On Land Use and Biodiversity Resilience: Hydrology, Temperature Regulation and the Fractal Nature of the Woodland-Grassland Interface

    

    

    Figure 6: Symbolic representation of the fractal notion of the Woodland-Grassland Interface. The borderline (symbolized by grey-white line) that at each increasing magnification shows a further splintering of minuscule, fimbriated details, in reality is a fractal system that also turns the 2-dimensional area surface into a virtual 3D volumetric system. Obviously, this demarcation not exhaustively corresponds to the geometrical border between the forest trees and the surrounding environment, but reflects all life forms that inhabit at both sides of the border (represented by shades of either green or pink). Therefore, the Woodpecker (Figure 7A) making holes high up in the Oak tree and foraging for caterpillars, bees and other insects in the grassland below, as well as the Roe Deer finding shelter in the forest and coming out at dusk for eating the green herbs, all constitute the complex interconnected web called the ecosystem’s biodiversity. The next question, how the biodiversity of the system changes with flattening or smoothing the border line, not only is interesting from an ecological viewpoint. It also forms an interesting heuristic for defining the entropy change of the ecosystem in relation to biodiversity changes (see also main text, Allaerts [in prep.] and 6).
    

It is well known (among naturalists and hunters) that wild grazing mammals, like deer (Cervidae) mostly stay in the forest during the day, but, during the early morning and twilight hours, they leave the forest to find richer food in grasslands or pastures surrounding their shelter. Moreover, the larger Red deer (Cervus elaphus) withdraw deeper into the woods than the smaller Roe deer (Capreolus capreolus) (Figure 4, b-c), and this correlation between body size and daily movements is seen in many animal groups, including birds. Withdrawing deeper into the wood also means evading disclosure by predators, or human disturbance of the environment. According to the hypothesis of Janis and Carrano (1992) [36], called the JC hypothesis, there is a negative correlation between body size and litter size in terrestrial mammals, which however didn’t seem to exist in distinct archosaurs and also not in contemporary non-passerine birds [36,37]. As a result, large mammals on the average show little reproductive success (with some exceptions like the big herd-forming Red deer, C. elaphus, at least in certain environments). For, when a species has few, respectively many enemies or predators, a correspondingly small/large number of offspring is needed to improve their survival potential. On the other hand, species with large offspring and few predators, like in some exotic animals (but also in plants and in the Dutch populations of Red deer), therefore, may become a plague to the ecosystem.

The fractal nature of (ecological) biodiversity thus is related to the survival probability or the rate of reproductive success. If a number of generations of a species fail to procreate new offspring, or the population becomes too small, local extinction may become the outcome (if no new individuals are immigrating from surrounding territories) [7]. The resulting local biodiversity appears to display characteristics of a dynamic multidimensional network of interacting ‘trees’ (= the survival path, from conception to successful reproduction of a species at a local number of habitats), similar to the ‘Hyper-objects’ suggested by Timothy Morton (2013) [38].

When it comes to defining the fractal nature of a system, two questions seem of primary importance, namely (a): What is the self-similarity dimension?; and (b): What is the critical dimensionality, defined as the percolation probability or the critical probability below which a network disintegrates? [6,35]. The problem in earlier studies, however, appears to be the attempt to characterize a mean-field approximation of biodiversity [6], similar to the areal approach of defining an area by a number of characteristics (like water consumption, crop yield, number of grazers, etc.).

In the fractal approach of the woodland-grassland interface, a possible representation of the local interference with the (local) biodiversity may be represented as a ‘flattening’ or smoothing of the fractal interface, analogous to the flattening of the coast line of the British isles in the seminal work of B.B. Mandelbrot [35] (Figure 6). A simplified representation in the two-dimensional plane, follows from

L (e) = F e 1 – D (see Allaerts, 2020) [6]

with F, the number of fragments of a chosen length e and D the fractal dimension [6]. The total length L (e) is the add up or the total of line segments. When replacing length by a biologically relevant, derived parameter r (N), that occurs N times in a given environment, the following relation results:

log r (N) = log 1/ N ^1-D= - (log N)/D (Mandelbrot, 1983) [35].

Or, when a positive measure (like the mass density) can be defined, within the ball B with radius r centered at x, for all x ∈ E, E being a regular set, then the fractal dimension equals the mass dimension [6]:

D = dim E = log μ [B_r (x)] / log r (Marcelli, 2019) [39].

The former equation of Mandelbrot shows a striking analogy with the formula for the information state (H) or negentropy of a system:

H = - S p_i log p_i (Brillouin, 1953) [40].

