Module 8: Conservation Biophysics — Models, Tools, and Economics

Conservation is increasingly a quantitative discipline. This capstone module integrates population viability analysis, telemetry energetics, acoustic anti-poaching arrays, satellite and UAV thermal surveillance, translocation physiology, human-wildlife conflict modeling, landscape-connectivity graph theory, and the economics of photo-tourism versus trophy hunting. The central message is that the tools of biophysics and computational ecology now underpin every major conservation decision from gene-level management to continental-scale policy.

1. Population Viability Analysis (PVA)

Introduced by Shaffer (1981), population viability analysis projects a population’s persistence probability under specified demographic, environmental, and genetic noise. Lande (1993) gave the canonical mathematical form, decomposing extinction risk into four sources:

Demographic stochasticity—Poisson sampling of births and deaths; dominant when $N < 100$.
Environmental stochasticity— correlated fluctuations in vital rates from climate, disease, resource pulses.
Genetic stochasticity—drift and inbreeding depression; dominant in very small populations.
Catastrophes—rare large events (epidemics, fires, severe drought).

Minimum viable population

The minimum viable population (MVP) is the smallest $N$ that maintains a specified persistence probability ($\geq 95\%$) over a specified time horizon (100–1000 years). For African elephants in a stochastic environment, MVP estimates range from 400 (demographic-only) to 3500 (including inbreeding and catastrophic poaching).

\[\Pr[\text{extinct in } T\text{ yr}] = 1 - \prod_{t=1}^{T} \Pr[N(t) \geq N_{\text{crit}}]\]

Leslie matrix projection

Age-structured PVA uses a Leslie projection matrix. For elephants (longevity ~65 yr, first reproduction at age 12) the matrix is 65×65 with:

\[\mathbf{n}(t+1) = \mathbf{L}(t)\,\mathbf{n}(t), \qquad \mathbf{L}_{i+1, i} = s_i(1 - p_i^{\text{poach}})\]

Stochasticity is injected by drawing $s_i(t), F_i(t)$ from process-noise distributions each step.

IPM — integrated population model

Modern PVAs are built as Bayesian state-space integrated population models (IPMs) that jointly fit census data, GPS-telemetry survival estimates, and genetic effective-size estimates. Model evidence is

\[p(\theta \mid \mathcal D) \propto p(\mathcal D_{\text{census}} \mid \theta)\,p(\mathcal D_{\text{telem}} \mid \theta)\,p(\mathcal D_{\text{genetic}} \mid \theta)\,p(\theta)\]

2. GPS Telemetry & Collar Energetics

GPS telemetry is the workhorse of modern megafauna ecology. Collar design is a biophysical optimization problem with four hard constraints: mass (<3% of body mass), battery energy, radio power budget, and environmental robustness.

The 3% rule

Collar mass is limited to approximately 3% of animal body mass—a widely adopted welfare guideline. For an adult African elephant ($\sim 4000$ kg) this gives a 120 kg ceiling, but operational collars weigh 8–10 kg to minimize behavior interference. Cheetah collars weigh ~200 g on 50 kg animals (~0.4%).

Fix-cost and battery lifetime

Each GPS fix consumes an energy budget that scales with satellite acquisition time:

\[E_{\text{fix}} = I_{\text{GPS}} \cdot V \cdot T_{\text{on}}, \qquad L_{\text{battery}} = \frac{E_{\text{bat}}}{f \cdot E_{\text{fix}} + P_{\text{idle}} \cdot T_{\text{day}}}\]

At fix rate $f = 4/\text{day}$ and elephant collar battery $E_{\text{bat}} = 250\,\text{Wh}$, lifetime $\approx 3$ years.

Modern low-power innovations

Ludwig et al. (2019) developed ultra-low-power LoRaWAN collars that relay GPS fixes via radio peer-to-peer rather than satellite uplink, reducing per-fix energy by$\sim 50\times$ and extending collar lifetime to 5+ years for small carnivores.

State-space movement analysis

Raw GPS tracks are analyzed with hidden-Markov or state-space models. A typical two-state model distinguishes “encamped” ($\sigma_1 \sim 10$ m/h) and “transit” ($\sigma_2 \sim 2$ km/h) modes:

\[\mathbf{x}_t \mid \mathbf{x}_{t-1}, s_t \sim \mathcal{N}\bigl(\mathbf{x}_{t-1} + \mu_{s_t}\,\Delta t, \; \Sigma_{s_t}\bigr)\]

3. Acoustic Anti-Poaching — Gunshot Detection

Acoustic monitoring networks provide wide-area real-time surveillance for poaching gunshots. Thel et al. (2022) describe the PAMGuard open-source platform adapted for savanna networks. The physics rests on time-difference-of-arrival (TDOA)triangulation.

