A niche-based theory of Island Biogeography

doi:10.21203/rs.3.rs-2727022/v1

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A niche-based theory of Island Biogeography

https://doi.org/10.21203/rs.3.rs-2727022/v1

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published 31 May, 2024

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The Equilibrium Theory of Island Biogeography (ETIB) is a widely applied dynamic theory proposed in the 1960s to explain why islands have coherent differences in species richness. The development of the ETIB was temporarily challenged in the 1970s by the alternative static Theory of Ecological Impoverishment (TEI), which suggests that the number of species on an island is determined by its number of niches or habitats. With no clear evidence relating species richness to the number of niches however, the TEI has been almost dismissed as a theory in favour of the original ETIB. Here, we show that the number of climatic niches on islands is an important predictor of the species richness of plants, herpetofauna and land birds, and we therefore propose a model called the Niche-based Theory of Island Biogeography (NTIB) that successfully, merges the ETIB and TEI into a unifying concept. To account for greater species turnover at the beginning of colonisation, we include higher initial extinction rates. When we test our NTIB for resident land birds in Krakatau Islands it reveals a good correspondence with observed species richness, immigration and extinction rates. We estimate that current species richness at equilibrium is ~48 species (range between 47.76 and 51.36) provided the environmental regime remains unchanged.

Biological sciences/Ecology

Biological sciences/Ecology/Biodiversity

Equilibrium Theory of Island Biogeography

Area-Species relationship

Theory of Ecological Impoverishment

MacroEcological Theory on the Arrangement of Life

Biodiversity

The Equilibrium Theory of Island Biogeography (ETIB) proposed by MacArthur and Wilson suggests that immigration and extinction dynamics on an island lead to an equilibrium in species richness S that is influenced by (i) island area A ^1–5 and (ii) its degree of isolation; the former influences ecological factors such as available resources and habitat heterogeneity ⁶ and the latter affects immigration rates ^4,6,7. Species turnover is a key aspect of the theory, the equilibrium on an island resulting from the continuing variation in the gain and loss of species and in this way, island area also affects positively species richness because a larger island intercepts more immigrating species, a phenomenon known as the target effect ^6,8. Further, a shorter distance to the mainland increases immigration rate, which also reduces stochastic extinction, a phenomenon known as the rescue effect ⁹; there is also a negative relationship between species richness and the distance of an island to the mainland because fewer immigrants arrive as distance increases. MacArthur and Wilson used the equation S = αA^β to model the species richness-area relationship, with α and β depending upon the taxon and the biogeographic regions ⁶. In the ETIB (Supplementary table S1 for all acronyms/variables meaning) the number of new species gained by immigration decreases monotonically with species richness, whereas species lost by extinction increases monotonically ¹⁰.

An alternative theory, the Theory of Ecological Impoverishment (TEI), was proposed a few years after the ETIB ^11,12. The TEI differs in the way it interprets the positive and negative effects of area and distance on species richness ^8,11. When Lack studied the island biogeography of birds ^11,12, he found there are more visiting birds on an island than breeders which led him to conclude that a newly arriving species makes the choice whether to remain or not. Lack hypothesised that this choice was driven by ecological conditions and he related the species richness of an island to the number of niches or habitats available ^11,12. A recent study in British islands supports Lack’s hypothesis ⁸.

The ETIB has been extensively tested since its introduction, frequently criticised or even revisited ^8,10,13−22. Among new models, the island immaturity – speciation pulse model, subsequently termed the general dynamic theory of oceanic island biogeography, has been proposed for volcanic islands to better consider the influence of island geodynamics on biodiversity dynamics, including phases of immigration, extinction and speciation that follow an island’s life cycle ^13–15.

Other island biogeography models have also been proposed ^23–28. BioGEEM (BioGeographical Eco-Evolutionary Model) is a grid-based model that integrates stochastic, ecological (e.g. demographic, dispersal and competition), evolutionary (e.g. mutation and speciation) and environmental processes (e.g. geoclimatic dynamics) ²⁴. A probabilistic model has also been specifically designed to work on functional traits as a function of habitat area and isolation ²⁶. A trophic Theory of Island Biogeography (TTIB) has been implemented to account for the trophodynamics of island ecosystems ²⁵. In particular, TTIB integrates the concept of bottom-up sequential dependency ^29,30 and predicts species with large diet breath to dominate at the beginning of island colonisation ²⁵. Some studies have also attempted to merge niche theory with island biogeography by considering habitat heterogeneity ^27,28. However, there is an important distinction between the habitat and the niche. A habitat is the place where a species lives whereas the ecological niche is the sum of all the abiotic and biotic conditions that allow an individual to grow and reproduce and consequently, habitats contain many niches and different habitats contain different number of niches ^31,32. The MacroEcological Theory on the Arrangement of Life (METAL) predicts that tropical areas are likely to have more niches (and therefore more species) than polar areas with the same degree of habitat heterogeneity ^33–35; this result is likely to hold true independently of the way heterogeneity is defined or measured ³⁶.

