil, promoting its germination [28,37]. As it is a species with a pioneer behavior, similar to Mediterranean heliophilous shrubs, whenever there is a clearing or an area without vegetation, it finds an opportunity to sprout and develop [38]. The factors that seem to be most unfavorable for its expansion are: neutral-basic soils (pH > 5.5), occurrence of frequent frosts (>21 to 40 days per year) and low annual precipitation (<500 mm) [39].

Characterization of the Area under Study
The area chosen for the present study covers the entire administrative territory of the parish of Cabeça, with approximately 850 hectares, located at Serra da Estrela (Portugal). This mountain range is the highest in mainland Portugal, with an altitude of 1997 m, presenting a unique flora with varied endemic species. In biogeographic terms, the selected location is part of the Montemuro and Estrela Mountain Sector [40]. This territory is characterized to as mesosubmediterranean humid to hyper-humid bioclimate, with an altitude between 400 and 700 m [41]. The substrates belong to schist-greywacke complex, dating back to the Pre-Cambrian Era, more than 400 million years old [42]. In pedological terms, the soils are characterized by lithosols and cambisols, with the presence of some superficial rocky outcrops [43]. The potential natural vegetation belongs to the domain of the oak (Quercus robur subsp. broteroana O. Schwartz), having as one of the most emblematic habitats the "Laurus nobilis bush scrubs", of the Azereirais subtype (European code of the natura 2000 network: 5230*pt2) [44,45]. These slopes sometimes have steep slopes, where there is an abandonment of agro-silvo-pastoral activities. Thus, there are surfaces covered by heliophilous scrub, especially Erica arborea L., E. australis L., Genista falcata Brot. and Cytisus striatus (Hill) Rothm., highly susceptible to the occurrence of fire. The last fire on these slopes occurred during the summer of 2005 [24].

Data Collection and Analysis
The identification of A. dealbata population was carried out on fieldtrips ( Figure 1). Spatiotemporal data were used to develop the equations to calculate the Annual Linear Increment (ALI) and the Annual Invasiveness Rate (AIR) of the populations of this species. To obtain spatial data, ortho-rectified aerial photographs of the territory were used, with very high-quality resolution, obtained through the SNIG platform (https://snig.dgterritorio.gov.pt, accessed on 25 May 2021). To obtain the invasiveness of A. dealbata, the time window chosen was from 2005 to 2019, avoiding fire events that could alter its natural growth [22,24]. For a better analysis of the acacia expansion, all the populations of A. dealbata growing in Cabeça were identified. For the data treatment and analysis, we used the software ArcGIS (version JSAPI 4.1).
For the calculation of ALI and AIR, we developed two arithmetic equations that allow us to obtain invasiveness rates when the growth of the population of the studied species appears to be of radial type. Based on this premise, the Annual Linear Increment (ALI) of a plant species is the result of the arithmetic mean of the growth increments of each sample. The coefficient of each sample is given by the ratio between the difference in the diameters (D f − D i ) and the double of the time difference (2 × (T f − T i )), to obtain the average growth of the sample. For the correct application of this equation, it is necessary that the diameter is measured in the direction of the slope orientation, especially in slopes with greater penchant, since the relief conditions can favor a greater expansion in the downstream direction (gravitational force, greater humidity of the soil, among other factors). To minimize the ecological constraints that can modify the dispersion of the trees, such as the presence of rocky outcrops or the existence of a water line, this equation was applied in fifteen different acacia populations to obtain an average value for the species growth in the chosen territory (Equation (1)). .
The Annual Invasiveness Rate (AIR) for a species is the result of the arithmetic average of the rates for each sample. The rate of each sample is given by the ratio between the difference in the occupancy areas (A f − A i ) and the product of the initial area by the . The value is obtained as a percentage of invasiveness (Equation (2)). For the calculation of ALI and AIR, we developed two arithmetic equations that allow us to obtain invasiveness rates when the growth of the population of the studied species appears to be of radial type. Based on this premise, the Annual Linear Increment (ALI) of a plant species is the result of the arithmetic mean of the growth increments of each sample. The coefficient of each sample is given by the ratio between the difference in the diameters (Df − Di) and the double of the time difference (2 × (Tf − Ti)), to obtain the average growth of the sample. For the correct application of this equation, it is necessary that the diameter is measured in the direction of the slope orientation, especially in slopes with greater penchant, since the relief conditions can favor a greater expansion in the downstream direction (gravitational force, greater humidity of the soil, among other factors). To minimize the ecological constraints that can modify the dispersion of the trees, such as the presence of rocky outcrops or the existence of a water line, this equation was applied in fifteen different acacia populations to obtain an average value for the species growth in the chosen territory (Equation (1)).
The Annual Invasiveness Rate (AIR) for a species is the result of the arithmetic average of the rates for each sample. The rate of each sample is given by the ratio between the difference in the occupancy areas (Af − Ai) and the product of the initial area by the time difference (Ai (Tf − Ti)). The value is obtained as a percentage of invasiveness (Equation (2)).