Given the intuitive relationship between biodiversity and information, it would be conceivable to define biodiversity alterations in terms of changes of entropy [41]. However, just like in Williams’ conclusion on the statistical approach of biodiversity estimation (see 4.1 ) [31], more information is needed both on the mathematical side and regarding the ‘nature’ of the biological data. For instance, neither the homogeneity nor geometrical regularity of the local biodiversity, represented as a set of ecological interactions, can be ascertained (see also ¶ 5. A Fractal versus Surface Approach for Ecosystem Development). But at least one (trivial) solution may be obtained from comparing the equations above, namely that reducing the number of elements in the set (whether or not homogenously distributed) results in augmenting the entropy as well as reducing the biodiversity at a local scale [6].

A Fractal versus Surface Approach for Ecosystem Development

Not only the Woodland – Grassland Interface, also other ‘border’ regions are of primary importance for the conservation of our planet’s ecosystems. Examples that so far have received much public attention are the Great Coral Reefs (of the Pacific Ocean), the Mangrove Forests and many other Coastal Ecosystems. In fact, every ‘natural’ river bed could be regarded as a ‘border’ ecosystem, although a too high proportion of river beds worldwide is lacking a ‘natural’ border or riparian zone. As was mentioned previously [7], coral reef biodiversity refuted Hubbell’s UNTB. The ecological biodiversity in coral reefs strongly depends on the interaction between groups of coral species, such as algae, the Coelenterata (the builders of the stony coral structure) and fish species, but many interactions between them are species-specific. Each of the latter groups is important for keeping the ecosystem in a locally balanced equilibrium, preventing the spread of parasites or the growth of one group at the cost of another. What are the benefits and the costs of choosing a fractal approach instead of a surface (or volume) approach?

Fractal geometry has the disadvantage of making used of geometrically non-differentiable functions [6]. In order to enable a developmental description of ecosystem, including its injury and possible resilience, a time-integrative mathematical convolution technique could be useful.

Taking advantage of the physiological and anatomical analogs of the world’s respiratory system, the mammalian lungs, in analogy with the power-law description of the lung airway scaling, we may also write:

S (z, n) = z ^μ. F (z, n) (Sturm, 2017) [42]

(with μ representing the ‘power-law index’ [= fractional dimension], z the generation order of a bifurcating network system such as the mammalian lungs and F (z, n) a tailor-made function representing the harmonic periodicity) [42]. Similarly, a function describing a power-law rating of lung injury (P_inj) was inferred:

P_inj (z, n, θ ) = z θ - μ = z θ . F (z, n, θ) / z μ . F (z, n, θ) (Allaerts, 2020) [43]

Reflecting the proportion of the injured part of the lung compared to the healthy lung. A time-integrative approach is the following step, making use of a convolution equation involving a Laplace transformation. When a function is piecewise continuous in a finite interval, like the Heavyside function, then it is integrable over that interval [44]. This mathematical property can prove useful to explore the convergence of the Laplace transform:

L { P inj (…) } = ∫0 ∝ e -pt [ ∫0t Pinj (…) dt ] (Allaerts, 2019 and Allaerts, [in prep.]) [45].

Also here, more information is needed to enable mathematical model fitting to the biological data, in particular, for fitting the model in question to the relevant time scales of ecosystem destruction and recovery rates or the time-dependency resilience.

In case of the coral reef and mangrove forest regeneration, some experimental and observational data have been gathered, enabling an estimation of both the local growth rate of individual colonies of a population of Porites divaricate (LeSueur, 1821), a coral species occurring on Caribbean reefs [46], as well as the growth (and decay) rates of the reef supporting mangrove forest roots [47]. The ultra-fast, catastrophic decay rates resulting from a natural storm, or following human interference are also well-known, for instance resulting in 86 % loss of Florida’s mangrove coverage since the 1940s [47]. Directly, or in combination with other processes that follow climate warming, an almost countless number of species that depend on the mangrove habitat, from large mammals like Manatees, Dolphins and numerous birds, reptiles, fishes, etcetera, are under direct threat. It is one thing to estimate the (slow) linear growth rate of a single colony-forming coral species (of Coelenterata) [46], or to derive a volume growth rate of coral forming species in laboratory conditions or in the open ocean [48]. For a restoration of the full complexity of the mangrove and coral ecosystem, however, this is only the beginning of a slow recovery process, where we need to give way to Nature.

Returning to the Woodland – Grassland Interface (see above), a similar situation may be discerned. It is one thing to plant an array of new tree sprouts after deforestation, the recovery of a natural forest and/or grassland ecosystem is a much more elaborate process. In order to develop a balanced ecosystem with its natural inhabitants included, two examples of the resulting complexity of ecological web interactions are given below (Table 4-5 and Figure 7, a-c).