Four-microphone hyperbolic intersection

With four sensors at positions $\vec r_i$ and times-of-arrival $t_i$, each pair constrains the source to a hyperboloid:

\[|\vec r_s - \vec r_i| - |\vec r_s - \vec r_j| = c(t_i - t_j)\]

Three independent hyperboloids localize the source in 3-D.

SNR and propagation in savanna

Gunshot spectra peak at 300–800 Hz (muzzle blast) plus a supersonic crack at higher frequencies. Detection range is limited by atmospheric absorption ($\alpha(f)$), terrain shadowing, and wind noise:

\[L_{p}(r) = L_{p,0} - 20 \log_{10}(r) - \alpha(f)\,r\]

Typical detection range 2–4 km in open savanna; shorter in dense acacia thicket.

Elephant distress recognition — ML on spectrograms

Wrege et al. (2017) deployed Cornell’s Elephant Listening Project to classify forest elephant calls in the Congo basin; Katzner et al. (2012) and Bernard et al. (2022) extended to CNN classifiers using transfer learning from bird-ID models. Reported accuracy on clean recordings exceeds 90% for distress rumbles versus contact calls.

Satellite thermal and UAV deployment

SmartParks deploys UAVs carrying thermal-IR cameras for night surveillance. Thermal contrast $\Delta T_{\text{human-background}} \approx 5$–10 °C at night produces reliable human detection at 500 m altitude with 640×512 sensors. Lethbridge et al. (2019) demonstrated operational deployment in Kruger and Liwonde.

4. Translocation Physiology & Capture Myopathy

Moving megafauna between reserves is a high-value conservation intervention but carries physiological risk. Capture myopathy(Oya Erciyas 2003; Brady 2019) is a stress-induced rhabdomyolysis in which skeletal muscle breakdown releases myoglobin into the bloodstream, causing kidney failure and death hours to days after capture.

Biochemistry of myopathy

Intense muscular effort under capture stress drives anaerobic glycolysis, producing lactate that lowers intramuscular pH to 6.0 or below. At this pH, calcium leaks from sarcoplasmic reticulum, triggering calpain-mediated proteolysis. Muscle cell membranes rupture, releasing creatine kinase and myoglobin. Serum CK levels above $5000$ U/L indicate critical risk.

\[\text{Risk index} = \alpha_1 \Delta \text{CK} + \alpha_2 \Delta \text{AST} + \alpha_3 \text{[lactate]} + \alpha_4 T_{\text{capture}}\]

Immobilization pharmacology

Standard chemical immobilization for elephants uses etorphine (an opioid agonist, ~9800× morphine potency) combined with azaperone(a butyrophenone tranquilizer that blunts cardiovascular stress). Reversal is with diprenorphine, a partial agonist/antagonist. The pharmacokinetic model is a two-compartment exponential decay:

\[C(t) = \frac{D}{V_d} \left[ A e^{-\alpha t} + B e^{-\beta t} \right]\]

Rhino dehorning — a contested intervention

Dehorning is proposed as a deterrent for rhino poaching. Lindsey et al. (2018) reviewed the evidence: dehorning reduces poaching risk modestly (approximately 30% reduction in Namibian private reserves) but has behavioral consequences including altered dominance hierarchies and reduced calf defence. Compound population effects require continued monitoring.

5. Human-Wildlife Conflict & Conflict Economics

Human-wildlife conflict is now the single largest proximate threat to large-mammal conservation. Two dominant forms in East Africa: elephant crop-raiding and lion livestock depredation.

Lion depredation model

The probability that a lion attacks livestock on a given night is modeled as a logistic function of covariates:

\[\Pr(\text{attack}) = \frac{1}{1 + \exp\!\left(-(\beta_0 + \beta_1 \rho_{\text{live}} + \beta_2 \rho_{\text{prey}} + \beta_3 d_{\text{water}} + \beta_4 M)\right)}\]

$\rho_{\text{live}}$ = livestock density, $\rho_{\text{prey}}$ = wild-prey index, $d_{\text{water}}$ = distance to waterhole, $M$ = full-moon binary.

