The dynamics underlying avian extinction trajectories forecast a wave of extinctions

Abstract

Population decline is a process, yet estimates of current extinction rates often consider just the final step of that process by counting numbers of species lost in historical times. This neglects the increased extinction risk that affects a large proportion of species, and consequently underestimates the effective extinction rate. Here, we model observed trajectories through IUCN Red List extinction risk categories for all bird species globally over 28 years, and estimate an overall effective extinction rate of 2.17 × 10⁻⁴/species/year. This is six times higher than the rate of outright extinction since 1500, as a consequence of the large number of species whose status is deteriorating. We very conservatively estimate that global conservation efforts have reduced the effective extinction rate by 40%, but mostly through preventing critically endangered species from going extinct rather than by preventing species at low risk from moving into higher-risk categories. Our findings suggest that extinction risk in birds is accumulating much more than previously appreciated, but would be even greater without conservation efforts.

1. Introduction

Recent global biodiversity loss is estimated to be at least one hundred times pre-human levels [1–3]. However alarming, these estimates may be too optimistic [4]. Estimates of current or recent extinction rates have typically been based on the numbers of species within a particular group that we know or suspect to have gone extinct over a set period of time [5,6]. However, this simple calculation combines species that are currently not at risk with those whose populations are declining but that have not yet been lost [7]. Given that species must decline from ‘not at risk’ through various levels of risk before extinction, including these trajectories in calculations would offer a more comprehensive measure of ongoing extinction dynamics. Here, we estimate the overall effective extinction rate from changes in the IUCN Red List [8] categories of extinction risk for all 11 064 recognized avian species over 28 years (1988–2016), and assess the impact of conservation efforts on this rate.

2. Material and methods

The IUCN Red List uses seven categories to classify extinction risk: least concern (LC), near threatened (NT), vulnerable (VU), endangered (EN), critically endangered (CR), extinct in the wild (EW) and extinct (EX). The classification of a species changes if it becomes more or less threatened over time, and we assume that this process can be modelled as a time-homogeneous Markov process with annual transition matrix Q. (We found no evidence of a trend over time that suggests a more complex model to better describe the data.) This process has EX as the absorbing state, because once a species is extinct, it will not re-appear.

The ongoing rate of extinction is calculated from Q, using standard Markov chain theory [9], as follows: let R denote the 6 × 6 transient segment of Q, that is, Q without the row and column EX (table 1). The matrix F = (I − R)⁻¹, where I is the identity matrix, is the fundamental matrix of Q: entry f_ij of F is the expected number of times that a species currently in the ith category will be in the jth category before going extinct. The expected time until extinction for each transient starting state is, therefore, T = Fc, where c is a 6 × 1 column vector of ones. Let K be a 1 × 6 vector with fractions describing the current distribution of species over the transient extinction risk categories (ΣK = 1; table 1). The average time to extinction is then KT, and the rate of extinction is the inverse of the average time to extinction: (KT)⁻¹. Thus, we can calculate the scalar extinction rate from transition matrix Q, which is based on transitions between all extinction risk categories, not just between the most threatened categories and EX.

Table 1.

Annual rates at which bird species moved between IUCN Red List categories. The values are based on genuine movements between categories (see §2 for abbreviations) from the years 1988–2016. For example, the value in row NT and column VU is the probability (0.0024) that a species currently classified as NT will next year be classified as VU. Thus, values across each row sum to one (with rounding errors). Shading intensity indicates the magnitude of transition rates, with reds denoting movement to higher, and greens denoting movement to lower, risk levels. #spp gives the numbers of currently recognized species per category in 2016, including extinct species, and K is the distribution of species over categories in 2016 excluding species already extinct. CR includes CR(PE) and CR(PEW). Lifetime T is the expected time to extinction in years for a species currently in a given category (see §2). ‘with conservation’ is the scenario where rate estimates include both up- and down-listings between extinction risk categories. ‘without conserv.’ is the scenario where estimates exclude those down-listings that were the result of conservation efforts.

from	probability (× 10−4 yr−1) of transition to category							#spp	K (%)	lifetime T (yr)
	LC	NT	VU	EN	CR	EW	EX			with conservation		without conserv.
LC	9993	5	2	0	0	0	0	8417	76.0	5161	(3770–7502)	3347	(2736–4287)
NT	6	9967	24	1	3	0	0	1017	9.2	3959	(2544–6230)	2161	(1578–3062)
VU	1	11	9950	33	5	0	0	786	7.1	3432	(2090–5664)	1691	(1140–2566)
EN	0	6	18	9937	37	1	0	461	4.2	3054	(1696–5253)	1371	(839–2241)
CR	1	1	6	57	9898	32	5	222	1.8	2503	(1226–4612)	1015	(537–1849)
EW	2	2	4	14	142	9679	156	5	0.1	1366	(482–2997)	598	(252–1249)
EX	0	0	0	0	0	0	104	156		0		0
	weighted average:									4780	(3418–7093)	2985	(2400–3893)

