The extinction of the dinosaurs and later, the Pleistocene Megafauna, has been hypothesized to have created a darker forest subcanopy benefiting large-seeded plants. Larger seeds and their fruit, in turn, opened a dietary niche space for animals thus strongly shaping the ecology of the Cenozoic, including our fruit-eating primate ancestors. In this paper, we develop a mechanistic model where we replicate the conditions of tropical forests of the early Paleocene, with small animal body and small seed size, and the Holocene, with small animal body and large seed size.  We first calibrate light levels in our model using stable carbon isotope ratios from fossil leaves and estimate a decrease of understory light of ~90 µmol m^-2 s^-1 (a 19% decrease) from the Cretaceous to the Paleocene. Our model predicts a rapid increase in seed size during the Paleocene that eventually plateaued or declined slightly. Specifically, we find a dynamic feedback where increased animal sizes opened the understory causing a negative feedback by increasing subcanopy light penetration that limited maximum seed size which matched the actual trend in angiosperm seed sizes in mid/high latitude ecosystems.  Adding that larger animals can increase ecosystem fertility to the model, further increased mean animal body size by 17% and mean seed size by 90%. Our model is a drastic simplification and there are many remaining uncertainties, but we show that ecological dynamics can explain seed size trends without adding external factors like climate changes.

Model: To understand the long-term interactions between angiosperm seed size, animal size and the understory light environment, we created an individual based model using Matlab (Mathworks) with a grid size of 50 by 50 cells (also tested at 100 by 100). Each grid cell was assigned an initial animal bodyweight of 1kg and a seed size of 0.038g to simulate the small seeds and animals present in the aftermath of the dinosaur extinction event (Eriksson, 2016; Smith et al., 2010). We focus on angiosperm not gymnosperm seeds because the fruit surrounding angiosperm seeds will attract dispersers.  At each timestep, animal/seed mass is assigned based on randomly choosing a value within a distribution with a mean based on the animal/seed size from the prior timestep and a normally distributed standard deviation of 2/3 for plants/animals (also as 1% percent of body weight in a sensitivity study) with lower mass truncated at 0.038g for seeds and 0.03kg for animals (but no upper threshold). Trees can produce more small seeds than big ones, but seedling survival is a linear function of seed size (Baraloto et al 2005).  Therefore, assuming the same energy input per tree into seed mass regardless of seed size, increased numbers of seeds do not increase survivability (or vice versa) and we do not change number of seeds in each grid cell at each iteration.  Based on the seed size for each grid cell, we calculate how tall the seedling (between 1cm and no upper limit) will become based on the following equation based on eight tropical trees species:

Eq 1 - Plant height (cm) =  18.9+ 5.2* log_n(seed size) (g)(r²=0.95, P<0.0001) (BARALOTO et al., 2005).

Next, we calculate understory light environment at the height of that seedling.  To do this, we estimate the vertical light environment under a disturbance gradient using the results of a logging experiment from Brazil (Fauset et al., 2017) with the following equation:

Eq 2 =  T(H) = a + exp(kz*H);

Where T is light transmission as a percentage of the top of canopy irradiance (2,000 µmol m^-2 s^-1) at height Z, a is T at 1 meter and k_z is an extinction coefficient based on height above the ground (H).  Faucet et al 2017 used values of 2.5 / 6.2 for a and 0.190 /0.213 for kz for intact/selective logged forests.  We used these same values but adapted them for animal induced disturbance.  Since the Cretaceous understory was very open (Carvalho et al., 2021), we assumed animals reaching the size of sauropods (~10,000 kg  - a median including several dinosaur size classes, not just the biggest) would mimic the impact of a “light logging” event. 