Although it seems logical that the species richness of an island should be related to the number of niches available ^31,32, this prediction, perhaps because of the difficulty in estimating the number of niches that an island contains, has been rarely tested. We have been able to overcome this difficulty using a METAL (MacroEcological Theory on the Arrangement of Life) model we recently developed to reconstruct global biodiversity patterns in the terrestrial and marine realms ³¹ and applying this to estimate the number of climatic niches on islands using temperature and precipitation as a proxy of water availability (Methods). To examine the relationships between species richness, area and distance to mainland, we chose three taxonomic groups: plants (62 islands), herpetofauna (35 islands) and birds (68 islands) (Supplementary tables S2 and S3)³⁷. We then included the number of climatic niches into an island model and propose a new way to consider the extinction rate to account for higher turnover rates generally observed at the beginning of colonisation ^17,38. This model is tested using resident land birds on Krakatau Islands.

Biological data

Data on the biodiversity and characteristics (e.g. species richness, area and distance to continent) of islands for plants and birds originated from Blackburn and colleagues ³⁷ (Supplementary table S2). Data on the biodiversity and characteristics of islands for herpetofauna were assembled in this work from a variety of sources (Supplementary table S3).

Resident land bird data of Krakatau islands (Sertung, Panjang Anak and Rakata) with respect immigration, extinction and species richness, originated from the Table 1 published in Thornton and colleagues ³⁹.

Environmental data

Mean monthly temperature (°C) and precipitation (mm) climatologies (period 1970–2000) were retrieved from the 1-km spatial resolution WorldClim version 2 dataset (http://worldclim.org/version2)⁴⁰. Climatologies were obtained by performing the thin-plate smoothing spline algorithm implemented in the ANUSPLIN package; more information on the numerical procedures was provided by Hijmans and colleagues ⁴¹ and Fick and Hijmans ⁴⁰.

Calculation of the number of climatic niches

We applied a model developed to reconstruct and investigate large-scale biodiversity patterns in the terrestrial and marine realms ³¹. The model developed as part of the MacroEcological Theory on the Arrangement of Life (METAL; https://biodiversite.macroecologie.climat.cnrs.fr) has been fully described and tested in Beaugrand and colleagues ^34,35,42. This model generates ecological niches sensu Hutchinson ⁴³, which then interacts with the local environmental regime, giving an estimate of the number of niches and therefore species that can occur in a region ^31–33. Although the concept of the niche is multidimensional, we focussed here on climatic niches, which were assessed using temperature and precipitation on each island ³¹. Climatic niches are critical for the long-term establishment of a species ⁴⁴ and individuals outside their climatic niches cannot occur for long in a region. Other ecological dimensions (e.g. soil pH and type) also explain species occurrence but we assume here that they play a secondary role at a global scale. The estimation of the mean number of niches on each island was performed following two main steps (Supplementary fig. S2):

Step 1: building of climatic niches

We calculated rectangular niches in this model with a 0 corresponding to an absence and a 1 to a presence (Supplementary fig. S2)³⁴. All potential thermal niches ranged from t_min=-1.8°C to t_max=44°C and all precipitation niches ranged from p_min=0 mm to p_max=3000 mm; these thresholds were investigated in previous works and best fit the data in the oceanic and terrestrial realms³¹. A total of 1,067,175 potential niches was considered in this study (255 precipitation x 4185 thermal niches). The mathematics of the model is presented in Supplementary text S1.

Step 2: niche-climate interaction

We then tested the pool of potential niches (1,067,175) on each island; niches were selected when climatic conditions were suitable for at least n month(s) (1 ≤ n ≤ 12) and in at least one ~ 1 km x ~ 1 km geographical cell. We therefore performed 12 simulations for each island: in the first simulation one niche was considered to be potentially represented on an island if only one month was suitable in any geographical cell. In the second, one niche was considered to be potentially represented on an island if only two months were suitable in any geographical cell. And so on until 12 months. In the twelve simulation, one niche was considered to be potentially represented on an island if all months were suitable in any geographical cell. We then calculated the average of the total number of niches that may be represented on each island from the 12 simulations. The total number of niches was calculated for 56 islands for plants (Supplementary table S2), 35 islands for herpetofauna (Supplementary table S2) and 62 islands for birds (Supplementary table S2). For some small islands (e.g. St Helena Island), estimation of niches was not possible because of the absence of temperature or precipitation values (Supplementary table S2). Ascension, Macquarie and Saint-Paul Islands were removed because there was no native bird species.

Statistical analyses

Relationships between observed richness, area, the number of climatic niches and distance to mainland

We investigated the relationships between (i) observed species richness and area, (ii) observed species richness and the number of climatic niches, and (iii) observed species richness and distance to mainland for three taxa: plants, herpetofauna and birds. We used scatterplots with latitude as a supplementary variable to examine these relationships (Fig. 1); the colour and the size of the points were proportional to the absolute value of latitude. To examine the magnitude and significance of the relationships, the ordinary linear coefficient of correlation was calculated for all pairs of variables.

