Microhabitats, latitude (solar radiation), abundance of water and food resources, competition, stable temperatures, vegetation diversity (therefore, food chains), and geography among other factors. The best way to get an answer to this question is keeping on the good reading, I'm attaching some interesting literature on this topic. Kind regards.

In short: the a.m. ecologic parameter in the tropics are at the physiological optimum of most species, which however compete on limited resources. The ambient conditions at higher lattitudes put more stress on overall living condtitions - for many species below their physiological minimum. The remaining fitter and adapetd species have therefore more resources available, leading to generally higher specific populations, than in the tropics.

Two great books that give a good introduction to this are:

G. MacDonald. 2001. Biogeography: Introduction to Space, Time and Life.

Cox & Moore. 2010. Biogeography: an ecological and evolutionary approach.

Evolutionary processes: allopatric, sympatric, parapatric, adaptation, mutation etc. Ecological processes (biotic and abiotic): predation, competition, mutualism, habitat heterogeneity, latitude, time, climate stability, energy availability, area, topography, and disturbance.

So, you answer depends on scale (temporal and spatial), marine vs. terrestrial, and which group of animals/plants etc you are looking at too.

@Gerardo, I have read books saying those various factors on the diversity, but didn't discuss the details. Thank you very much. I will read these as soon as possible

@Stephan, Thank you, I didn't think of it in that manner.

@Rachel, I am dealing mainly on the marine setting, and I haven't done any reading on the evolutionary approach. Thank you for the suggestion.

With marine diversity, you have to also consider things like: depth (shore, shelf, bathyal, abyssal, hadal), age of ocean basin, major currents, past connectivity to other oceans and continental shelf areas, upwelling, temperature, stratifiction, salinity, and sediment runoff. As well as considering what types of organisms you are looking at: benthic or pelagic, invertebrate or vertebrate etc, mobile vs sessile, reproductive capabilities and dispersal capabilities of progeny, and competition, symbiosis and predation in communities. In high latitude regions, ice coverage and scouring impacts marine communties greatly, with productivity limited to just a few months in the summer. However, this productivity can be incredibly high. The Arctic is quite different in marine species richness to the Antarctic. But increased research is showing that both are a lot richer than previously thought, particularly the Antarctic (potentially due to it's isolation from other continents).

You might also want to consult papers by Crame JA who provides an deep time perspective on latitudinal diversity patterns in the marine realm.  In particular

Crame 2000, Evolution of taxonomic diversity gradients in the marine realm. Paleobiology 26 188 to 214

Crame and Rosen 2001 Cenozoic palaeogeography and the rise of modern biodiversity patterns in Geological Society of London Special Publication 194, 153 to 168

Crame 2002 Evolution of taxonomic diversity gradients int he marine realm a comparison of Late Jurassic and recent bivalve faunas  Paleobiology 28 184 to 207

There are several more recent papers by the same author on other aspects of these patterns.

The classic ecology answers have been very well addressed above, with excellent reading: Simply put: the more recourses and type of variations of these resources, allow for more radiation and expansion into more sub-species and species into various niches.  Also the Tropics can be more dimensional with the tree canopies.  One other item: the more north you go, the more adaptations have to deal with cold and limited resources (fur, hibernation, fat storage, "anti-freeze in insects" etc...).  In tropical or costal climates there is not the "kill-off" due to sever cold and dry; i.e.  "freeze-drying" of roots of trees (for plants), lack of food from long winter (animals),  that can happen in some winters.  Hence warmer climates are less likely to "kill off" species.  Warmer climates have many more parasites though!   I like David's and Rachel marine information, I tend not to think of "marine" when it the larger part of the planet! ( I need to re-think, including the oceans!) 

I agree college  Heidi Fain's answer

The WHY of latitudinal taxonomic diversity is the mother of all biogeographic questions. Most answers so far are too complex to my taste and partly tautological (like most species grow at optimal temperatures). Such clear biodiversity patterns may have clear drivers. Let me try to contribute with a short story and a question.

