This increase in size within a group animals through time, i.e. larger species and larger species are constantly showing up on the evolutionary state, is a well known rule of biology.  We refer to this pattern as Cope’s Rule, named after an American paleontologist Edward Drinker Cope.  At broad levels, Cope’s Rule is definitely true.  The start of life on this planet was microscopic and now we have whales and redwoods. However, a mixed bag of patterns of increasing, decreasing, and no change is body size is seen in organism as diverse as molluscs and mammals.  Even within a single group like mammals, some groups like rodents show little change with time, while whales get larger with time, and horses get both bigger and smaller.

Godzilla appears to be following Cope’s Rule.  So how big will Godzilla be in 2050?  Rhett Allain at Dot Physics calculates this to be 170 meters.  But I, as nerds debating meaningless things will, disagree.  Allain appears to use multiple dates for each iteration of Godzilla.  For example, the 50 meter Godzilla occurs in movies from 1954-1975 and again in 2001.  In Allain’s plots, 50 meter Godzilla occurs in 1954, 1960, 1970, and 1991.  This artificially weights the analysis and treats separate iterations, i.e. species, of Godzilla the same as a single individual of the same species of Godzilla.  To restate, different sightings, e.g. different movies, of the same individual of Godzilla are put into the analysis multiple times even though they are presumably the same individual. I prefer to use a standard paleontological method, specifically the size at first occurrence.

So redoing the analysis, I first find no actual statistical increase in size with time.  That is because the second smallest Godzilla, 55 meters, did not appear until 1999 (purple dot in the graph), the regression between size and time is not significant with this point included.  I am also not sure why the artist of the plot decided to place the 55 meter purple Godzilla out of temporal order. If purple Godzilla is thrown out of the analysis we get the equation

Log 10 Height = -13.94 + 0.008 Year

So in 2050, I calculate that Godzilla would be 288.4 meters not 170 meters.

So why is Godzilla obtaining ever larger sizes with time?  Skyscrapers.  Skyscraper height has increased dramatically over the last century.  For Godzilla to continue to plow through buildings in major metropolises, a more formidable size is needed.  Of course this size change can only be evolutionarily adaptive if it changes the fitness of Godzilla, i.e. in the simplest case the number of offspring passed to the next generation.  If Godzilla is able to topple buildings this might allow for greater acquisition of resources in this case food in the form of people. This would increase the lifespan of Godzilla allow for more reproduction or allow for greater amount of energy to be passed to the offspring increasing their rate of survival  Or perhaps toppling buildings is a sexual display that sexual partners cue on.  Sexual selection!

Of course the real problem of a 55,000 ton Godzilla is the urine production. Using the handy Kaiju post, we can quickly calculate that, 151,436,928 12,921,400 gallons per day.  That is about 1.8 about quarter of the hold of the largest production oil tankers.

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For background, biologists know that much of an animal’s biology, everything from limb length, heart volume, lung capacity, territorial range, and urine production, all scale with body size. We use an equation, based on data from lots of animals, to calculate all of these. The equation usually takes the form of Variable of interest = a (mass)^b. a the intercept usually varies among groups like birds, mammals, frogs, carnivores, nocturnal, carnivores, etc.. b the slope can as well but usually scales as a multiple of 0.25.

By knowing the mass of an animal, we can gain some insights even in the absence of direct observation, like how many people a day a Kaiju would consume.

Many people questioned basing my equations on Komodo Dragons, arguing that Kaiju were more like mammals, other reptiles, birds, fish, or crustaceans. A commenter also noted that the weights of each Kaiju are known.

So with actual weights and assuming that Kaiju are like different types of organisms in their physiology, the number of people per day needed to sustain a Kaiju is

Of course I assumed that the tons were not metric tons but long tons. At least one commenter disagreed. If we use metric tons instead

A commenter also suggested that digestive efficiency would not be 100%, i.e. a that all the energy of human would not be accessible to a Kaiju. Perhaps Kaiju are complete crap at digesting bone or their guts are just designed really poorly. Assuming they have an efficiency of 50% and long tons

So if Kaiju are essentially mammals, complete rubbish at digestion, and assuming long tons, then the largest Kaiju, Slattern at 6,750 tons, would require 314.2 people per day. In 61.7 years it could eat its way through Hong Kong, assuming of course there were no births and no other non-Kaiju related deaths. Who has time for sex when they’re running from a 6750 ton alien?

But what about other aspects of Kaiju biology?

In the table above, I calculate different biological features of the largest Kaiju, Slattern, based on different animals (mammals, birds, frogs, fish, etc.). Slattern’s heart beat would be an order of magnitude slower than most humans, beating less than 5 times per minute. The heart would be anywhere from 2 tons upwards of 30.5 tons. Based on either birds or mammals, it wouldn’t even be able to even muster a single offspring per birthing event. On the other hand if Kaiju are reptilian, we are all severely screwed. Lifespan would be measured in 100’s of years.

