(a) The tropics had more evolutionary time. Speciation is generally a function of time, and unlike temperate regions subjected to frequent glaciations in the past, tropical latitudes have remained relatively undisturbed for millions of years, giving a long evolutionary time for species diversification. Test: compare the age of tropical and temperate lineages from fossil and molecular evidence; if the hypothesis holds, tropical clades should on average be older and temperate biotas should show signs of recent recolonisation after glacial retreat.

(b) Tropical environments are less seasonal, relatively more constant and predictable. Such constant environments promote niche specialisation, which leads to greater species diversity. Test: measure the breadth of diet, habitat and activity period of related species in tropical and temperate communities. The hypothesis predicts narrower niches and more overlap-free packing in the tropics.

(c) There is more solar energy available in the tropics, which contributes to higher productivity, and this in turn might contribute indirectly to greater diversity. Test: compare species richness against measured productivity across many sites at similar latitudes. If energy is the driver, richness should track productivity rather than latitude as such.

Why all three are offered together. They explain different things: (a) why there was time for species to appear, (b) why specialists can persist once they do, and (c) why enough resource exists to support many populations at once. None of them excludes the others, and the chapter presents them as hypotheses rather than conclusions because the question remains open.

What the slope is. The species-area relationship is a rectangular hyperbola on arithmetic axes, which becomes a straight line on a logarithmic scale, described by log S = log C + Z log A, where S is species richness, A is area, Z is the slope of the line, or regression coefficient, and C is the Y-intercept. Z therefore measures how fast species richness rises as area increases.

Its remarkable constancy within regions. Ecologists have found that Z lies in the range of 0.1 to 0.2 regardless of the taxonomic group or the region — plants in Britain, birds in California, molluscs in New York state all give amazingly similar slopes. That a single number should describe such different organisms in such different places suggests a general ecological rule rather than a local accident.

Its significance when the slope is steep. For very large areas such as entire continents, Z rises to between 0.6 and 1.2 — 1.15 for frugivorous birds and mammals in the tropical forests of different continents. A value near 1 means richness rises almost in proportion to area, because each continent contributes an almost entirely different set of species, having had its own separate evolutionary history. A shallow slope means additional area mostly adds more of the same species; a steep slope means it adds new ones.

Why it matters practically. Read backwards, the relationship predicts how many species will be lost when a habitat is reduced in area — which is the basis for estimating extinctions from deforestation, and for deciding how large a reserve must be to retain a given fraction of a region's species.

Why the curve flattens. The relation between species richness and area is a rectangular hyperbola, which rises steeply at first and then approaches a ceiling. The reason is that the number of species available in a region is finite. A small plot samples only some of them, so each addition of area finds several new ones. As the plot grows, most species in the regional pool have already been recorded, and further area adds only the rarest — so the gain per unit area falls steadily towards zero.

Why it does not flatten completely in practice. Expanding an area eventually crosses into a different habitat type, or a different region altogether, and then a fresh set of species appears. This is precisely why the slope becomes much steeper when very large areas such as entire continents are compared, with Z rising from 0.1–0.2 to 0.6–1.2.

What this implies for survey design.

(i) There is an efficient stopping point. Effort spent expanding a survey beyond the flattening of the curve buys very few additional species. Plotting a species-accumulation curve as the survey proceeds shows when that point has been reached.

(ii) Spread the effort rather than concentrating it. Several smaller plots in different habitats will record more species than one large plot of the same total area, because each plot begins again on the steep part of its own curve.

(iii) Never compare raw species counts from areas of different size. A larger sample will always yield more species. Comparisons must either use equal areas, or use the equation to standardise them.

What it reveals about biology: diversity is concentrated in small organisms. Among animals, insects are the most species-rich taxonomic group, making up more than 70 per cent of the total, so that out of every ten animals on the planet, seven are insects. Small body size means a single tree offers many separate niches — different leaves, bark, flowers, fruits, roots and stages of decay — where a mammal needs a territory. Short generation times also allow genetic divergence and reproductive isolation to accumulate faster.

What it reveals about our knowledge: the figures are not equally reliable. The mammal and amphibian counts are close to complete, because these animals are large, conspicuous and long studied. The invertebrate figure of 1,25,000 is a record of what has been found, and the estimate of at least two million insect species still awaiting discovery shows how far from complete it is. The uncertainty in our knowledge is concentrated exactly where the diversity is.

Why this is more than an academic gap. A large fraction of these species faces the threat of becoming extinct even before we discover them — nature's biological library is burning even before we have catalogued the titles of all the books stocked there. Undescribed species cannot be assessed, listed as threatened, or legally protected.

And a caution about using such figures. When comparing regions or arguing for conservation, remember that a low count may reflect low sampling effort rather than low diversity. This is the same difficulty that makes global estimates range from 7 million to 50 million species, and that leaves prokaryotes out of the count altogether.

The calculation. From log S = log C + Z log A, richness varies as S ∝ A^Z. Reducing area to 90 per cent of the original gives

\( \dfrac{S_{new}}{S_{old}} = (0.90)^{0.15} \approx 0.984 \)

So about 1.6 per cent of the species would be expected to be lost — a small figure, and this is the reassuring part of the arithmetic. A shallow slope means that losing area removes species slowly at first.

Why the real loss is likely to be greater.

(i) Fragmentation, not just loss. A road does not merely remove 10 per cent of the area; it cuts the remainder in two. When large habitats are broken up into small fragments, mammals and birds requiring large territories, and animals with migratory habits, are badly affected, leading to population declines. The species-area equation assumes one continuous area of the new size, not two disconnected halves.

(ii) Which 10 per cent matters. The equation treats all area as equivalent. If the cleared strip includes a river, a salt lick, a breeding site or the only patch of a particular soil, the loss can be out of all proportion to the area — Ehrlich's point that loss of rivets on the wings is more serious than loss of rivets on the seats.

(iii) Endemism raises the stakes. In a biodiversity hotspot, species may be confined to that region and found nowhere else, so a local extinction is a global one.

(iv) Roads bring more than roads. Access enables logging, hunting, settlement and the introduction of alien species — each of which is an independent cause of biodiversity loss.

The honest conclusion. The species-area relationship gives a lower bound on the expected loss, and a useful one. It is not the whole answer, because it counts hectares and ignores their arrangement and their contents.