We also calculated the correlations between island area and the number of climatic niches for all islands and taxonomic groups. To examine how latitude may influence these relationships, we also assessed these correlations exclusively for islands between the Tropics of Cancer and the Tropics of Capricorn (i.e. tropical biome).

Species richness as a function of the number of niches available, area and distance to mainland

We estimated species richness (Z) using a multiple linear regression based on the number of niches available (M), island area (A) and distance to mainland (d)(Fig. 2). All variables were log₁₀-transformed. The model, performed individually for each taxonomic group (plant, herpetofauna, bird), was as follows:

Log₁₀(Z)= ϒ_MLog₁₀(M) + ϒ_ALog₁₀(A) + ϒ_dLog₁₀(d) + β (1)

With ϒ_M, ϒ_A and ϒ_d the conventional partial regression coefficients of M, A and d, respectively, and β the y-intercept (Supplementary table S4). We expected species richness to be proportional to M and A but inversely proportional to d.

Three multiple linear regression analyses were performed on (i) plants, (ii) herpetofauna and (iii) birds. Then, we applied Eq. (1) to estimate species richness on all islands and examined the respective influence of each component in Eq. (1) (Fig. 2). We then calculated the overall coefficient of correlation between predicted and observed species richness. The conventional partial regression coefficients and the y-intercepts of the three multiple linear regression analyses are shown in Supplementary Table S4.

For the three multiple linear regression analyses, we assessed the contribution of each variable by calculating the standard partial regression coefficients ϒ’_M, ϒ’_A and ϒ’_d from the conventional partial regression coefficients, as follows ⁴⁵:

$${\gamma {\prime }}_{M}={\gamma }_{M}\frac{{\varphi }_{M}}{{\varphi }_{Z}}$$

$${\gamma {\prime }}_{A}={\gamma }_{A}\frac{{\varphi }_{A}}{{\varphi }_{Z}}$$

$${\gamma {\prime }}_{d}={\gamma }_{d}\frac{{\varphi }_{d}}{{\varphi }_{Z}}$$

With ϕ_M, ϕ_A, ϕ_d and ϕ_Z the standard deviation of M, A, d and Z, respectively. The advantage of the standard partial regression coefficients is that they can be used to assess the magnitude of the influence of each standardised (i.e. centred and reduced) independent variable on the standardised dependent variable ⁴⁵. Therefore, they give an information on the importance of each independent variable.

Model of island biogeography

Description of the model

We designed a dynamic model, based on the same rationale than the Equilibrium Theory of Island Biogeography (ETIB), but jointly considering area (A), distance to mainland (d) and the mean number of climatic niches (M). The model was tested using bird data for Krakatau Islands. The number of climatic niches, fixed by METAL, was 105,082 for the whole archipelago, including Rakata, Panjang, Sertung and Anak islands. Our model calculates species richness of an island using long-term immigration rates, short-term and long-term extinction rates. Species richness on an island at age t was assessed as followed:

$${B}_{t+1}={B}_{t}+{I}_{t}-{E}_{t}-{F}_{t}$$

Where B_t and B_t+1 were species richness at time t and t + 1, respectively, with t expressed in year. I_t and E_t were the immigration and the long-term extinction rates at year t, respectively. We included a new term F_t in Eq. 5, which was the initial short-term extinction rate. We added this term because, at the beginning of colonisation time, habitats can be rapidly altered and populations remain small, which initially increase the extinction rate ^6,46.

Immigration rate I_t (species.yr^− 1) on an island was calculated by using a negative exponential function standardised between I₀ and I_s, with I₀ and I_s the immigration rates at t = 0 and t = s (saturation), respectively:

${I}_{t}={I}_{0}\frac{\left({{e}^{-{\left(\frac{{B}_{t}}{{B}_{s}}\right)}^{{b}_{1}{I}_{0}}}-e}^{-1}\right)}{1-{e}^{-1}}$ I₀ ≤ I_t ≤ I_s and B_t ≤ B_s (6)

Where B_t was the species richness at time t and B_s the species richness at saturation (B₀ = 0 at t = 0) and

B_s assessed as follows:

B_s = ϕM (7)

where ϕ was a constant that depends upon the taxonomic group and M the mean number of climatic niches on the island. We assumed here that all niches could be colonised by a unique species after the principle of competitive exclusion ⁴⁷. b₁ is a constant (dimensionless) that depends upon the taxonomic group. The constant influences the speed with which the immigration rate diminishes between I₀ and I_s. At saturation, we assumed that I_s=0 species.yr^− 1 (Fig. 3).

Long-term extinction rates G_t were estimated as follows:

${G}_{t}={G}_{s}\frac{\left({{e}^{{\left(\frac{{B}_{t}}{{B}_{s}}\right)}^{{b}_{2}{G}_{S}}}-1}^{}\right)}{{e}^{1}-1}$ G₀ ≤ G_t ≤ G_s and B_t ≤ B_s (8)

With G_s=1 at B_s; this means that the long-term extinction rate G_t is 1 when species richness is at saturation. b₂ is a constant that depends upon the taxonomic group. The constant influences the speed with which the long-term extinction rate increases between G₀ = 0 and G_s.