Compensation schemes

Compensation programs reimburse herders for verified depredation losses. They reduce retaliation killing but do not reduce incidents. Insurance-based schemes (e.g. the Maasai Mara Predator Compensation Fund) require rapid verification and are vulnerable to moral hazard if not paired with husbandry incentives.

Integrated Protection Zoning (IPZ)

Linnell et al. (2005) formalized the three-zone framework:

Core protected area—no human settlement; wildlife priority.
Buffer zone—conditional use; limited livestock; wildlife tolerance incentives.
Agricultural matrix—mixed-use; wildlife corridors connect cores.

Graph-theory connectivity metrics

Landscape connectivity can be quantified using graph-theoretic metrics on the patch network. Habitat patches are nodes; dispersal probability between patches $i, j$ defines edge weights. The probability of connectivity (Saura & Pascual-Hortal 2007) is

\[PC = \frac{\sum_{i,j} a_i a_j p_{ij}^*}{A_L^2}\]

where $p_{ij}^*$ is the maximum product probability over all paths.

6. Serengeti Ecosystem Lessons & IUCN Red List

Rinderpest elimination cascade

Rinderpest was a cattle-origin viral epidemic that historically crashed East African wildebeest populations. Its elimination in cattle in the late 1950s cascaded: wildebeest rose from 250,000 to 1.5 million, grass pressure on dry-season refugia increased, fire frequency decreased, and tree cover collapsed. McNaughton (1979) formalized the resulting grass-wildebeest-fire triangular stability system—the textbook case of a disease-driven trophic cascade.

IUCN Red List criteria

The IUCN Red List applies five quantitative criteria:

A: population reduction >30/50/80% over 10 yr or 3 generations.
B: geographic range <20,000 / 5000 / 100 km².
C: small population ($N < 10\,000$) with continued decline.
D: very small population ($N < 1000$ or range restricted).
E: quantitative extinction probability >10% over 100 yr (via PVA).

Climate projections for East Africa

CMIP6 multi-model ensembles project East African warming of 2–4 °C by 2100 under SSP3-7.0, with rainfall changes spatially heterogeneous. Wet-bulb-temperature exceedance of the human/bovine survival threshold of 35 °C begins to occur in northern Kenya and the Horn of Africa in the 2050s under high-emission scenarios.

\[T_{\text{wb}} = T \arctan\!\left[0.151977 \sqrt{RH + 8.313659}\right] + \cdots\]

7. Economic Valuation & Success Stories

Economic arguments increasingly drive conservation policy.

Photo-tourism valuation

Naidoo et al. (2016) estimated that a single African lion generates $13–36 million per year in photo-tourism revenue across its range, concentrated in high-traffic reserves such as the Serengeti and Masai Mara. The travel-cost method quantifies consumer surplus:

\[\text{CS} = \int_{p_0}^{\infty} D(p)\,dp\]

Total annual value = gate fees + lodging + consumer surplus; the last term often dominates.

Trophy hunting debate

Trophy hunting is a contested revenue model. Lindsey et al. (2019) argue that sustainably managed hunts on private conservancies provide economic incentives for landowners to retain habitat that would otherwise be converted to cattle. Critics counter that trophy hunting is ethically unsupportable and that photo-tourism produces more revenue per animal on the same footprint. Empirical evidence supports both positions depending on site and species.

Community conservancies — Namibia model

Namibia’s communal conservancy program devolves wildlife rights to 86 community conservancies covering 20% of Namibia. Elephant, black rhino, lion, and oryx populations have all increased measurably since 1995. Revenue from both photo-tourism and sustainable hunting is distributed to local households, aligning incentives.

Success stories

Mountain gorilla—from 600 in 2008 to over 1000 in 2018 through community ranger programs.
Black rhino—from 2400 in 1995 to 6200 in 2023 through dehorning, fencing, and anti-poaching.
Elephant in Tanzania—several core parks show recovery after 2015 ivory-ban enforcement.
Iberian lynx—from 94 in 2002 to 1600 in 2023 through captive breeding and habitat corridors.

8. Camera-Trap Analytics & Machine Vision

Camera traps are now deployed at continental scale. The Snapshot Serengeti project alone generated 1.2 million images over 5 years (Swanson et al., 2015). Human classification is prohibitive; modern pipelines rely on deep-learning classifiers.