Piss…how much would it produce? Every day a Kaiju, if mammalian, would produce about 40 barrels worth of urine. If Kaiju are like frogs, then Slattern would produce 92 Olympic swimming pools worth of urine per day (roughly 0.8% of flow rate of the River Thames).

With the scariness of that settling in, the density of Slatterns supported on Earth could be alarming. At the smallest this would still top out over 20,000. It strikes me that Kaiju are probably territorial. Why else would they always be so damn angry and smashing things all the time? If this is true then the numbers drop radically. If they are avian or mammalian, then Earth could support one, like beta fish in an aquarium. If on the other hand they are like hunting primates or lizards, we are looking at thousands.

McNab, B.K. (2009) Resources and energetics determined dinosaur maximal size. PNAS 106:12184-12188

Nagy, K.A., Girand, I.A., and Brown, T.K. (1999) Energetics of free-ranging mammals, reptiles, and birds. Annu. Rev. Nutr. 19:247-277

Peters, R.J. (1983) The ecological implications of body size. Cambridge University Press.

The post How much urine can a Kaiju produce? And other fun information first appeared on Deep Sea News.

 The short answer is not as many as you think.

I spent Saturday watching Pacific Rim.  The movie has everything I want in a flick—big-ass sea monsters, big-ass robots, and big-ass robots fighting big-ass sea monsters.  Pacific Rim is undoubtedly the no-holds-bar-over-the-top-action-flick-who-gives-damn-about-plot-or-character-development-o-yeah-it-has-Ron-Motherf’n-Perlman kind of movie we all need.  My wife disagrees but I still love her.

The stars of Pacific Rim are the Kaiju (怪獣) a Japanese word that literally translates to “strange creature”.  Kaiju films are a staple of Japanese cinematography with Kaijuu, like Godzilla, Mothra, or Rodan, attacking each other or better yet a whole city.

Being the complete nerd I am, I waited patiently until I heard the magical words I needed to hear during the move. “That Kaiju weighed 2500 tons.” At 2500 tons and a puny category 3, this monster didn’t even top the scales as the largest.

Kaiju are creatures of a highly toxic nature and have been categorized on the “Serizawa Scale”. Each Kaiju is classified under five different categories. Categories 1 through 2 represent the weakest of the Kaiju, while Categories 3 through 5 are the strongest. The Serizawa Scale measures water displacement, toxicity and ambient radiation levels given off by their bodies when they pass through the breach.

Knowing a Kaiju’s weight I can tell you a lot about Kaiju biology, like how many humans they need to eat per day to survive.

First we need to calculate what is the field energy expenditure, i.e. the number of joules per day to survive, for a Kaiju.  During the film the “scientist” states the Kaiju are related to the dinosaurs.  A previous paper suggests the equation for dinosaurs should be based on those for Komodo Dragons, i.e. active carnivorous lizards.  So

2500 tons = 2,267,961,850 grams

The equation is

FFE=1.07(mass)^0.735

FFE=8.05*10^6 kJ/day

Given the 2500 ton size of the Kaiju, you might be surprised this doesn’t come close the energy demand, 10.14*10^6 kJ/day, for a blue whale at a mere 160 tons.  The Kaiju estimate is just a single order of magnitude higher than that of elephants and rhinos, 5.36*10^5 and 7.10*10^6 kJ/day.

So what’s going on? The FFE is higher for carnivores than herbivore. More energy is required to chase and subdue prey.  That constant search for prey may also require muscle structure for endurance [pdf], increasing muscle mitochondria density, and requiring more energy.  But we accounted for that by using the total bad us flesh munching, bone crushing Komodo Dragon equation.

The real reason? Lizards don’t run as hot as mammals, i.e. they don’t regulate their internal temperature. Komodo Dragons, an active carnivorous lizard, actually do heat up bit, but still don’t suck energy like a mammal.  Keeping the body warm is energetically expensive to maintain, as exampled by heating bills in Boston to keep my Southern butt warm.

So real question is how many humans would a Kaiju need to eat daily to survive?  The human body contains, depending on athleticism, anywhere from 600,000 to 750,000 kilojoules of energy.  Per day the Kaiju would need to eat anywhere between 10.7 to 13.4 humans.  This would mean that it would take a Kaiju, at the quick side, 1,472 years to to eat through the population of Hong Kong, home of the Shatterdome base.

If we assume a Category 5 Kaiju weighs 5,000 tons, then it would only need 17.9 humans per day, taking it 1,102 years to eat its way through Hong Kong.  Perhaps we shouldn’t be so worried about them.

The post How may people does a Kaiju need to eat every day? first appeared on Deep Sea News.