Short-term extinction rates F_t was a function of the immigration rate:

${F}_{t}=\sigma {I}_{t}{e}^{{-b}_{3}{B}_{t}}$ with F₀ ≤ F_t ≤ F_s (9)

With $\sigma$ a constant (species^− 1) that determines the initial rate of short-term extinction rate, b₃ a constant (dimensionless) that affects the speed with which short-term extinction rate diminishes and cancels off. F_t is a function of both species richness and the immigration rates at time t. In this study F_s=0.

Total extinction rate E_t is the sum of short (F_t) and long-term (G_t) extinction rates:

E_t = F_t + G_t with E₀ ≤ E_t ≤ E_s (10)

Because G_s=1 at B_s, E_s=1 as F_s=0.

Test of the model for Krakatau islands

The test was conducted by using resident land bird data from the Krakatau Islands ³⁹, which was sterilised by a volcanic eruption in 1883. Island colonisation was subsequently investigated in 1908, 1919–1924, 1928–1934, 1951–1952 and 1984–1986.

We had to estimate six parameters to model the recolonization of the island: b₁ (Eq. 6), b₂ (Eq. 8), b₃ (Eq. 9), I₀ (Eq. 6), σ (Eq. 9) and ϕ (Eq. 7). Estimation of the parameters of the model was done by calculating 1,935,360 combinations and by minimising the Root Mean Square Error (RMSE) between modelled species richness, immigration and total extinction rates of resident land bird for different time periods. RMSE is calculated as follows ⁴⁸:

$$RMSE=\sqrt{\frac{\sum _{i=1}^{n}{\left({H}_{i}-{O}_{i}\right)}^{2}}{n}}$$

Where H_i and O_i are modelled and observed species richness, immigration or total extinction rate at observation i, respectively, and n the number of observations. The three RMSEs were subsequently standardised between 0 and 1 and the sum of the three RMSEs, called hereafter total RMSE (range between 0 and 3), were calculated. (We took the three RMSEs to ensure that immigration and extinction rates, as well as species richness, were all best reproduced by the model.) We kept the 1000 combinations that had the smallest total RMSE and finally retained the combination with the lowest total RMSE (Fig. 4).

Values for b₁ were 0.01 0.03, 0.05, 0.08, 1, 1.2, 1.4, 1.6, 1.8, and 2, a total of 10 values; values for b₂ were 0.1, 1, 2, 3, 4, 5, 8, 10, 25, 40, 50, 60, 75, 100, 110, and 150, a total of 16 values; values for b₃ were 0.00005, 0.0001, 0.0002, 0.0003, 0.0004, 0.0005, 0.00075, 0.001, 0.005, 0.01, 0.02, 0.04, a total of 12 values; values for I₀ were 0.71, 0.8, 0.9, 0.95, 1, 1.05, 1.1, 1.2, 1.6, 2, 2.5, 3, 3.5, 4, 5 and 6, a total of 16 values; values for σ were 0.2, 0.30, 0.35, 0.40, 0.45, 0.5, 0.55, 0.6 and 0.8, a total of 9 values; values for ϕ were 0.0002 0.0003 0.0004 0.0005 0.0006 0.0008 and 0.001, a total of 7 values; I_S=0 and G₀ = 0; G_s=E_s=1; F_s=0; F₀ and therefore E₀ were fixed as a function of I₀.

Ordinary linear coefficient of correlations were calculated between modelled and observed species richness, immigration and total extinction rates ⁴⁵.

Species richness at equilibrium B_eq (species) is reached when E_t crosses I_t (Fig. 3). The number of years after the eruption when B_eq is reached T_eq (year) can be easily assessed graphically or by examination of the matrices (Fig. 3). The year is then deduced by adding T_eq to 1883. In practice here, T_eq was determined when less than one species remained to reach B_eq.

Relationships between species richness, area, the number of climatic niches, distance to mainland and latitude

