The effects of climate change on biodiversity should depend in part on climate displacement rate (climate-change velocity) and its interaction with species' capacity to migrate. We estimated Late Quaternary glacial-interglacial climate-change velocity by integrating macroclimatic shifts since the Last Glacial Maximum with topoclimatic gradients. Globally, areas with high velocities were associated with marked absences of small-ranged amphibians, mammals, and birds. The association between endemism and velocity was weakest in the highly vagile birds and strongest in the weakly dispersing amphibians, linking dispersal ability to extinction risk due to climate change. High velocity was also associated with low endemism at regional scales, especially in wet and aseasonal regions. Overall, we show that low-velocity areas are essential refuges for Earth's many small-ranged species.

Urban residence is associated with a higher risk of some psychiatric disorders, but the underlying drivers remain unknown. There is increasing evidence that the level of exposure to natural environments impacts mental health, but few large-scale epidemiological studies have assessed the general existence and importance of such associations. Here, we investigate the prospective association between green space and mental health in the Danish population. Green space presence was assessed at the individual level using high-resolution satellite data to calculate the normalized difference vegetation index within a 210 × 210 m square around each person’s place of residence (∼1 million people) from birth to the age of 10. We show that high levels of green space presence during childhood are associated with lower risk of a wide spectrum of psychiatric disorders later in life. Risk for subsequent mental illness for those who lived with the lowest level of green space during childhood was up to 55% higher across various disorders compared with those who lived with the highest level of green space. The association remained even after adjusting for urbanization, socioeconomic factors, parental history of mental illness, and parental age. Stronger association of cumulative green space presence during childhood compared with single-year green space presence suggests that presence throughout childhood is important. Our results show that green space during childhood is associated with better mental health, supporting efforts to better integrate natural environments into urban planning and childhood life.

IntroductionIn this paper we settle several longstanding open problems in theory of indexability and external orthogonal range searching. In the first part of the paper, we apply the theory of indexability to the problem of two-dimensional range searching. We show that the special case of S-sided querying can be solved with constant redundancy and access overhead. From this, we derive indexing schemes for general 4-sided range queries that exhibit an optimal tradeoff between redundancy and access overhead.In the second part of the paper, we develop dynamic external memory data structures for the two query types. Our structure for 3-sided queries occupies @N/B) disk blocks, and it supports insertions and deletions in O(log, N) I/OS and queries in O(log, N + T/B) I/OS, where B is the disk block size, N is the number of points, and :I' is the query output size. These bounds are optimal.Our structure for general (4-sided) range searching occupies 0 ((N/B) (log( N/B))/ log log, N) disk blocks and answers queries in O(log, N + T/B) I/OS, which are optimal.It also supports updates in O((log, N)(log(N/B;l)/ log log, N) I/OS. remission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that topics are not ma& ,-,r distributed for profit or commercial advantage and that copies hear this notice and l;ht: full citation w the first page. To 'WV otherwise, to qmblish, to post on servers or to redistribute to lists. rcuuircs prior specific perrrission and/or a kc.PbDS '$9 Philadelphia PA Copyright ACM 1999 I-581 13-062-7/99/05...$5.00There has recently been much effort toward developing worst-case I/O-efficient external memory data structures for range searching in two dimensions 11,2,4,8,12,13,20,26,28, 291. In their pioneering work, Kanellakis et al. [13] showed that the problem of indexing in new data models (such as constraint, temporal, and object models), can be reduced to special cases of twodimensional indexing. (Refer to Figure 1). In particular they identified the 3-sided range searching problem (Figure l(c)) to be of major importance.In the first part of this paper (Section 2), we apply the theory of indexability [lo] to two-dimensional range searching problems. In indexability theory the focus is on bounding the number of disk blocks containing the answers to a query (access overhead) given a bound on the number of blocks used to store the data points (redundancy). The search cost of computing which blocks to access is ignored. We generalize the results in [26, 14:] and show a lower bound on redundancy for a given access overhead for the general 4-sided problem. We then show that this bound is tight by constructing an' indexing scheme with a matching tradeoff between redundancy and access overhead. The indexing scheme is based upon an indexing scheme for the 3-sided range searching problem with constant redundancy and access overhead.In the second part of the paper, we develop optimal dynamic external data structures for S-sided range searching ...