CNN species classification

Norouzzadeh et al. (2018) demonstrated that a ResNet-152 fine-tuned on Snapshot Serengeti achieves 94.9% top-1 accuracy on 48 species, reducing human annotation effort by 99%. The loss function is standard cross-entropy with class-balanced reweighting because most photos are of wildebeest or zebra:

\[\mathcal{L}_{\text{CE}} = -\sum_k w_k\, y_k \log \hat{p}_k, \qquad w_k = \frac{1 - \beta}{1 - \beta^{n_k}}\]

Class-balanced weights (Cui 2019) with $\beta \approx 0.999$ upweight rare species such as serval or African wild dog.

Individual recognition — stripe/rosette metric learning

Zebras, tigers, giraffes, and whale-sharks carry individually distinctive natural markings. The WildMe Wildbook project uses triplet-loss metric learning to produce an embedding $\phi: \mathbb R^{H \times W \times 3} \to \mathbb R^{128}$where conspecific individuals cluster:

\[\mathcal{L}_{\text{triplet}} = \max\!\left(0,\; \|\phi(a) - \phi(p)\|^2 - \|\phi(a) - \phi(n)\|^2 + \alpha\right)\]

anchor $a$, positive (same individual) $p$, negative (different individual) $n$, margin $\alpha$.

Occupancy modelling from detection data

Camera-trap data feeds into MacKenzie et al. (2002) occupancy models. The probability that a site is occupied given $K$ visits with detection histories $h$ is

\[\Pr(\psi=1 \mid h) = \frac{\psi \prod_{k} p_k^{h_k}(1-p_k)^{1-h_k}}{\psi \prod_k \cdots + (1-\psi)[h=0]}\]

9. Genetic Monitoring & eDNA

Non-invasive genetic sampling of scat, hair, and environmental DNA (eDNA) transforms population assessment for cryptic species. For elephants, dung-DNA genotyping with 10+ microsatellite loci estimates population size via closed-capture mark-recapture without any animal handling.

Genetic mark-recapture

Each unique multilocus genotype is a “capture”. Lincoln–Petersen for two samples:

\[\hat N = \frac{(M+1)(C+1)}{R+1} - 1\]

Chapman-corrected for small samples. Uncertainty propagates from genotyping error rate.

Environmental DNA from waterholes

eDNA extracted from waterhole sediment detects species presence down to the picogram level. qPCR with species-specific primers produces a threshold cycle $C_t$ related to template concentration by

\[\log_{10}(N_0) = -\frac{C_t}{\log_2(1+E)} + \text{const}\]

PCR efficiency $E \approx 0.9$–1.0 ideally. Detection limits reach single-copy template in optimized assays.

Genome-scale monitoring

Whole-genome sequencing of 20–50 individuals now produces runs of homozygosity, genome-wide heterozygosity, and recent effective-population-size estimates via IBDNe that inform Red List assessments directly. For the Javan rhino (N = 76) low genome-wide heterozygosity (~0.0005 per base) is the clearest indicator of long-term bottleneck.

Simulation 1: African Elephant PVA — Poaching Scenarios

Stochastic Leslie-matrix projection with three poaching scenarios (1%, 4%, 8% adult mortality), environmental noise on fecundity (climate-food availability), and Poisson demographic noise. The model runs 300 replicates over a 100-year horizon and produces median population trajectories, time-varying extinction probability, 100-year quasi-extinction risk, and cumulative population-years as a conservation-value proxy.

Python

script.py150 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# African Elephant Population Viability Analysis (PVA)
# Stochastic Leslie-matrix projection with three scenarios:
#   (A) Low poaching (1%/yr)
#   (B) Mid poaching (4%/yr) — representative 2010-era
#   (C) High poaching (8%/yr) — peak illegal ivory crisis
# Adds environmental noise on fecundity (climate-driven forage) and
# demographic stochasticity at small N.

np.random.seed(11)
n_trials = 300
horizon = 100  # years
ages = np.arange(0, 65)
n_ages = len(ages)

# Baseline survival (Moss 1988 Amboseli) and fecundity schedule
S = np.ones(n_ages) * 0.97
S[0] = 0.82           # first-year survival
S[1:5] = 0.93
S[55:] = np.linspace(0.93, 0.70, 10)  # senescence
F_schedule = np.zeros(n_ages)
F_schedule[12:50] = 0.25   # one calf per ~4 yr across reproductive years