We first examined the relationships between species richness, area, the number of climatic niches, distance to mainland, and latitude (Fig. 1). The defined niche is the climatic conditions created by temperature and precipitation that enables a species’ individuals to grow and reproduce ³¹; this niche definition is close to the one proposed by Hutchinson ^43,49. The number of climatic niches of an island was assessed using a biodiversity model developed as part of the MacroEcological Theory on the Arrangement of Life (METAL) using temperature and precipitations as an index of water availability (Methods). As we expected, plants, herpetofauna and birds all showed a positive correlation between species richness and area (0.57 < r < 0.75; Fig. 1a-c). A clear effect of latitude was also evident on the scatterplots where high-latitude islands always exhibited less than expected species richness (see red bullets, Fig. 1a-c, i.e. islands located in the lower triangular part of the diagram). Using the number of climatic niches that an island may contain instead of island area improved the correlations for all taxa other than birds (0.62 < r < 0.74; Fig. 1d-f). It is noteworthy that high-latitude islands were better distributed on the scatterplots, even for birds, (i.e. distributed along the major axis of the cloud of points), indicating a clear positive influence of the number of climatic niches on species richness for all taxonomic groups. MacArthur and Wilson highlighted that the species-area relationship will hold only for islands belonging to the same biogeographic region ⁶ and our results concur and therefore, also support Lack’s argument that species richness of an island is influenced by the number of niches available ^11,12, which is influenced by the biogeographic region. As expected, the relationships between species richness and distance to mainland were less consistent and we only found significant negative correlations for plants and birds (-0.60 < r<-0.41), not for herpetofauna (r=-0.01; Fig. 1g-i); no effect of island latitude was detected on these scatterplots. We warn that some continental islands in Fig. 1g-i had been colonised before being separated from the continent (e.g. islands from the United Kingdom).

We further examined the correlation between area and the number of climatic niches of islands and found them to be positively correlated significantly for all groups, although the correlation was not always strong when all islands (i.e. all latitudes) were considered; plants: linear correlation coefficient r = 0.28, probability p = 0.04, number of points n = 56; herpetofauna: r = 0.70, p < 0.001, number of points n = 35; birds: r = 0.52, p < 0.001, n = 65. As we expected, the correlation improved for all taxonomic groups when the influence of latitude was accounted for. For islands within the Tropic of Cancer and the Tropic of Capricorn; plants: r = 0.53, p = 0.007, n = 24; herpetofauna: r = 0.91, p < 0.001, n = 16; birds: r = 0.62, p < 0.001, n = 32.

To examine how area, the number of climatic niches and distance to mainland jointly affect species richness for each taxonomic group, we performed three multiple linear regressions (see Methods); these analyses also allowed us to examine the respective linear contribution of each variable (Fig. 2 and Supplementary table S4). When combined together, predictions from the three regressions were highly correlated positively with observed species richness (Fig. 2). Contribution of the mean number of climatic niches was highest (positive contribution) for plant and herpetofauna (Supplementary table S5). Distance to mainland had a significant negative influence for plants and no for herpetofauna. Area also had a positive influence for herpetofauna but less for plants. For birds, area had the greatest positive contribution, closely followed by the mean number of climatic niches and distance to mainland (negative contribution). Interestingly, we found that distance to mainland had a more negative contribution for plants and birds than herpetofauna that has poor dispersal capability, even though there was no clear distinction among taxonomic groups for area and the number of climatic niches (Supplementary table S5). In a global-scale analysis, insularity also had a weak influence on herpetofauna spread rates ⁵⁰. To conclude, our analyses suggest that considering the mean number of climatic niches of an island increased the predicted species richness substantially (Fig. 1–2 and Supplementary table S5).

A dynamic model including the number of climatic niches

Because our results suggested that a consideration of the mean number of climatic niches was an important island property to assess species richness on an island, we built a dynamic model based on the same rationale as the ETIB, but also considering the mean number of climatic niches (M; Methods). We have called our model the Niche-based Theory of island Biogeography (NTIB). The rationale of our NTIB, as for the ETIB, can be explained by plotting both immigration and extinction rates as a function of species richness and examines when the two curves cross (Fig. 3). In ETIB, the immigration and extinction curves are monotonic (Fig. 3a). In contrast to the ETIB however, our NTIB calculates species richness of an island using short-term F_t and long-term G_t extinction rates (See Supplementary table S1 for variable meaning) (Fig. 3b). The use of short-term extinction rates F_t is justified by the fact that at the beginning of colonisation, populations are small and the environment is changing rapidly due to the effects of colonisation, which increase the likelihood of extinction ^17,51,52. Consequently, the short-term extinction rate F_t diminishes exponentially to a minimum as the long-term extinction rate G_t rises exponentially to G_s (Fig. 3b). The addition of F_t and G_t yields the total extinction rate E_t, which varies between E₀ and E_s; the latter parameter was fixed to 1 in this study. The joint consideration of immigration and short-term extinction rates enables the consideration of the high turnover rate of birds that is observed on some islands (e.g. Channel Islands of California)¹⁷. In our NTIB model, there is therefore no necessary monotonic increase in extinction rate and the shape can sometimes be similar to the shape suggested by Bush and Whittaker, their Fig. 2 ⁴⁶; it all depends upon the parameters of the model (Methods and Discussion). Although not explicitly included in our NTIB, an allogenic influence (e.g. wind, oceanic currents, precipitation, heat wave) probably dominates at the beginning of colonisation and an autogenic influence (e.g. density-dependence phenomena and species interaction) is more likely towards species richness at equilibrium B_eq (Supplementary table S1). Of course, allogenic or autogenic perturbations may prevent the system reaching B_eq. In addition, B_eq may be modified by environmental changes originating from geodynamics or climate change (see Methods and Discussion) and our model can therefore account for a time-varying species carrying capacity ⁵³. The NTIB can therefore be considered as a generalisation of ETIB, the latter being a particular case when short-term extinction rate F_t is nil and for a stable environmental regime, because the environmental regime controls the number of potential niches M, and therefore species richness at saturation B_s (Methods).

