Organisms and the physical environment

Every organism lives inside a physical envelope set by temperature, water, light, oxygen and chemistry. Within that envelope it can grow and reproduce; at the edges it merely survives; beyond them it dies. Physiological ecology studies how organisms cope with their physical environment, and it explains much about where species occur. A wood frog can freeze solid in an Ontario winter and thaw in spring; a desert kangaroo rat may never drink water; an Arctic willow grows only a few centimeters tall but survives temperatures far below −40 °C. This lesson looks at the principles behind these feats: tolerance ranges and limiting factors, the effect of temperature on biological rates, how organisms gain and lose heat, how they manage water, and how body size and shape follow climate.

Tolerance ranges and limiting factors

In the early twentieth century, the American ecologist Victor Shelford proposed that each species has a range of tolerance for each environmental factor, with an optimum in the middle and limits at either end. Near the optimum, individuals grow and reproduce well; toward the limits, they are stressed; beyond the limits, they cannot survive. A species' geographic range often reflects where all the important factors fall within its tolerance at once.

An older idea, from the nineteenth-century chemist Justus von Liebig, is the law of the minimum: growth is limited by the resource in shortest supply relative to need, not by the total of all resources. Adding more nitrogen to a crop does nothing if phosphorus is limiting. In lakes, as lesson 11 shows, phosphorus is usually the limiting nutrient, which is why it controls algal blooms. In practice, organisms are often co-limited by several factors at once, but Liebig's principle remains a useful starting point.

Temperature and the rate of life

Almost every biological process, from enzyme reactions to growth and movement, speeds up with temperature over the range that an organism normally experiences, until high temperatures begin to damage proteins and membranes. Ecologists describe the sensitivity of a rate to temperature with the temperature coefficient, Q10: the factor by which a rate increases for a 10 °C rise.

Here \( R_1 \) and \( R_2 \) are rates measured at temperatures \( T_1 \) and \( T_2 \). Most biological processes have Q10 values between about 2 and 3, meaning they double or triple with each 10 °C increase. This is why a cold-blooded animal is sluggish on a cool morning and why decomposition of leaf litter is so slow in the boreal forest: at 5 °C, a process with a Q10 of 2.5 runs at only about 40 percent of its rate at 15 °C.

def q10(r1, r2, t1, t2):
    return (r2 / r1) ** (10 / (t2 - t1))

def rate_at(r_ref, t_ref, t, q):
    return r_ref * q ** ((t - t_ref) / 10)

# Invented respiration data for a soil sample (micrograms CO2 per gram per hour)
print("Q10 from 6 C -> 16 C:", round(q10(1.8, 4.6, 6, 16), 2))
print("Q10 from 12 C -> 20 C:", round(q10(3.1, 6.2, 12, 20), 2))
for t in (0, 5, 10, 15, 20, 25):
    print(f"{t:3d} C  predicted rate {rate_at(3.0, 10, t, 2.5):5.2f}")

Q10 from 6 C -> 16 C: 2.56
Q10 from 12 C -> 20 C: 2.38
  0 C  predicted rate  1.20
  5 C  predicted rate  1.90
 10 C  predicted rate  3.00
 15 C  predicted rate  4.74
 20 C  predicted rate  7.50
 25 C  predicted rate 11.86

The rise in rate with temperature cannot continue indefinitely. Plotting an organism's performance, such as sprint speed, growth rate or feeding rate, against body temperature gives a thermal performance curve. It rises slowly from a critical thermal minimum (CTmin), peaks at an optimum temperature (Topt), then falls steeply to a critical thermal maximum (CTmax). The curve is asymmetric: performance drops much faster above the optimum than below it. This asymmetry matters for climate change, because a few degrees of warming can push an organism already living near its optimum onto the steep falling side of its curve.

import numpy as np

def performance(T, ctmin=5.0, topt=30.0, ctmax=38.0):
    """A simple asymmetric curve: Gaussian rise, quadratic fall (illustrative)."""
    T = np.asarray(T, dtype=float)
    rise = np.exp(-((T - topt) / ((topt - ctmin) / 2.0)) ** 2)
    fall = 1 - ((T - topt) / (ctmax - topt)) ** 2
    p = np.where(T <= topt, rise, fall)
    return np.clip(p, 0, None)

temps = np.array([10, 20, 26, 30, 33, 36, 38])
for t, p in zip(temps, performance(temps)):
    print(f"{t:3d} C  relative performance {p:.2f}")
habitat_max = 31.0
print("thermal safety margin (CTmax - habitat max):", 38.0 - habitat_max, "C")

 10 C  relative performance 0.08
 20 C  relative performance 0.53
 26 C  relative performance 0.90
 30 C  relative performance 1.00
 33 C  relative performance 0.86
 36 C  relative performance 0.44
 38 C  relative performance 0.00
thermal safety margin (CTmax - habitat max): 7.0 C

Ectotherms and endotherms

Organisms differ in where their body heat comes from. Ectotherms, which include most invertebrates, fish, amphibians and reptiles, gain heat mainly from their surroundings. Their body temperature tracks the environment unless they regulate it by behavior, such as basking in the sun, seeking shade or burrowing. Endotherms, mainly birds and mammals, generate most of their heat by metabolism and keep their body temperature nearly constant. Endothermy allows activity in the cold but is expensive: a mammal needs several times more food than a reptile of the same mass.