We estimated Q from the extinction risk categories of 11 064 bird species in 1988, 1994, 2000, 2004, 2008, 2012 and 2016 (the years in which the status of all species has been assessed) according to the IUCN Red List, which is based on data provided by BirdLife International [10,11]. Improved knowledge about taxonomy or threat factors was retroactively applied [10,12] (electronic supplementary material, Data). We used a Bayesian algorithm (electronic supplementary material), which allowed us to take into account uncertainty about the status of species, including those CR species tagged as ‘possibly extinct’ (PE) or ‘possibly extinct in the wild’ (PEW).

3. Results

From our estimate of the full matrix Q (table 1), we estimate the expected time to extinction per species and therefore its inverse, the per-species, per-year extinction rate: the global average across all birds in 2016 was 4780 years (95% credible interval: 3418–7093). (Henceforth, intervals following estimates are 95% credible intervals.) This corresponds to an overall extinction rate of 2.17 × 10⁻⁴ (1.41–2.92 × 10⁻⁴)/species/year (≈2090 extinctions per million species years (E/MSY) [13] but see electronic supplementary material, Methods). Because times to extinction are exponentially distributed, the median time to extinction is considerably shorter than the mean: 50% of present-day species would be lost already after log_e(2) · 4780 = 3313 (2369–4917) years. This projection is 1000-fold shorter than the 3 Myr estimate for pre-human avian species durations [14].

Importantly, our Q-based estimate of the time to extinction, which takes into account transition rates between all categories from LC through EX, is much shorter than traditional estimates that only count transitions to EX. To illustrate the underestimation of the extinction rate caused by lumping all non-EX categories and considering only transitions between ‘non-EX’ and EX, we can sum the product of the columns labelled ‘EX’ and ‘K’ in table 1 to get the per-year extinction probability of an average species: 1/24 492 (1/42 788–1/15 983)/species/year. Thus, lumping all non-EX categories causes a 24 492/4780 = 5-fold (3.4–8.5) overestimation of the time to extinction, because it neglects the net tendency for species at low risk to move into higher-risk categories. More directly, consider that during the past 500 years, about 187 of 11 064 avian species are documented to have gone extinct [15]. If the per species per year probability of extinction is p_e, then the fraction of species expected to be extinct after 500 years is 1 − (1 − p_e)⁵⁰⁰. Equating that fraction to 187/11 064 yields an expected time to extinction of p_e⁻¹ = 29 333 years: six times longer (4.1–8.6) than our current estimate based on Q.

To illustrate how the tendency for low-risk species to move to higher-risk categories affects the extinction rate, we used the matrix product QK (see §2) to project the classification of the present-day species far into the future (figure 1). We emphasize that this is an illustration of the process currently taking place and not a prediction of what will happen in the future, because Q would not remain constant over such long time periods. During the next 500 years, this approach suggests that 471 (226–589) species would go extinct, about three times as many as we have lost over the past 500 years. About 109 of these are projected to be species currently classified as ‘least concern’. The graver problem is that most species become more threatened. This build-up of extinction risk [16] then causes a sharp increase in the number of extinctions. Using the current Q, this would last for about 2000 years, after which the wave gradually fades as ever fewer species remain under this illustrative model.

Figure 1.

Illustration of ongoing bird extinction dynamics as implied by the rate matrix Q, based on the rates at which bird species have moved between IUCN Red List categories from 1988 to 2016. We project these dynamics to illustrate how current bird species diversity would hypothetically decrease in the future given recent trends, rather than to represent realistic predictions, because Q is unlikely to remain constant over this time period. Solid lines: projected extinctions based on Q estimated using all observed category transitions. Dashed lines: projected extinctions based on Q estimated without category transitions attributed to conservation efforts. (a) Projected yearly number of extinctions, which first rise as the extinction wave passes, and then ultimately fall as the pool of species shrinks. (b) Projected changes in the numbers of species in each extinction risk category, with (c) showing magnified detail over the first 500 years during which many species become more threatened. (Online version in colour.)