We explore this in figure 2 using data from Ehleringer et al 1986 relating light environment to d13 carbon isotopic ratios (Ehleringer et al., 1986).  On this graph, we added the minimum d13 values from a Cretaceous forest compared to the minimum from a Paleocene forest (H. V Graham et al., 2019).  We justify using the minimum because it is unknown which part of the canopy the fossil leaves were from, but the understory will always be the darkest and that is the part of the forest of interest for our study.  When we place the minimum values from each site into our equation, we estimate a change in light levels of 89.9 µmol m^-2 s^-1 (a 19% decrease from the Cretaceous to the early Paleocene) (Figure 2).  We therefore estimate the structural impact of an animal with a size of 10 kg in a grid cell using the coefficients of an unlogged forest (2.5/0.19) and an animal with a size of 10,000 kg animals with the coefficients of a logged forest (6.2/0.213) with linear interpolation in between.  For the fine scale light differences at the bottom meter of the canopy, we used data from Montgomery 2004 who found that light transmittance decreased from 16 to 9 to 2% in light in three tropical forests in Brazil, Panama and Peru between ~0-1 m height above ground surface (Montgomery, 2004).  Therefore, 1m light levels are calculated using Eq 2 and below this, light decreases linearly to the ground by an additional 9% (also 2 and 16%).  In a sensitivity study, we test all these values and we also run a dynamic change model where the larger the mean body size the more open the bottom meter is (toward 16%).

We then calculate the likelihood of sapling survival based on the height of the seedling and the light level at that height.  Baraloto et al 2005 found a significant positive relationship between light and survivorship for eight tree species that represent a range of seed sizes with a standardized regression coefficient of 0.14 after 5 years for all species (Baraloto et al 2005).  An increase in survivorship of 0.14 when light changed from 1.3% (50%) to 4.1% (95%) of full sun (assuming top of canopy maximum of 2,000 µmol m^-2 s^{-1 )} means understory species ability to survive increased by 14% per 28 µmol m^-2 s^-1 increase or 0.5% per µmol m^-2 s^-1 increase.  The light compensation point for photosynthesis can vary between species but one study found it averages ~10 µmol m^-2 s^-1 (Craine & Reich, 2005), and eq 3 gives 0% survival at 10 µmol m^-2 s^-1 and below.

Eq 3 –  survival = (0.5*(light level-10))/100

In a sensitivity study, we use a non-linear equation (eq 4) which will increase survival more greatly as lower light levels are increased.

Eq 4 - survival= (18.62*log(light level -10)-15.61)/100

At each timestep, the seed will replace the seed size of the previous iteration if survival is greater than a random number between 0 and 1, if not, the old seed size will remain.  As understory light levels increase, we assume the more numerous smaller seeds will begin to outcompete the bigger seeds with a 50% chance of a 5-fold decrease in seed size between light levels of 75 and 100 µmol m^-2 s^-1, a 75% chance of a 10-fold decrease in seed size between 100 and 150 µmol m^-2 s^-1, and a 95% chance 20-fold decrease in seed size above 150 µmol m^-2 s^-1 (varied in a sensitivity study – Table 1). 

Larger animals will competitively exclude smaller animals for access to terrestrial resources (Abraham et al., 2023) and based on this, in our model, we allow larger bodied animals primary access to fruit (Gautier-Hion et al., 1985).  We allow for the evolution of larger bodied animals in the model over time to replicate the dramatic increase in animal body size of the Paleocene (Smith et al., 2010).  The edibility (E) of the seeds by frugivores is based on esophagus size, which we assume is linearly related to animal size with the equation:

Eq 5 - esophagus size (cm) =  0.0027 * M (kg) +1.734   Doughty et al.  2016

If the seed in the grid cell is too small, then it is ill suited for that animal and in the cell, the animal will be replaced by a smaller one (if seed is between 3-6 times smaller than the throat, the current animal will be replaced by an animal 4.5 times smaller, between 6-12 times size of throat, an animal 9 times smaller, and less than 12 times the size of the throat, an animal 20 times smaller).  If the seed size is too big to be consumed, then we assume that it will not succeed and be replaced by the average seed size of all touching pixels.  We estimate mammal movement of seeds using equations 6-8 from Wolf et al 2013.