Indeed, at the global extent and a resolution of say 109 km2 diversity in 2D for mammals, reptiles, amphibians and seed plants on land peaks at equatorial latitudes/bio-climates. However, this relation applies best to Asia and the Americas, less so to Africa. Possibly because Africa has less of a humid tropical belt, suggesting high water availability at constant, moderate (compared to the desert belt) temperatures may be the correlate. However, when we look only at endemic plants the Mediterranean latitudes/bio-climates enter the scene as a botanical biodiversity hotspot. Here, the relatively high (compared to the cloudy equatorial belt) received solar radiation suggest itself as a hypothesis. See also Kraft & Jetz 2007 referenced in the attached.

At the continental extent and say at the 104 km2 resolution, the nice latitudinal gradient disappears, at least in Europe and West-Asia. Here the biodiversity appears to associate with altitudinal range and the Mediterranean hotspots appear more montane than Mediterranean (attached).

The global pattern of marine biodiversity is less known to me. What I take from your answers so far is that oceans show a similar latitudinal taxonomic gradient, high at the equator, low at the poles. Is that correct? If so, ambient temperature and received solar radiation could be the correlate as on land. And altitude (depth; 3D) could be an additional variable as well as on land.

Article Fine resolution distribution modelling of endemics in Majell...

Like most things in evolution, the answer is probably a complex and shifting interplay of many co-dependent factors. Although each of the following might be considered naive in isolation (and I have certainly presented them simplistically), they are three appealing hypotheses for explaining the latitudinal diversity gradient. There are many others.

[1] Low-latitude areas have a greater incidence of solar energy, and often a higher air moisture content than higher-latitude areas. This fuels an elevated primary-productivity, providing more resources to the ecology as a whole, enabling competition, specialization and speciation. More sun + water => more plants => more biomass => more trophic levels => more diversity.

[2] Tropical areas experience diminished seasonal variations. Without an annual fluctuation in resources, species can concentrate on their niche food supply and reproductive strategy, rather than having to deal with annoying things like having to stockpile food, hibernate, migrate, co-ordinate and synchronise reproductive behaviours, or generally have their lives dictated by the seasons. Less hassle => more time for sex => more competition => more diversity.

[3] Elevated evolutionary rates are observed at low latitudes. The nature of evolutionary rates is far from being understood, but higher temperatures, shorter generation times and higher mutation rates might all play a part. Elevated evolutionary rates would make speciation "easier" since reproductive isolation would be achieved in less time. Faster evolution => quicker differentiation => more diversity.

As mentioned, there are plenty of other factors to consider, but the above are worth looking into and will no doubt lead you to (very reasonable) criticism of these hypotheses, and alternative mechanisms.

Bruce Archibald and I also tackled this topic in our 2010 paper available for download on my RG profile:

Archibald SB, Bossert WH, Greenwood DR, Farrell BD. 2010. Seasonality, the latitudinal gradient of diversity, and Eocene insects. Paleobiology, 36(3): 374 – 398.doi: 10.1666/09021.1

In many tropical and mediterranean environments, species have small ranges, often allopatric or parapatric with close relatives occupying very similar niches. In some groups, at least, local ( say a few km squared) diversity is no, or not much higher than in temperate and boreal regions. I think that climatic fluctuation has a part to play here, creating expanding and contracting refugia in relatively warm climates, but causing wipeouts and recolonisation nearer the poles. Here is one paper that considers some of these issues

The literature on this is gigantic. Probably the most recent wide-ranging review is

Turner JRG 2013  Energy and biodiversity.

Encyclopaedia of the Life Science.s John Wiley & Sons Ltd: Chichester http://www.els.net/ [DOI: 10.1002/9780470015902.a0022551]

This is written at advanced undergraduate and graduate student level, and for reseachers in other fields and cites other reviews. An extended abstract appears among my publications on this website; unfortunately the copyright holders don't allow me to post the full text.

Hi Danielle, this paper may help you

This is not true for all plant groups. Several recent studies could not find conclusive evidence for a latitudinal gradient in moss (Bryophyta) species richness - see Global moss diversity by Geffert et al. (2013) J. Bryol. 35(1): 1–11. DOI: http://dx.doi.org/10.1179/1743282012Y.0000000038