# Poaching scenarios — age-targeted (adults with ivory)
def poaching_mortality(scenario):
    p = np.zeros(n_ages)
    if scenario == 'low':
        p[15:] = 0.01
    elif scenario == 'mid':
        p[15:] = 0.04
    elif scenario == 'high':
        p[15:] = 0.08
    return p

def build_L(S, F, poach):
    L = np.zeros((n_ages, n_ages))
    # Fecundity -> age 0
    L[0, :] = 0.5 * F   # female-only projection
    # Survival transitions
    for i in range(n_ages - 1):
        L[i + 1, i] = S[i] * (1 - poach[i])
    return L

def run_trial(scenario, seed):
    rng = np.random.default_rng(seed)
    poach = poaching_mortality(scenario)
    N0 = 400.0  # starting pop (femaled half-count)
    # Stable age distribution approximation
    L0 = build_L(S, F_schedule, poach)
    w, v = np.linalg.eig(L0)
    idx = np.argmax(w.real)
    stable = np.abs(v[:, idx].real)
    stable /= stable.sum()
    n = N0 * stable
    N_hist = np.zeros(horizon)
    for t in range(horizon):
        # Env noise on fecundity (climate-food index)
        env = 1.0 + rng.normal(0, 0.15)
        F_t = F_schedule * max(env, 0)
        L = build_L(S * rng.normal(1, 0.02, n_ages).clip(0.8, 1.1), F_t, poach)
        # Demographic stochasticity (Poisson) at small N
        n = L @ n
        # Add Poisson demographic noise
        n = rng.poisson(np.maximum(n, 0)).astype(float)
        N_hist[t] = n.sum()
        if N_hist[t] < 2:
            N_hist[t:] = 0
            break
    return N_hist

scenarios = ['low', 'mid', 'high']
labels = {'low': '1%/yr poaching', 'mid': '4%/yr poaching', 'high': '8%/yr poaching'}
colors = {'low': '#4ade80', 'mid': '#facc15', 'high': '#f43f5e'}

all_hist = {}
ext_prob = {}
for sc in scenarios:
    H = np.zeros((n_trials, horizon))
    for i in range(n_trials):
        H[i] = run_trial(sc, seed=i * 31 + {'low': 1, 'mid': 2, 'high': 3}[sc])
    all_hist[sc] = H
    ext_prob[sc] = (H[:, -1] < 5).mean()

years = np.arange(2025, 2025 + horizon)

fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(14, 11))
fig.patch.set_facecolor('#0a0a1a')
for ax in [ax1, ax2, ax3, ax4]:
    ax.set_facecolor('#0a0a1a')
    ax.tick_params(colors='#fdba74')
    for sp in ax.spines.values():
        sp.set_color('#7c2d12')
    ax.grid(True, color='#7c2d12', alpha=0.3)

# Panel 1: Median trajectories with quantile envelopes
for sc in scenarios:
    H = all_hist[sc]
    med = np.median(H, axis=0)
    lo = np.percentile(H, 10, axis=0)
    hi = np.percentile(H, 90, axis=0)
    ax1.plot(years, med, '-', color=colors[sc], linewidth=2.2, label=labels[sc])
    ax1.fill_between(years, lo, hi, color=colors[sc], alpha=0.15)
ax1.set_xlabel('Year', color='#fdba74', fontsize=11)
ax1.set_ylabel('Elephant population (female count)', color='#fdba74', fontsize=11)
ax1.set_title('PVA: Population Trajectories (median + 10-90%)', color='#fed7aa', fontsize=13, fontweight='bold')
ax1.legend(facecolor='#1e293b', edgecolor='#7c2d12', labelcolor='#fed7aa', fontsize=10)

# Panel 2: Extinction probability curves over time
for sc in scenarios:
    H = all_hist[sc]
    pe_t = (H < 5).mean(axis=0)
    ax2.plot(years, pe_t, '-', color=colors[sc], linewidth=2.2, label=labels[sc])
ax2.set_xlabel('Year', color='#fdba74', fontsize=11)
ax2.set_ylabel('Pr(N < 5)', color='#fdba74', fontsize=11)
ax2.set_title('Extinction Probability Over Time', color='#fed7aa', fontsize=13, fontweight='bold')
ax2.legend(facecolor='#1e293b', edgecolor='#7c2d12', labelcolor='#fed7aa', fontsize=10)