We tested the NTIB model using resident bird data from the Krakatau Islands (Anak, Rakata, Sertung, Panjang). Values of the six parameters used in Equations 6–9 were determined using a total of 1,935,360 combinations (Methods). We retained the 1000 curves (grey curves in Fig. 4) with the lowest Root Mean Square Error (RMSE) to provide a confidence interval (grey curves in Fig. 4) and chose ultimately the curve with the smallest RMSE (red curve in Fig. 4). Our NTIB reproduced well the dynamics of bird species richness on the island (Fig. 4). Although the number of observations was limited to have unambiguous correlations, especially for immigration (five year/time periods) and total extinction (four years/time periods) rates, ordinary linear correlation coefficients between modelled and observed species richness (six years/time periods), immigration and total extinction rates were r₁ = 0.91 (p < 0.001), r₂ = 0.65 (p = 0.003) and r₃ = 0.37 (p = 0.13), respectively.

We assessed species richness at equilibrium B_eq = 47.94 species (range of values based on 1000 curves with smallest RMSE, 47.76–51.36 species); such an equilibrium depends upon the number of climatic niches, which can be readjusted if climate changes. Our estimate of ~ 48 (47–51) species at equilibrium is higher than values of 30 in MacArthur and Wilson ⁶, 36–38 of Thornton and colleagues ¹⁹ and 40–45 of Mayr ⁵⁴. The number of years to reach equilibrium T_eq was also estimated while there was no alteration in the number of climatic niches (i.e. for a stable environmental regime). We found T_eq = 166 years (131–187 years) after 1883, i.e. year_eq=2049 (2025–2133). It is therefore clear that the species richness of resident land birds did not reach an equilibrium in 1933, as proposed early by MacArthur and Wilson ⁶ and already highlighted by Thornton and colleagues ⁵⁵. As the species richness of the archipelago trends toward an equilibrium that is based upon the current island configuration and climatic regime, it would be interesting to conduct a new inventory of the resident land birds on the Archipelago in order to confirm or refute our estimates.

Although some models of island biogeography have attempted to include niche theory, it has been done by means of habitat heterogeneity (i.e. number of habitats available in an area) ^27,28. In contrast, our NTIB model assesses the number of potential niches that an island may contain due to environmental heterogeneity in temperature and precipitation. Island area correlates positively with the number of climatic niches within a biome; in this paper, we tested it for the tropical biome. Therefore, our NTIB provides evidence that the number of ecological niches available on an island explains why island area often correlates with species richness ^6,7,16. However, the correlation between the number of niches and area diminished when all latitudes were considered together because tropical islands (as a given oceanic or terrestrial area) have more niches, and therefore more species, than temperate or polar islands (or areas) of the same size ^31,33.

The METAL theory we included in the NTIB considers the number of niches/species to be higher on tropical than temperate or polar islands, irrespective of the influence of environmental heterogeneity ^31,32,34, which we consider is a fundamental feature influencing the generality of the model. In the species richness-area plots (Fig. 1a-c), high-latitude islands had systematically lower than expected values of species richness, an issue that was solved when species richness was plotted against the number of niches (Fig. 1d-f). By including the number of climatic niches on an island, the NTIB improves our understanding of island biogeography and enables it to be generalised to all latitudes. This inclusion of the number of niches is also more ecologically meaningful than area, which has always lacked a clear ecological explanation ¹⁶.

Although the niche dimensions we considered here are important ecologically ⁴⁴, we acknowledge that the niche sensu Hutchinson ⁴³ is multi-dimensional and so other ecological dimensions should be considered to account for full niche complexity (e.g. pH, soil humidity, soil composition)^56,57. Since METAL can generate multidimensional niches, the consideration in the future of more ecological dimensions (ecological dimensions where there is long-term global high spatial resolution data) may improve our current estimates.

Area also influences positively species interception, a phenomenon called the target effect ^6–8. Total area of islands that compose the Krakatau archipelago was relatively small (24.45 km²) and probably affected immigration rates less than distance to mainland (distance between Krakatau Islands and Sumatra or Java is ~ 40 km). If our NTIB is used to compare species richness on different islands, I₀ could be calculated as a function of area A and distance to mainland d. For example, the following equation could be used. ${I}_{0}={m}_{1}\text{ln}\left(A+1\right)-{m}_{2}\text{l}\text{n}(d+1)$, with m₁ and m₂ two constants.

Area might also affect extinction rates; the higher the area, the greater population size and the lower the extinction rate ^38,58. Although E_s did not vary here (E_s was fixed to 1 species.yr^− 1), E_s could also be adjusted to account for the influence of area on extinction rates if our model is used to compare different islands. In our study, we assumed that this effect of area on extinction rates was implicitly considered through B_s, the higher the number of species at saturation, the lower the extinction rate at B_t < < B_s (and F_t≈0; Eq. 8, Fig. 3).