Results and Discussion
In the parish of Cabeça, 15 subpopulations of A. dealbata were identified, totaling 54,000 m 2 , corresponding in 2019 to about 0.6% of the chosen territory. However, in 2005, there were only 13 subpopulations occupying an area of around 24,000 m 2 . The population nuclei of A. dealbata studied in Serra da Estrela have seen over the past 14 years, an average linear increment of 9.86 m, corresponding to an annual linear increase of 0.82 m (Table 1). The A. dealbata invasion rate for the 14-year period was 94%, corresponding to an annual area increase of 8% (Table 2). Through the analysis, it was verified that the expansion of A. dealbata was very accelerated in relation to its initial occupation area, showing a factor that must be considered in the control actions of this species. In this sense, the economic resources for the control of A. dealbata expansion must follow the same dimension, which is why the control of acacia populations should be carried out preferably when plants are young.
The appearance of A. dealbata on the slopes of Cabeça seems to be positioned at an early stage, preferably close to the water lines. This position favors a more intense dispersion due to the edaphic compensation. However, the relic communities of Prunus lusitanica L., recognized through the Sectorial Plan of the Natura 2000 Network (Council Directive 92/43/EEC of 21 May 1992 on the conservation of natural habitats and of wild fauna and flora), as a priority habitat for conservation in Europe (arborescent communities of Laurus nobilis, of the Azereirais), have in these areas their best ecological position. In this sense, it is expected that this habitat, a priority for conservation at the European level, is one of the most affected by the invasion of A. dealbata. Thus, if the progression of the acacia populations remains the same as the past 14 years, it is expected that, according to the projections calculated, the A. dealbata populations located in Cabeça can increase in the next 20 years by about 16.43 linear meters surrounding the existing areas. If there are no human-driven actions, especially fires, the expansion of acacias is expected to continue. A significant increase in the acacia area from 2019 to 2039 is projected, from about 54,000 m 2 to 433,000 m 2 , which corresponds to an Invasiveness Rate of 807% (Table 3).  The use of orthophotomaps for spatiotemporal analysis was found to be adequate for the calculation of ALI and AIR for the population of A. dealbata in Serra da Estrela. To calculate the linear increment, the mean of the rays between the highest and the lowest elevation was considered. However, the ease of calculation used in the present study allows its easy replication for the study in other areas invaded by exotic plants.
Several studies on invasive plants calculated the advance of their areas over time [46][47][48][49]. However, the majority used data obtained in the National Forest Inventory to calculate the invasiveness rate in relation to the studied territory and not to the species population. Some examples can be found in the studies presented by Hernández et al. [50], which has growth rates of 0.1% within the studied area of northwestern Spain, while others, such as Higgins et al. [51] use empirical data. Therefore, the present study has the advantage of using real data for specific populations. The progression of the species depends on the edaphoclimatic conditions of each location, and in that sense, the invasiveness rates must be calculated at least at the level of the biogeographical district, especially in the Mediterranean area, where these mesological conditions vary within a few kilometers [52,53].
Although other studies propose the calculation of the risk of invasion, answering a set of questions [6,54], the linear advance of invasive plant populations is in fact crucial to calculate the time traveled to cover a specific area or to some physical limit, as is a property or a water line. However, the expansion of acacia populations seems to be favored by the proximity to water lines, as has been identified in other studies [21,55]. This capacity for growth and space occupation is clearly visible in the present (Figure 2). Since 2005, A. dealbata has been progressing mainly following the water lines' margins. This rapid occupation of the water lines is most likely related to the fact that theseeds are dragged by rainwater and because these areas are more humid, enhancing their development.
Thus, it is necessary to control the invasions of A. dealbata and other invasive species, such as Eucalyptus globulus in Serra da Estrela, which, in addition to releasing allelopathic substances inhibiting the growth of autochthonous flora, has high calorific power that increases the risk of spreading fire [56]. Since this is a species with a pioneering and heliophilous behavior, it is necessary to promote forest environments with autochthonous species, thus reducing the ecological conditions necessary for the germination of A. dealbata. However, for this, there must be a stimulus, so that rural areas do not continue to be depopulated. calculate the time traveled to cover a specific area or to some physical limit, as is a property or a water line. However, the expansion of acacia populations seems to be favored by the proximity to water lines, as has been identified in other studies [21,55]. This capacity for growth and space occupation is clearly visible in the present (Figure 2). Since 2005, A. dealbata has been progressing mainly following the water lines' margins. This rapid occupation of the water lines is most likely related to the fact that theseeds are dragged by rainwater and because these areas are more humid, enhancing their development. Thus, it is necessary to control the invasions of A. dealbata and other invasive species, such as Eucalyptus globulus in Serra da Estrela, which, in addition to releasing allelopathic substances inhibiting the growth of autochthonous flora, has high calorific power that increases the risk of spreading fire [56]. Since this is a species with a pioneering and heliophilous behavior, it is necessary to promote forest environments with autochthonous species, thus reducing the ecological conditions necessary for the germination of A. dealbata. However, for this, there must be a stimulus, so that rural areas do not continue to be depopulated.

Conclusions
The development of the Annual Linear Increment (ALI) formulas and the Annual Invasiveness Rate (AIR) were validated by calculating the growth impact of A. dealbata population on the slopes of Serra da Estrela, Portugal. Their implementation benefits from homogeneous conditions from an ecological point of view, as the passage of a water plane or the presence of large rock outcrops can alter the growth behaviour of the species. Thus, we believethat these formulas will be very useful to quickly calculate the expansion of

Conclusions
The development of the Annual Linear Increment (ALI) formulas and the Annual Invasiveness Rate (AIR) were validated by calculating the growth impact of A. dealbata population on the slopes of Serra da Estrela, Portugal. Their implementation benefits from homogeneous conditions from an ecological point of view, as the passage of a water plane or the presence of large rock outcrops can alter the growth behaviour of the species. Thus, we believethat these formulas will be very useful to quickly calculate the expansion of invasive species in other territories. In fact, the prediction of invasion through future scenarios allows the adoption of more effective measures and control strategies, aiding in preventive measures rather than reaction. Thus, actions to control exotic species should preferably be carried out from upstream to downstream, decreasing the possibility of reseeding the intervention areas. It is concluded that the control of A. dealbata should be carried out as early as possible, since the control of this species becomes significantly more difficult over time, due to the high volume of seeds generated annually.