Figure 7: A. Schematic ecological web (detail) for the Red Mason Bee (Osmia bicornis) with 4 major predators and parasites (see Table 4 for estimated threat levels); B. One of the most iconic species of the Dutch Wet Grasslands, the Black-tailed Godwit (Limosa limosa) has become a Red List species (Status = Near threatened); C. General threat levels for the Black-tailed Godwit in The Netherlands (©2023, Photographs and Drawings by Biological Publishing A&O).

    

    

    Figure 7: A. Schematic ecological web (detail) for the Red Mason Bee (Osmia bicornis) with 4 major predators and parasites (see Table 4 for estimated threat levels); B. One of the most iconic species of the Dutch Wet Grasslands, the Black-tailed Godwit (Limosa limosa) has become a Red List species (Status = Near threatened); C. General threat levels for the Black-tailed Godwit in The Netherlands (©2023, Photographs and Drawings by Biological Publishing A&O).
    

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Table 4: Detail of Ecological web for two wild bee species (called key species), one rather common, polylectic species (*), the Red Mason Bee (Osmia bicornis) and one rather rare, vulnerable, oligolectic species (*) of the genus of Sand Bees (Andrena hattorfiana). Threats are scaled 1 to 10 (bold numbers) according to data by P. Van Gampelaere and others (personal communication, 2023). The estimated threat level for the Asian Hornet is uncertain, because unlike in the Honey Bee, the impact of this exotic species on both the common and rare wild bee species is largely unknown.

  

    
Key species (Protection status)
    
(Natural) Predators
    
Parasites and Parasitoids
    
General threats/dependencies or    indirect effects of human interference
  
  

    
Red Mason Bee

      (Osmia bicornis)

      [= Osmia rufa] 

      (No direct threat or Least concern)
    
Green Woodpecker (Picus viridis) (5)

      European Beewolf (Philanthus triangulum) (2)
    
Common Parasite Wasp (Cratichneumon sicarius ) (7)

      Bee-fly or Bombyliid Fly (Anthrax anthrax) (8)
    
Threatened by cold weather in early spring (3)

      Asian or Yellow-legged Hornet (Vespa velutina) (4-5?)
  
  

    
Large Scabious Mining Bee (Andrena hattorfiana) (genus of Sand    Bees)

      (Vulnerable)
    
(see above)
    
Kleptoparasitic Cuckoo Bee, e.g. Nomada    armata (2)

      Sand Bee parasites like Stylops melittae (3)
    
Feeds primarily on pollen of Knautia arvensis (secondly on Knautia    dipsacifolia ) (4)
  
  

    
(* Polylectic    species: feeds on (pollen of) many different plant species; oligolectic    species: feeds on only a small number of plant species) 
  

Table 4: Detail of Ecological web for two wild bee species (called key species), one rather common, polylectic species (*), the Red Mason Bee (Osmia bicornis) and one rather rare, vulnerable, oligolectic species (*) of the genus of Sand Bees (Andrena hattorfiana). Threats are scaled 1 to 10 (bold numbers) according to data by P. Van Gampelaere and others (personal communication, 2023). The estimated threat level for the Asian Hornet is uncertain, because unlike in the Honey Bee, the impact of this exotic species on both the common and rare wild bee species is largely unknown.

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The rare occurrence of e.g. Andrena hattorfiana, also results from the scarcity of its food source, the pollen of the so-called Field Scabious (Knautia arvensis /K. dipsacifolia) flower (Figure 5A). This flowering herb of the Honeysuckle family (Caprifoliaceae), at present is a Red List species in NW-Europe (Belgium and The Netherlands). It became especially rare, primarily because of the disappearance of the traditional mowing practices using sickle and scythe, being replaced by the more industrialized machine mowing practices. Secondly, Knautia species prefer the non-fertilized, moderately limy soil grasslands (both in the class of the Sandy Dry Grasslands or Grey Dune Plant Communities, known as Koelerio-Corynephoretea) [49] and in the classis of Nutrient-poor Wet Grasslands (Molino-Arrhenatheratea) [50]. As a result, the anthropogenic influence has a major negative impact on these rare wild bee species. The same holds for a typical Wet Grassland bird species, the Black-tailed Godwit (Limosa limosa) (Table 5 and Figure 7, b-c).

Table 5: Detail of Ecological web for two bird species, one typical for forest habitat, the Golden Oriole (Oriolus oriolus) and a typical breeding species of Wet Grasslands, the Black-tailed Godwit (Limosa limosa). (Data on protection status of L. limosa obtained from Data Zone of BirdLife International) [1].

