The effects of habitat destruction and environmental disasters

As we stated at the beginning of this chapter, it is particularly important not only to predict under what conditions a species hosted by a fragmented landscape can persist, but also how robust its persistence is. In fact, many metapopulations must compensate, via effective dispersal mechanisms, not only for the natural habitat fragmentation, but also for the fragmentation due to man-made land-use change. Also, they must withstand other occasional disturbances originated by a fluctuating environment and/or human activities that threaten their viability (environmental catastrophes).

It is important to comment on the difference between the two different types of disturbance (habitat loss vs. environmental catastrophes). As a prototypical example of environmental catastrophes, think of forest fires, which can occur with different frequencies in different biomes and at intervals more or less regular (Casagrandi and Rinaldi, 1999). They may be due to both natural causes (typically heat waves in Mediterranean forests) and human activity. The fire has often the power to wipe out most of the plants of a forest fragment. However, in many cases it does not destroy the habitat of plants. On the one hand, in fact, the dead organic matter deposited to the ground before the fire occurs is more rapidly mineralized. Some chemical elements (such as nitrogen) are lost to the atmosphere as gases, while others (such as calcium and potassium) are instead the main constituents of ashes and can act as fertilizers. If the fire is not too hot and does not give rise to big convective motion, most ashes fall on the burnt site. Therefore, the availability of soluble mineral nutrients may increase and, if they are absorbed by soil, may reduce soil acidity and stimulate primary production. Raising soil temperature may also favour seed germination and root development. In other words, even if the local population of plants in the burnt patch is destroyed, this fragment may still have features that make it suitable to re-colonization. In boolean terms, we can say that the fire event (the environmental catastrophe) switches the state of the fragment from “occupied” to “empty”. Similar examples of environmental catastrophe are possible in other ecosystems, of course, for instance the occasional emergence of deadly diseases, the erratic occurrence of very unfavourable microclimatic conditions (very harsh winters or hot summers), or the occurrence of disastrous floods in riverine environments. Grasshoppers of the species Bryodema tuberculata, for example, inhabit gravel bars along braided rivers in Central Europe. In these metapopulations the frequency of flood occurrence is fundamental to determine the viability of the species in the river ecosystem (Stelter et al., 1997).

The loss of habitat caused by human activities on natural landscapes have instead very different effects on the persistence of a metapopulation. The conversion of vast portions of pristine tropical forests to agriculture, as well as the construction of buildings and roads, or the channelling of rivers, permanently alters or destroys the habitat fragments involved. By permanently we mean that these actions cause not only the death of individuals that inhabited the fragment before human intervention, but also, so to say, the death of the same fragment, which is thus made unavailable to possible future colonization. Sometimes the destruction is only partial, e.g. due to urbanization, thus leading to habitat erosion and the decrease of the carrying capacity of the involved patches. Although habitat loss directly caused by land-use change is the commonest way of landscape destruction, it is not the only cause. Other important drivers are climate change (as argued in the introduction to chapter ) or the deterioration of abiotic conditions (such as the alteration of the availability and abundance of limiting nutrients in the patches). Although it might be important to make a distinction between habitat loss and habitat erosion (see Casagrandi and Gatto, 2002b), here we confine the analysis to the effects of the first type of disturbance. Thus we assume that the destruction of a certain fraction of habitat fragments is complete.

Levins' model can easily incorporate both disturbances (habitat loss and environmental catastrophes). Fig. 5 shows in schematic way how to model the alterations produced by both types of disturbance. If we denote by $h\leq 1$ the fraction of the pristine habitat that is still suitable after the possible destruction made by man, and with $m\geq 0$ the occurrence probability of an environmental disasters per unit time, Levins' model can be modified as follows

$$\dot{p}(t)=cp(t)\cdot\left(h-p(t)\right)-(e+m) p(t)$$ (6.4)

The fraction of colonizable landscape, made up by fragments that are empty but can still be occupied - because they have not been destroyed - is no longer equal to $1-p(t)$, like in the original model, but to $h-p(t)$. Dispersers will still try to colonize a fraction $1 -h$ of the landscape but their dispersal to those locations will be unsuccessful. As a result of this change, the constraints for the state variable become $0\leq p(t)\leq h$. Note that this implies the assumption that the propagule rain is purely passive, namely dispersers are not able to actively search for fragments to colonize. In fact, we assume that individuals move to destroyed patches but fail to settle there, thus being lost forever. As for the role of environmental catastrophes, they can be simply modelled by assuming that they raise the rate of extinction of local populations of a quantity equal to $m\cdot p(t)$.