# Panel 3: 100-year extinction probability bars
ax3.bar(list(labels.values()),
        [ext_prob[sc] for sc in scenarios],
        color=[colors[sc] for sc in scenarios], edgecolor='white')
for i, sc in enumerate(scenarios):
    ax3.text(i, ext_prob[sc] + 0.02, f'{ext_prob[sc]*100:.0f}%',
             ha='center', color='#fed7aa', fontsize=12)
ax3.set_ylabel('Extinction probability at year 100', color='#fdba74', fontsize=11)
ax3.set_title('Quasi-Extinction Risk by Scenario', color='#fed7aa', fontsize=13, fontweight='bold')
ax3.set_ylim(0, 1.05)

# Panel 4: Cumulative area under trajectory using np.trapezoid (population-years)
pop_years = {}
for sc in scenarios:
    med = np.median(all_hist[sc], axis=0)
    pop_years[sc] = np.trapezoid(med, years)
ax4.bar(list(labels.values()),
        [pop_years[sc] for sc in scenarios],
        color=[colors[sc] for sc in scenarios], edgecolor='white')
ax4.set_ylabel('Cumulative population-years (median)', color='#fdba74', fontsize=11)
ax4.set_title('Cumulative Conservation Value', color='#fed7aa', fontsize=13, fontweight='bold')

plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')
print('Elephant PVA complete.')
for sc in scenarios:
    med = np.median(all_hist[sc], axis=0)
    print(f'{labels[sc]:20s}  N_median(2100)={med[-1]:7.1f}  Pr(extinct)={ext_prob[sc]*100:5.1f}%  pop-years={pop_years[sc]:.0f}')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Simulation 2: Lion-Livestock Conflict ML Model

Synthetic incident data generator (livestock density, wild prey, waterhole distance, moon phase) used to fit a logistic regression via manual gradient descent. The fitted model predicts depredation probability over a covariate grid and compares three management scenarios: baseline, habitat-connectivity retrofit that raises wild prey and moves bomas away from waterholes, and compensation-only. Annualized cost per square kilometer is computed for each.

Python

script.py148 lines

import numpy as np
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt

# Lion-Livestock Depredation Prediction
# Generate synthetic incident data conditioned on:
#   x1 = livestock density (head/km^2)
#   x2 = wild prey index (0..1)
#   x3 = distance to nearest waterhole (km)
#   x4 = full moon binary (affects visibility)
# True coefficients unknown to the model; we fit logistic regression from
# scratch (manual gradient descent) and predict depredation probability.
# Compare: baseline, habitat-connectivity retrofit scenario, compensation cost.

np.random.seed(13)
N = 1500

# Covariates
livestock = np.random.gamma(2.0, 25.0, N)                    # head/km^2
wild_prey = np.clip(np.random.beta(2.0, 2.5, N), 0, 1)        # 0..1
d_water   = np.abs(np.random.normal(3.0, 2.0, N))             # km
full_moon = (np.random.rand(N) < 0.12).astype(float)          # 12% nights

# True logistic model (unknown to the learner)
beta0 = -2.5
b_live = 0.020
b_prey = -3.5
b_wat  = -0.20
b_moon = 0.75
logit = beta0 + b_live * livestock + b_prey * wild_prey + b_wat * d_water + b_moon * full_moon
p_true = 1.0 / (1.0 + np.exp(-logit))
y = (np.random.rand(N) < p_true).astype(float)

# Fit logistic regression via gradient descent
X_raw = np.column_stack([livestock, wild_prey, d_water, full_moon])
mu = X_raw.mean(axis=0)
sd = X_raw.std(axis=0)
Xs = (X_raw - mu) / sd
X = np.column_stack([np.ones(N), Xs])

w = np.zeros(X.shape[1])
lr = 0.1
for it in range(4000):
    z = X @ w
    p = 1.0 / (1.0 + np.exp(-z))
    grad = X.T @ (p - y) / N
    w -= lr * grad

# Predict on test grid
live_grid = np.linspace(0, 120, 80)
prey_grid = np.linspace(0, 1, 80)
LL, PP = np.meshgrid(live_grid, prey_grid)
Xg = np.column_stack([LL.ravel(), PP.ravel(),
                      np.full(LL.size, d_water.mean()),
                      np.zeros(LL.size)])
Xg_s = (Xg - mu) / sd
Xg_a = np.column_stack([np.ones(Xg.shape[0]), Xg_s])
p_grid = 1.0 / (1.0 + np.exp(-(Xg_a @ w))).reshape(LL.shape)