We suggest that considering higher initial extinction rates is important to better reproduce early island colonisation, because this allows a better reproduction of greater species turnover generally observed at the beginning of colonisation ¹⁷.

Our NTIB was well suited to birds because they are mobile and widespread ¹⁹. It would be interesting to test our model on other taxonomic groups that might exhibit different turnover rates ³⁸. Note that our NTIB can adapt to taxonomic groups for which short-term extinction rates are smaller or even negligible; for example, in Eq. 9 (Methods), σ can be chosen low enough to have F₀ close to 0 (Fig. 3), which implicates F_t negligible so that E_t (Eq. 10) is largely driven by G_t (Eq. 8). Indeed when σ = 0 and E_t=G_t, we refind the classical dynamic model proposed by MacArthur and Wilson ⁷, although area A is here replaced by the number of climatic niches M and therefore species richness at saturation B_s.

The Krakatoa volcano eruption sterilised the island on August 27, 1883 ⁵⁹. The current configuration of the archipelago is therefore young and our NTIB, which does not explicitly consider speciation, reconstructed well the species richness dynamics and associated turnover. On older islands, our NTIB may therefore be less accurate if speciation is not explicitly considered; observations and theoretical models have shown that this process is also important to explain biodiversity dynamics ^{13–15, 60}. Speciation could be integrated in our model in Eq. 5 (Methods). Immigration and speciation equal 0 at species richness at saturation B_s, however. B_s was determined by Eq. 7 through the estimate of ϕ = 0.0005. Because M = 105,082 niches (determined by METAL), B_s = 52.5 species. (For the Krakatau Islands, it is therefore unlikely that the absence of a direct implementation of speciation in the model had an effect on our estimate of B_eq=48 (47–51) species because our estimate is only slightly below B_s = 52.5 species.) For more mature or distant islands, we think that speciation should be integrated into the model to explicitly account for high level of endemism observed in some remote islands ^6,60−62.

An important prediction from our model, due to the fact that B_s strongly influences B_eq, is that islands far from mainland should have a greater proportion of endemic species, a prediction that might hold providing island age and dispersal capacity of a taxonomic group are accounted for ⁶⁰; this arises because potential niches of islands close to the mainland are rapidly filled with existing species originating nearby in contrast to remote islands where speciation is the only niche-filling alternative to the low immigration rate ²⁷. This prediction is consistent with some studies that have suggested that patterns of species accumulation through evolution in remote islands is analogous to islands close to continents where species gain takes place through immigration ⁶². The author proposed that this might suggest that universal principles may underly processes of community assembly. Studies have found a positive correlation between species richness and the level of endemism in islands ⁶³. Although this may also be explained by some methodological considerations or misinterpretations ^64,65, the correlation may be due to higher endemism when the number of available niches, and therefore species richness, is greater. As mentioned by Witt and Maliakal-Witt ⁶⁶, speciation may be both accelerated and impeded by niche availability. We therefore suggest that the universal mechanism mentioned by Gillespie ⁶² may be related to niche availability that fixes the number of species that can establish in an island either by immigration or speciation, a mechanism recently suggested to explain large-scale patterns in biodiversity or niche saturation in the marine and terrestrial realms ^31–33. Distance to mainland is also important because it affects immigration rates and especially I₀ in our NTIB and therefore, initial values of I_t. Among values ranging from 0.71 to 6, the best estimate was I₀ = 1 species.yr^− 1 (0.9–1.1). Such a value is relatively high, which can be explained by the closeness of the Krakatau Islands to the mainland, i.e. Java and Sumatra (Western Indonesia).

Since the development of ETIB, many models have been proposed to improve our knowledge of the processes that shape insular biodiversity patterns ^{15,23–28,67−69}. Among models, the general dynamic theory of oceanic island biogeography has significantly increased our knowledge of how species richness and associated biological rates may evolve on volcanic islands ^14,15,20. Island geodynamics affects local climate and environment that in turn alter biodiversity dynamics. Since we determined a unique number of niches for each island, our model is a simplification of real life and the number of niches will inevitably change as islands evolve in term of elevation, size and configuration, or as climate changes. High-resolution monthly climatologies were the only data available at the time of our analysis but as climatic data becomes more accessible (e.g. on a year-to-year basis) M - and therefore B_s - can be reassessed making B_eq a more dynamic equilibrium. B_eq is therefore not constant through time in the NTIB in contrast to the ETIB. Not only species richness is likely to fluctuate around B_eq through immigration-extinction dynamics (and on more mature or/and remote islands through speciation) but B_eq also changes as a function of island geodynamics and climate or environmental change, whether natural or anthropogenic. It follows therefore that equilibrium cannot be reached and that species richness fluctuates around an attractor that is permanently shifting as environmental conditions change ⁷⁰. The NTIB is therefore a nonequilibrium model. Our nonequilibrium model remains a simplification of the reality and some further processes (e.g. speciation) could be implemented in future versions to make it more useful to understand eco-evolutionary dynamics or to consider island geodynamics ^{13–15, 18,23,67,68}. Finally, we acknowledge that a consideration of the trophic structure of an island is important in the species richness that is supported ^25,71. Birds may depend upon the presence of predators and the vegetation type, the latter for food, for cover and for their nest sites and vegetation depends upon the substrate and the number of climatic niches. Future versions of the model may be adapted to consider the trophic status of a taxonomic group.

