Use the same conditional optimal normal-fault dip relation as in question 1, with $\delta =55^{\circ }$:The second panel of the original Mohr circle figure has ${\sigma }_3^{\prime }=1$ and ${\sigma }_1^{\prime }=2.03961$; its tangent from the origin has slope $0.364$. Resolving the stresses onto a $55^{\circ }$ plane places its stress point at that tangency. The diagram assumes negligible cohesion, a vertical maximum principal stress and an optimally oriented new or equivalently oriented sliding plane. Without those assumptions, a dip and a statement that sliding began do not uniquely determine the coefficient of friction.

For an Andersonian faulting regime appropriate to the stated normal fault, take ${\sigma }_1$ vertical, ${\sigma }_2$ north–south along strike, and ${\sigma }_3$ east–west. Thus the minimum horizontal compression is normal to the fault’s north–south strike. In an east–up cross-section, draw ${\sigma }_1$ vertically and ${\sigma }_3$ horizontally, with ${\sigma }_2$ perpendicular to the page. These are plausible regional principal stress directions, rather than measured directions uniquely recoverable from one photograph.

Allopatric speciation is the predominant classical model and is generally regarded as especially important in animals. Geographic separation directly reduces gene flow, making it easier for divergent adaptation and incompatibilities to accumulate. The exact frequency across all organisms and historical events is not directly observable; a universal numerical fraction is not established by this statement.

Evidence combines the geographic arrangement of close relatives, phylogenetic trees, genetic divergence and independently reconstructed barrier histories. Sister lineages on opposite sides of barriers, island radiations founded by colonization, and differentiated biological populations that remain reproductively isolated after contact are mutually reinforcing observations. They are stronger when separation is independently dated and the origin of reproductive barriers is distinguished from later range changes.

A concrete primary example is the comparison of 15 trans-isthmian snapping-shrimp pairs using allozymes and mitochondrial COI. Concordant genetic differences support separation of lineages by the developing Isthmus of Panama, but divergence varied substantially between pairs. This cautions against assigning every pair to one simultaneous final closure event.^[ref]

The inference is not exclusive. The island-palm study of Howea forsteriana and Howea belmoreana used sister relationships, island history, soil association and flowering-time differences to support a sympatric origin.^[ref] Such cases show that sympatric speciation is possible. Conversely, sister-species allopatry by itself cannot prove historical allopatry, because extinction and range shifts can change their present distributions. The case for the common mode rests on combined historical evidence and the widespread effect of barriers on gene flow.

Examples of prezygotic reproductive isolation, all acting before a zygote forms, include:

The first four primarily reduce mating or gamete transfer; the last can occur after mating while still preceding fertilization. These differ from postzygotic isolation, such as hybrid inviability or hybrid sterility, which acts after the zygote has formed. Distinguishing these stages prevents “premating” from being used as a synonym for every prezygotic barrier.

In allopatric speciation, geographically separated biological populations experience sufficiently reduced gene flow for divergence to accumulate through natural selection, genetic drift and other evolutionary processes. A barrier can split a former biological population, or a colonizing biological population can become isolated. The eventual species distinction requires persistent reproductive isolation, not merely physical separation at one instant.

In sympatric speciation, reproductive divergence originates without the initial geographic separation required by the allopatric model, at the spatial scale relevant to mating and dispersal. Divergent ecological selection and assortative mating, or some forms of polyploidy, can reduce gene exchange despite geographic overlap. Present-day sympatry alone does not establish this history: previously isolated species can meet through secondary contact. The difference concerns the geography of the origin of isolation, not whether the resulting species currently occupy different places.

One fossil-record study is Selectivity of end-Cretaceous marine bivalve extinctions by David Jablonski and others, which compared survival of marine bivalve genera across the end-Cretaceous mass extinction against their pre-event attributes. Geographically widespread genera had lower extinction intensity than narrowly distributed ones. In the same analysis, body size, burrowing versus exposed life position, and shelf bathymetric position were not significant selectors; the apparent feeding-mode contrast was concentrated in particular groups rather than establishing a universal feeding rule.^[ref]

The logic of the test is to define the pre-event genera at risk, classify their geographic ranges using pre-event occurrences, then compare the fractions becoming extinct. Using pre-event rather than surviving ranges avoids measuring the predictor after the outcome. A two-by-two contingency table gives an elementary broad/narrow-range comparison; a logistic regression can instead retain a continuous range measure and include correlated covariates. These are explanations of the inferential design, not a claim that this paper used that exact regression specification.

A persuasive interpretation must address unequal rock exposure, collecting intensity, taxonomic revision, incomplete occurrence records and the difference between local loss and global extinction. The important result is selective survival in a real fossil dataset and the failure of several plausible alternative predictors in that setting. It is observational evidence: geographic range can correlate with unmeasured ecological properties, so the association alone does not prove a unique kill mechanism.

Four documented examples, each tied to its actual context, are:

These examples demonstrate event- and group-dependent selectivity. They do not define one universal vulnerability ranking: the bivalve study, for instance, did not find body-size selectivity at the same end-Cretaceous genus-level event.

Extinction selectivity is systematic variation in the probability or rate of extinction among lineages with different traits, rather than trait-independent loss. Traits may be biological, ecological or geographical: for example, survival may differ between narrow-ranging and widespread taxa within the same extinction interval.

A test needs an explicit denominator of taxa at risk, a defined taxonomic level and time window, and a specified trait measurement. Regional disappearance is not automatically global extinction. Nor is an association necessarily a causal mechanism: traits covary with habitat, abundance and preservation, and their effects can change between background intervals and mass extinctions.

The along-strike rupture time is $L/v_r$, where $v_r$ is rupture velocity. Taking a representative crustal $v_r\simeq 3\mathrm{km}{\mathrm{s}}^{-1}$ gives about $2$ s for a $6$ km unilateral finite-source rupture. A different assumed rupture velocity changes this estimate. The local slip rise time at one patch is not specified and need not equal the whole-fault rupture time.

For comparable distance and ground conditions, the eastern observer lies in the forward rupture directivity direction. Radiation from successive patches arrives closer together, producing a shorter, more concentrated and generally larger-amplitude ground-velocity pulse. The western observer receives the contributions spread over a longer interval, generally with less concentrated shaking. This concerns pulse duration and amplitude; it does not imply an equally large permanent displacement at the eastern site.^[ref]

For distant observers approximately along strike, an elementary seismic travel time construction giveswhere $\beta$ is the shear-wave velocity. With $v_r=3$ and $\beta =3.5\mathrm{km}{\mathrm{s}}^{-1}$, these propagation contributions are about $0.29$ and $3.71$ s, respectively; finite local rise time broadens them. Double-couple radiation pattern, receiver geometry and local site response can change the observed amplitudes, so location east or west alone is not an unconditional intensity prediction.

Assuming pure dip-slip faulting, use an east–west striking, $65^{\circ }$ north-dipping normal fault, with the northern hanging wall moving down dip. In a right-hand-rule strike convention this is strike $270^{\circ }$, dip $65^{\circ }$, rake $-90^{\circ }$. The auxiliary nodal plane strikes east–west and dips $25^{\circ }$ south. The focal mechanism has a predominantly vertical P axis and a predominantly north–south horizontal T axis; the steep central direction is dilatational.

The sketch is a double-couple seismic moment tensor calculation, not a claim that first motions uniquely identify which nodal plane slipped. The mapped north-dipping surface supplies that additional geological choice.