To gain insight into the overall effect of global conservation efforts [3,17] from 1988 to 2016, we estimated Q excluding category changes for species whose status, owing to conservation action, improved sufficiently to qualify for down-listing to a lower Red List category, but including category changes for six species down-listed owing to natural factors (electronic supplementary material, table S1). As expected, conservation has had the largest impact on the most threatened categories (table 1). For instance, the fate of species categorized as CR may seem less dire based on recent trajectories than their category implies, because they are twice as likely to improve as to deteriorate (table 1). Without conservation, however, these species are twice as likely to deteriorate as to improve (electronic supplementary material, table S2). Conservation efforts resulting in the ‘down-listing’ of a single species from CR to EN extend that species' expected time to extinction by 551 years, from 2503 to 3054 years under our model (table 1). Efforts targeting CR species increase the expected time to extinction of LC species as well, because these will become CR before going extinct. Thus, global conservation efforts have increased the projected time to extinction of the world's bird species by 1795 (44–4045) years per species, from 2985 to 4780 years (table 1), resulting in 40% (1.4–60%) reduction of the effective extinction rate. These estimates (electronic supplementary material, table S2) are very conservative because they consider only conservation efforts that resulted in improvements in status that were of sufficient magnitude to down-list species to lower categories of risk, while conservation actions presumably more often allow species to remain in their current category or to transition to more threatened categories at a lower rate [18].

4. Discussion

Red List assessments of extinction risk are based on a broad literature on population demography [19] so that different species may qualify under a particular IUCN Red List category for very different reasons and may have substantially different population sizes, range extents and threatening factors. Owing to inaccurate estimates of e.g. population size, rate of decline or extent of occurrence or owing to time-lags in information reaching Red List assessors, some assessments will be erroneous. It is challenging to model such error. We assumed that species may be erroneously classified in a category adjacent to the true category, including the distinction between CR and EX, although Red List assessors are very cautious about assigning taxa to EX. (Most media stories about ‘lazarus’ bird species relate to species still classified as critically endangered, rather than extinct.) Compared with assuming that assessments are error-free, our modelling of error yields lower estimates of extinction rate (electronic supplementary material). Furthermore, deteriorations in status are more likely to go undetected than improvements, because species benefiting from conservation action tend to be well monitored, such that our estimates of the rates at which species are moving towards extinction may be conservative. Because some extinction risk categories contain few species, estimates of their transition rates are also influenced by the choice of prior. Appropriate choice of priors and modelling of assessment error will, therefore, likely be crucial to better estimate current extinction rates.

Importantly, however, transitions of large numbers of species through broad classes of relative extinction risk [19] provide useful information on the dynamics of extinction given the diversity and pattern of human impacts on the natural world. As shown in the electronic supplementary material, relaxing simplifying assumptions of the model or using alternative priors on transition rates and classification error has little effect on estimates of the extinction rate compared with estimates that treat all extant species as secure. Comparatively few avian species are currently critically endangered [8] and many of these appear to be benefiting from conservation efforts [5,12,20,21], so failure to account for species becoming more threatened leads to considerable underestimation of effective extinction risk. We expect that analyses for other taxa would show similar patterns. Most other taxa are less well studied than birds and contain a significant proportion of data deficient species, which complicate risk assessment [22]. In such cases, information about e.g. ecology, geography [23], traits [24] and phylogeny [25] could be combined to assign prior probabilities to the categorization of these species.

The build-up of potential future extinction should inform assessment of progress towards international conservation obligations such as the UN Convention on Biological Diversity's Aichi Targets [26]. Conservation efforts have mainly targeted species that are already threatened. According to our calculations (table 1), these efforts have considerably extended the projected time to extinction of all avian species, because all species become threatened before going extinct. However, such efforts may not be the most cost-effective strategy in the long term [27] because they do not prevent least concern species from becoming more threatened, and thus do not prevent increasing numbers of species in immediate need of conservation. Therefore, it is important that any post-2020 biodiversity framework negotiated through the Convention includes a renewed target to prevent extinctions, but, as emphasized by our analyses, also to prevent non-threatened species or those at low risk from moving into higher-risk categories, i.e. keeping common species common and improving the status of currently threatened species. This latter emphasis would help dampen an ever-building wave of conservation need.

Data accessibility

The data and code used in this study are available as electronic supplementary material.

Authors' contributions

M.J.M. and F.B. conceived the study. S.H.M.B. oversaw data collection and compiled the dataset. M.J.M. prepared data for analysis. F.B. developed algorithms and analysed the data. A.O.M. and F.B. interpreted results and designed model comparisons. M.J.M., F.B. and A.O.M. framed and wrote the manuscript with input from S.H.M.B. All authors approved the final version and agree to be held accountable for the work it presents.

Competing interests

The authors declare no competing interests.

Funding

Funding was provided by the Swedish Research Council (VR) (M.J.M., grant no. 637-2013-274) and NSERC Canada (A.O.M.).