Eq 6 – Day range (km/d) = 0.453 * M^0.368

Eq 7 – Passage time (d) = 0.29 * M^0.26

Eq 8 - Linear distance moved (km) = Day range*passage time

Based on the above equations, we separate animal size into three categories (below 5kg, between 5 and 50kg, and above 50 kg – these numbers are varied in a sensitivity study in Table 2).  Animals the size of 5kg or less access only the grid cell they are in. Between animal sizes of 5 and 50 kg the animals can access neighboring grid cells (3 by 3) and above 50kg can access 5 by 5 grid cells.  We assume each grid cell is ~0.25 km², or the approximate maximum distance across a 5kg mammal could spread a seed (0.5 km).  The animal will spread the seeds into the neighboring cells (with 75% probability – varied in a sensitivity study - Table 1) if the seed can fit in the animal’s throat but are not less than 3-12 (explained above) times smaller than can fit since such small seed/fruit may not interest large animals.  If the animal replaces the seed in the grid cell, it will also replace any smaller (but not bigger) animal present in the grid cell.    This replicates how larger bodied animals will often competitively access resources at preferential times over smaller bodied animals(Abraham et al., 2023).  The understory light environment is based on the size of the animal in the grid cell following eq 2.  An animal is less likely to disperse a seed further away (i.e. 2 grid cells versus 1), but nearby cells will have higher density dependent seed mortality, and therefore, our model gives seeds in both near and far pixels the same success probability (75% but varied in a sensitivity study – Table 2).  We recognize the key role of birds in dispersing seeds, but the focus of this study is only mammal frugivores.

Fertility: We then explored the implications of how changing animal body size could impact fertility.  Larger body size can increase fertility at continental scales over millions of years (Doughty, 2017).  Here we expand that work to show nutrient diffusion capacity for the last 100 million years in greater detail.  We first calculate nutrient diffusion capacity (Doughty et al., 2013; Wolf et al., 2013) for the last 100 million years based on the largest bodied animal in each time period using data from (Benson et al., 2014; Smith et al., 2010).  We then compare this to coal (fossilized leaves) chemistry data from COALQUAL (CQ20166334750) (Palmer et al., 2015) for three time periods – the Cretaceous (N=680), Cretaceous-Tertiary (N=4) and the Paleogene-Neogene (labeled Tertiary in COALQUAL) (N=991) for the critical plant nutrients P, K, Mg and S as a ratio following the methodology from Doughty 2017. K is excluded due to its absorption during clay formation (Kumari & Mohan, 2021), hence concentrations of K in coal cannot be expected to show good correlation with general plant availability.  Cretaceous-Tertiary coal is mainly from the Chuckanut Formation which began ~54 Ma. We compare these data to aluminum, a proxy for abiotic rock weathering.  We use the exact data and methodology from Doughty, 2017. 

We then explore how the relationship between body size and fertility might impact seed and understory light dynamics.  To do this, in our model we make fertility an increasing function of average body size and then fertility can impact seed size because seed standard deviation is a function of fertility.  We varied seed standard deviation between 1 and 2; as the mean body size increased towards 5,000 kg the seed standard deviation moved closer to 2.  Increased mean body size increases fertility which allows seed size to potentially get bigger but does not preferentially choose bigger seeds.  We acknowledge there is little empirical data to support the direct relationship between fertility and standard deviation of seed size, but fertility generally increases fruit abundance with, for instance, a fivefold increase in soil phosphorus leading to a fourfold increase in fruit abundance (Doughty et al., 2014).

Simulations: With the above described model, we simulate three scenarios: Early Paleocene where we start with animal size = 1 kg, seed size = 0.038g, light environment =  1 µmol m^-2 s^-1, future scenario 1 where we start with animal size = 10 kg, seed size = 100 g, light environment =  1 µmol m^-2 s^-1, and future scenario 2 where we start with animal size = 10 kg, seed size = 100 g, light environment =  150 µmol m^-2 s^-1.

To test why seed size may have differed across the C -Pg boundary between low and higher latitude ecosystems, we add a temporal climate variability aspect to our model.  In our model, in mid to high latitude systems (Naware & Benson, 2024), on even time steps the standard deviation of potential seed size is three and on odd steps it is 1.  For low latitude systems, the standard deviation is always 2. This replicates the greater variability inherent in mid/high latitude systems which might vary between good years (SD 3) and bad, more conservative years (SD 1).    

Datasets: We use isotopic data from Graham et al 2019 and from Ehleringer et al 1986 to predict understory light differences.  We used data from Baraloto et al 2005 to establish relationships between seed size, height and survivability under different light conditions.  We use results from Faucet et al 2017 to predict vertical light profiles along a disturbance gradient and results from Montgomery 2004 to predict light profiles in the bottom meter of the canopy.  We use data from COALQUAL (CQ20166334750) (Palmer et al., 2015) to show chemical differences between time periods following the methodology from Doughty 2017 (Doughty, 2017).