Heat balance for any organism can be summarized as a budget: heat gained from metabolism and absorbed radiation must equal heat lost by radiation, convection, conduction and evaporation, otherwise the body warms or cools. Animals adjust each term. Arctic foxes and caribou have thick insulating fur that cuts convective and conductive loss; many birds tuck in their legs and fluff their feathers; beavers and ducks use countercurrent heat exchange in their legs and tails, where warm arterial blood flowing out passes heat to cool venous blood flowing back, so the extremities stay cold and little heat is lost.

In winter, many small animals escape the cold rather than resist it. Hibernating mammals such as the little brown bat and the Richardson's ground squirrel drop their body temperature close to freezing and cut their metabolic rate by more than 90 percent. Others overwinter beneath the snow in the subnivean space, where temperatures stay near 0 °C even when the air above is −30 °C. The wood frog, found as far north as the Arctic treeline, freezes solid: up to about two-thirds of its body water turns to ice, while glucose produced by the liver protects its cells, and it thaws and hops away in spring.

Body size, shape and climate

Heat is produced in proportion to body volume but lost through the body surface. As an animal gets larger, its volume grows with the cube of its length but its surface area only with the square, so larger animals have less surface per unit of volume and lose heat more slowly. In 1847, Carl Bergmann observed that within groups of related endotherms, populations and species in colder climates tend to be larger. Joel Allen later noted that extremities such as ears, tails and limbs tend to be shorter in colder climates. The Arctic hare's short ears, compared with the long ears of desert jackrabbits, are a textbook example. These rules are tendencies, not laws, and many exceptions exist, but they illustrate how climate shapes form.

import numpy as np

rng = np.random.default_rng(208)
# Invented data: mean body mass (kg) of white-tailed deer populations by latitude
lat = np.array([28, 32, 35, 38, 41, 44, 47, 50, 53])
mass = 45 + 1.6 * (lat - 28) + rng.normal(0, 4, lat.size)
slope, intercept = np.polyfit(lat, mass, 1)
r = np.corrcoef(lat, mass)[0, 1]
for a, m in zip(lat, mass):
    print(f"lat {a:2d} N  mass {m:5.1f} kg")
print(f"fitted slope: {slope:.2f} kg per degree, r = {r:.2f}")

# Surface-area-to-volume ratio of spheres of increasing size
for radius_cm in (2, 10, 40):
    sa = 4 * np.pi * radius_cm**2
    vol = 4 / 3 * np.pi * radius_cm**3
    print(f"radius {radius_cm:3d} cm  SA/V = {sa / vol:.3f} per cm")

lat 28 N  mass  43.9 kg
lat 32 N  mass  45.4 kg
lat 35 N  mass  50.7 kg
lat 38 N  mass  64.0 kg
lat 41 N  mass  63.4 kg
lat 44 N  mass  68.3 kg
lat 47 N  mass  78.4 kg
lat 50 N  mass  73.5 kg
lat 53 N  mass  85.9 kg
fitted slope: 1.69 kg per degree, r = 0.97
radius   2 cm  SA/V = 1.500 per cm
radius  10 cm  SA/V = 0.300 per cm
radius  40 cm  SA/V = 0.075 per cm

Water balance

Life evolved in water, and every terrestrial organism must keep its internal water within narrow limits while living in air that constantly pulls water away. Animals gain water by drinking, in food, and from metabolism (oxidizing food produces water), and lose it in urine, faeces, breath and through the skin. Desert animals such as the kangaroo rat survive almost entirely on metabolic water, producing extremely concentrated urine and staying in cool, humid burrows by day. Freshwater fish face the opposite problem: water floods in by osmosis, so they excrete large volumes of dilute urine, while marine fish lose water and drink seawater, excreting salt through their gills.

Plants face a fundamental trade-off. To take in carbon dioxide for photosynthesis, they must open the stomata on their leaves, but open stomata let water vapor escape. Transpiration pulls water from the soil through the roots and up the stem. Plants in dry environments limit water loss with thick waxy cuticles, small or hairy leaves, sunken stomata, deep roots, or alternative photosynthetic pathways. CAM plants such as cacti open their stomata only at night, storing carbon dioxide as organic acids and using it by day with stomata closed. C₄ grasses, common on warm prairies, concentrate carbon dioxide inside the leaf and so can photosynthesize with stomata partly closed.

Light, oxygen and chemistry

Light varies with latitude, season, canopy cover and depth in water. On a forest floor in summer, only a few percent of full sunlight may reach the ground, and shade-tolerant plants such as sugar maple seedlings can survive there for years, waiting for a gap. In lakes, light declines exponentially with depth, limiting photosynthesis to the upper zone. Oxygen is plentiful in air but scarce in water, especially warm or still water, where oxygen dissolves poorly, and it can disappear entirely in the deep water of nutrient-rich lakes. Soil and water chemistry, including pH and salinity, also limit where species can live; acid rain lowered the pH of thousands of lakes on the Canadian Shield and in the northeastern United States in the late twentieth century, eliminating acid-sensitive fish and invertebrates. BIOL-460 covers aquatic environments in detail.