In this paper, we show that insular species richness is highly influenced by the number of climatic niches available on an island. This island property enables us to generalise the ETIB to all latitudes, reconciling the theory with TEI; this is even when niche definition in our study was not exactly as envisioned by Lack ^11,12 who defined it in terms of resource ⁷². When Mac Arthur and Wilson said “There exists within a given region of relatively uniform climate an orderly relation between the size of a sample area and the number of species found in that area”⁶ they realised that their theory was only valid for islands belonging to a similar biome. In our NTIB, the number of climatic niches not only enables the area to be considered but we can also weight the area by the latitudinal influence and this is where our NTIB has better ecological relevance.

Our NTIB nevertheless remains based on the MacArthur and Wilson’s pioneering theory and while our implementation of a short-term extinction rate into our NTIB is an improvement to account for higher turnover rates observed at the beginning of colonisation, we do not think this alters their original theory drastically; the only difference is that the total extinction rate becomes non-monotonic. The most important development in our NTIB is, in our opinion, the consideration of the number of niches (here the climatic niches) that can be recalculated as island environment changes, making our NTIB a nonequilibrium model at the time scale of an island’s life cycle. There has been a debate whether or not biodiversification follows an equilibrium model ^73,74. A recent molecular phylogenetic survey of the Avian communities at four Macaronesian archipelagos (e.g. Azores, Madeira, the Canary Islands and Cape Verde) has provided evidence that a diversity plateau can be rapidly reached and remain stable for millions of years, supporting an equilibrium ⁷⁵. It remains to be understood if such results can be generalised to all oceanic islands and views on this important subject remain controversial ^53,76. We think that our NTIB may help to resolve this controversy because it suggests that the interplay between the timing needed to reach the equilibrium and the frequency of the perturbations or the timing to next environmental changes is critical; an equilibrium might never be achieved if the environment changes before an equilibrium is reached.

Our NTIB is a generalisation of ETIB, the latter being a particular case when the short-term extinction rate is nil and when the environmental regime is stable. Along the life cycle of an island, environmental changes are likely to occur either through climate change or because of island configuration ^13–15. When this occurs, the number of niches is altered, which affect species at equilibrium and a new dynamic occurs. Our NTIB could therefore be used as part of the general dynamic theory of oceanic island biogeography developed by Whittaker and colleagues ^13–15. Taken together with other works ^15,22,60,77, we think that our findings may help to improve our understanding of island biodiversity dynamics and to progress toward a new synthesis of island biogeography. Our results have important implications for ecological restoration and our model could be applied (i) to determine the degree of direct human disturbance on species richness and (ii) to examine how climate change might affect island biodiversity, because B_s in our model is fixed by the number of available climatic niches that will be altered as climate changes.

ACKNOWLEDGEMENTS

This work was supported by the ‘Centre National de la Recherche Scientifique’ (CNRS), the Research Programme CPER CLIMIBIO (Feder, Nord-Pas de Calais), the regional programme INDICOP (Pas-de-Calais) and the ANR project TROPHIK. The authors also thank the French Ministère de l'Enseignement Supérieur et de la Recherche, the Hauts de France Region and the European Funds for Regional Economical Development for their financial support to this project.

Competing financial interests

The authors declare no competing financial interests

Data accessibility statement

The biological data that support the findings in this study are available in Supplementary Table S2-S3. Data on plants, herpetofauna and birds originated from Blackburn and colleagues³⁷.

AUTHORS CONTRIBUTION

GB conceived the study and designed the models. GB, LK and EG prepared the data. GB and LK made the data analyses. GB prepared the first draft. GB, RRK, LK, CL and EG discussed the results and contributed to writing.

Materials and correspondence

Correspondence and requests for materials should be addressed to G.B. ([email protected])

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No competing interests reported.

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A niche-based theory of Island Biogeography

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Abstract

Figures

Introduction

Materials And Methods

Biological data

Environmental data

Calculation of the number of climatic niches

Step 1: building of climatic niches

Step 2: niche-climate interaction

Statistical analyses

Relationships between observed richness, area, the number of climatic niches and distance to mainland

Model of island biogeography

Description of the model

Test of the model for Krakatau islands

Results

Relationships between species richness, area, the number of climatic niches, distance to mainland and latitude

A dynamic model including the number of climatic niches

Discussion

Concluding Remarks

Declarations

References

Additional Declarations

Supplementary Files

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