## 1 Introduction  
Habitat destruction is a known cause of species extinction over the past billion years. Dominant species are not endangered if their habitat is not completely destroyed, as their territory might be randomly spread across the whole habitat and, hence, they can survive in undisturbed areas. Consequently, extinctions of rare species are assumed to be biased. Early work in this area by [PERSON] and [PERSON] [1] analyzed the effect of habitat removal of two species that are regionally abundant. Later, [PERSON] et al. [2] developed the coexistence model, which became widely applied to competitive multi-species' habitat loss. In the [PERSON] study, extinction in abundant species may be due to habitat loss with time delay. In a subsequent work by [PERSON] et al. [3], an analytical model of competitive coexistence in spatial habitats is introduced. Here, the extinct species with the poorest distribution are the best competitors. However, since the model assumptions are on dispersal ability and mortality rates, this extinction model is considerably biased. [PERSON]'s models have been widely studied over the past three decades. A wider range of parameters is investigated by [PERSON] [4], and a critical habitat size for a single species was also examined using a spatially explicit model. A prey-predator metapopulation model in [PERSON] and [PERSON] [5] indicates that dispersal rate is crucial for habitat destruction. The extension of this model by [PERSON] et al. [6] shows that the effect of habitat destruction on the coexistence of prey and predator depends on the invasion or colonization rate of prey and predator. More works related to space utilization on prey-predator interaction model can be found in [7; 8; 9]. Accounting for spatial structure and heterogeneity, the work of [PERSON] and [PERSON] [10] demonstrates that a predator-prey metapopulation is affected by habitat destruction. Their model is similar to the NMH model of [PERSON] et al. [11]. However, in their model, prey are dispersed in inhabited patches of both predator and prey. The single-species argument NMH model is generally not enough to explain the effects of predator-prey interaction since it allowed the feedback loop into the model. In a later work by [PERSON] and [PERSON] [12] on metacommunities of mutualistic species, they vary the strength of mutualistic interaction and fraction of suitable habitat. In [PERSON] [13], an eigenvalue-eigenvector relationship was analytically studied to find the effects of habitat destruction and restoration in a metapopulation model using simple models. Earlier, Mean-field theory (MFT) had been used by [PERSON] et al. [14] to develop a model of ecosystems containing two or three species and study the relationships between habitat destruction and species extinction. A nonlinear n-population metapopulation model was also improved from [PERSON]'s model by [PERSON] et al. [15], whose work showed that the extinction number of superior competitors is related to the disharmony exponent of metapopulation. [PERSON] and [PERSON] [16] demonstrated the odd-even evolution rule to show that the extinctions of some species are biased. [PERSON] et al. [17] used MFT to simulate and showed that a parity law reveals even-odd species different behaviors. Species-area and endemics-area relationships (SAR and EAR) models have also been used to predict extinctions. [PERSON] et al. [18] showed that EAR underestimated extinctions due to habitat loss while SAR gave a good approximation of short-term extinction unless the remaining habitat is so highly fragmented that SAR also underestimated the extinctions. [PERSON] et al. [19] used SAR model to predict the rates of bird species loss in fragmented forests and the results showed that SAR underestimated actual losses in the Panama Canal region due to nonrandom patterns of species distributions. Due to a lack of temporal data, long-term losses have not been widely investigated compared to short-terms losses.