Figure 5: Simple scheme that shows how habitat loss and environmental catastrophes can be incorporated into Levins' model.

By requiring that $\dot{p}=0$ in model (34) it is easy to obtain the following equilibrium conditions

$$\bar{p}_+=\left\{ \begin{array}{ccll} h-\dfrac{e+m}{c} & \qqu... ...quad\quad & \text{if } & h\leq \frac{e+m}{c} \end{array}\right.$$ (6.5)

Similarly to what we previously stated for the undisturbed Levins model, one can show that the non-trivial equilibrium, when it is feasible, i.e. positive, is also asymptotically stable. It therefore represents the persistence equilibrium of the metapopulation.

Before analysing the combined effect of environmental catastrophes and habitat destruction, it is reasonable to study the effects independently caused by each of the disturbance parameters introduced in the modified Levins model  (34). The parameter space in which it is useful to carry on the discussion regarding the effects of the disturbances is certainly the extinction-colonization plane, that is $(e,c)$. Each point in this two-dimensional parameter space can be ideally imagined as representative of a particular metapopulation whose organisms belong to a species living in a specific fragmented territory. As such the metapopulation has its own capacity of colonization (and reproduction, as previously described ) and is subject, because of both demographic and dispersal characteristics, to a certain risk of local extinction. The condition of persistence of the undisturbed Levins model (33) is represented in the parameter space $(e,c)$ as the bisector of the first quadrant. This line is then what we call the persistence-extinction boundary, or the curve in the parameter space that divides regions where persistence is guaranteed from regions where extinction is certain . The points of the black region in Fig. 6 thus correspond to metapopulations doomed to become extinct in fragmented landscapes even if they are undisturbed. The region above the bisecting line, instead, represents metapopulations that are guaranteed to persist, if anthropogenic or environmental disturbances are not acting.

Figure 6: Persistence-extinction boundaries in the Levins model (34) which includes anthropic and environmental disturbance. The black region below the solid line corresponds to global extinction of the undisturbed metapopulation as represented by the undisturbed Levins model (33). The dotted and the dashed lines, respectively, correspond to the persistence-extinction boundaries in the cases of environmental catastrophes only ($m=0.1$, $h=1$) and habitat loss only ($m=0$, $h=0.7$). The dash-and-dotted line represents the boundary when both disturbances act synergistically.

We first analyse the effect on persistence of environmental catastrophes only. The condition for equilibrium (35) to be positive for $h=1$ becomes $c > e + m$. Compared to the case of the undisturbed Levins model ($c>e$), the persistence-extinction boundary moves upward in the plane $(e,c)$, as shown in Fig. 6. Environmental catastrophes are therefore responsible for the extinction of all the metapopulations whose parameters belong to the region between the black region and the dotted line. The fact that environmental catastrophes imply a simple translation of the persistence-extinction boundary suggests that metapopulations with both high and low extinction rates are likewise influenced by the occurrence of natural or anthropogenic disasters. On the other hand, we have seen in the previous chapter that the critical area of a reserve increases with the diffusion coefficient, in other words, the probability of extinction in a patch of a given area increases with the species dispersal rate. Therefore, in the simple Levins model the dispersal ability of a population is somehow included in the rate of local extinction $e$; thus, we can conclude that both species that disperse frequently and those that disperse rarely are similarly sensitive to environmental catastrophes.

On the contrary, habitat destruction has a rather selective effect on the likelihood of extinction in different metapopulations. In the absence of environmental disasters ($m=0$), the positivity and stability condition of equilibrium (35) becomes $h>\frac {e}{c}$. As shown by the dashed straight line in Fig. 6, the persistence-extinction boundary rotates counter-clockwise in the space $(e,c)$ with respect to the undisturbed situation ($h=1$). Therefore, metapopulations doomed to extinction uniquely because of habitat loss are those corresponding to the region comprised between the dotted curve and the bisector. This region considerably widens for increasing $e$. We can thus infer that species dispersing more frequently are more affected by this type of disturbance (Casagrandi and Gatto, 1999).

Note that, if the two types of disturbance act simultaneously, namely $m>0$ and $h <1$, the persistence-extinction boundary becomes the dash-dotted line in Fig. 6. Since the set of metapopulations doomed to extinction by the co-occurrence of the two types of disturbance is larger than the union of the two sets obtained earlier, we can conclude that these drivers actually act in a synergistic way, which is thus a phenomenon that contributes to significantly increase the risk of metapopulation extinction.