  

    
Key species

      (Protection status)
    
(Natural) Predators
    
Competitors
    
General threat
  
  

    
Golden Oriole

      (Oriolus oriolus)

      (No concern)
    
Several species of Birds of Prey (Accipitriformes; incl Eagles,    Sparrow-hawks,..); Stork (Ciconiiformes)
    
Woodpeckers (Piciformes); Corvidae
    
Diminished area of Forest habitat
  
  

    
Black-tailed Godwit

      (Limosa limosa)

      (Near threatened – Red List species)
    
Beech Marten (Martes foina); Red Fox (Vulpes vulpes);    (Sea) Gulls, Birds of Prey.
    
Several sp. Geese (Anseriformes) and other charadriiform birds    (Charadriiformes)
    
Loss of habitat owing to wetland drainage and agricultural    intensification; notable decline in wintering areas in Morocco and Senegal (51).
  

Table 5: Detail of Ecological web for two bird species, one typical for forest habitat, the Golden Oriole (Oriolus oriolus) and a typical breeding species of Wet Grasslands, the Black-tailed Godwit (Limosa limosa). (Data on protection status of L. limosa obtained from Data Zone of BirdLife International) [1].

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Conclusions and New Challenges of the Anthropocene

Historically, the importance of a significant proportion of land covered with forests has been recognized merely since the last two centenaries, at least for protecting the coastal dune areas (¶ 1. Introduction: (Modern) History of Woodland Cultivation). That was more than a century before climate warming became a matter of global concern. The opportunistic use and/or economic appreciation of woodland cultivation, however, hasn’t changed much in these 200 years, it appears. Woodland cultivation came to the forefront of climate awareness in recent years, also because of the increased risk of massive wildfires following periods of heatwaves and exceptional drought. It became especially harmful in the Portuguese summer fires of 2017, where in the vast, monocultural Eucalyptus forests, a tree species known for fueling the fires with exhaling highly inflammable, oleaginous substances, a record number of human casualties were counted [52]. In our short historical introduction, we mentioned that a certain criticism of the potential risks of monocultures already existed in the nineteenth century [3].

In an era where ecology is superseded by planimetry, and agriculture became a national, economical asset (or a burden), a plea for the restoration of the natural forestry and grassland management practices seems a desperate effort. But all the more, in this study we argue that the biodiversity paradigm requires the renewed appreciation of the notion of a border interface, albeit in Mangrove forests, coral reefs, in natural river beds and also in the grassland-woodland interface described in this paper. It is well known that grasslands may generate biotopes with the highest biodiversity on the globe, at least the natural steppes of the great plains in the Americas, Eurasia and Africa. Temperate forests on the other hand, from a managerial point of view, are often regarded as less interesting for the local biodiversity. Depending on the species, however, the size of these temperate forests matter, because the size of the habitat also defines the distance from a specific niche forming shelter to the border of its safety zone. Therefore, for those animals that seek shelter and especially the absence of human interference, which for most species on the planet constitutes the biggest threat, the size of forest habitats does matter. But the crucial parameter is the distance to the fractal border ‘line’, which as we have described, in the biome of the species involved in fact forms a space-filling, convoluted surface area (Figure 6). The physical characteristics of both the grassland and the forest habitat, like their role in hydrology and temperature regulation, reinforce the complicated role of forests and grasslands in protecting biodiversity as well as the direct effects of climate warming on the biosphere (similar to the pivotal role of mangrove forests, coral reefs and underwater ecosystems of seagrass meadows) [53].

The intensive, economically relevant use of terrestrial areas for woodland cultivation, or the modification of grasslands (of all kinds) for agricultural exploitation, seems a continuous threat for the survival of these ecosystems and for the biosphere as a whole. Not only the difficulties arising from combining agricultural intensification with the protection of natural reserves (see above) is menacing a large number of species. But more and newer threats are resurging from the drawing tables of human creativity. It has been found that agricultural activities of the past decennia, since a long time have spoiled the quality of the soil. In a negative way, this has affected their potential for growing new forests. One important reason for this deterioration is the distorted balance of bacterial infestation versus the mycological flora in the forest soil. Indeed, the mycorrhizal fungi are necessary for trees to effectively pick up nutrients from the soil [54]. However, the most significant threat looming from a corner of economic opportunism and some sort of scientific hubris, probably is the tendency or wish of certain stakeholders to replace the existing soil micro-organisms by genetically modified organisms, engineered in some highly specialized laboratories. For obvious reasons their names and studies will not be mentioned in a study devoted to the protection of global biodiversity, as long as possible and necessary to resist their greed and foolish ambitions.

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Citation: W Allaerts. On Land Use and Biodiversity Resilience: Hydrology, Temperature Regulation and the Fractal Nature of the Woodland-Grassland Interface. Austin Environ Sci. 2023; 8(2): 1097.

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