# Scenarios
# (a) Baseline — current landscape
# (b) Habitat-connectivity retrofit: wild prey +30%, d_water +0.5 km (bomas moved away)
# (c) Compensation scheme — financial only, no behavioral change
p_baseline = p_true.mean()
wild2 = np.clip(wild_prey * 1.3, 0, 1)
d_water2 = d_water + 0.5
logit2 = beta0 + b_live * livestock + b_prey * wild2 + b_wat * d_water2 + b_moon * full_moon
p_scenarioB = (1 / (1 + np.exp(-logit2))).mean()
p_scenarioC = p_baseline   # compensation changes economics not incidents

# Economics
cost_per_incident = 180   # USD value of depredated livestock
compensation_rate = 1.0   # 100% of loss compensated in scenario C
retrofit_cost = 320       # USD/km^2/year for connectivity retrofit
annual_incidents_per_km2 = 52  # nights/yr * p(attack | night)

costs = {
    'Baseline': annual_incidents_per_km2 * p_baseline * cost_per_incident,
    'Connectivity': annual_incidents_per_km2 * p_scenarioB * cost_per_incident + retrofit_cost,
    'Compensation only': annual_incidents_per_km2 * p_baseline * cost_per_incident * (1 + compensation_rate)
}

# Panel 1: Heatmap of depredation risk
im = ax1.imshow(p_grid, origin='lower', extent=[0, 120, 0, 1],
                aspect='auto', cmap='magma', vmin=0, vmax=0.8)
ax1.set_xlabel('Livestock density (head/km^2)', color='#fdba74', fontsize=11)
ax1.set_ylabel('Wild prey index', color='#fdba74', fontsize=11)
ax1.set_title('Predicted Depredation Risk', color='#fed7aa', fontsize=13, fontweight='bold')
cb = plt.colorbar(im, ax=ax1)
cb.set_label('Pr(attack | night)', color='#fdba74')
plt.setp(plt.getp(cb.ax.axes, 'yticklabels'), color='#fdba74')

# Panel 2: Coefficients
names = ['intercept', 'livestock', 'wild prey', 'd_water', 'full moon']
ax2.bar(names, w, color='#fb923c', edgecolor='white')
ax2.axhline(0, color='#fed7aa', linewidth=0.8)
ax2.set_ylabel('Standardized coefficient', color='#fdba74', fontsize=11)
ax2.set_title('Logistic Regression Fit', color='#fed7aa', fontsize=13, fontweight='bold')
for i, v in enumerate(w):
    ax2.text(i, v + 0.03 * np.sign(v), f'{v:.2f}',
             ha='center', color='#fed7aa', fontsize=10)

# Panel 3: Scenario incident rates
ax3.bar(['Baseline', 'Connectivity', 'Compensation only'],
        [p_baseline, p_scenarioB, p_scenarioC],
        color=['#f43f5e', '#4ade80', '#facc15'], edgecolor='white')
ax3.set_ylabel('Mean Pr(attack | night)', color='#fdba74', fontsize=11)
ax3.set_title('Per-Night Incident Probability', color='#fed7aa', fontsize=13, fontweight='bold')

# Panel 4: Annualized cost per km^2
ax4.bar(list(costs.keys()), list(costs.values()),
        color=['#f43f5e', '#4ade80', '#facc15'], edgecolor='white')
ax4.set_ylabel('Annual cost (USD/km^2)', color='#fdba74', fontsize=11)
ax4.set_title('Conflict Economics', color='#fed7aa', fontsize=13, fontweight='bold')
for i, k in enumerate(costs):
    ax4.text(i, costs[k] + 50, f'\${costs[k]:.0f}', ha='center', color='#fed7aa', fontsize=10)

# Cumulative expected incidents via np.trapezoid over livestock density axis
density_axis = np.linspace(0, 200, 300)
Xline = np.column_stack([density_axis,
                         np.full(density_axis.size, wild_prey.mean()),
                         np.full(density_axis.size, d_water.mean()),
                         np.zeros(density_axis.size)])
Xline_s = (Xline - mu) / sd
Xline_a = np.column_stack([np.ones(Xline.shape[0]), Xline_s])
p_line = 1.0 / (1.0 + np.exp(-(Xline_a @ w)))
cum_risk = np.trapezoid(p_line, density_axis)
plt.tight_layout()
plt.savefig('output.png', dpi=120, bbox_inches='tight', facecolor='#0a0a1a')

print('Lion-livestock conflict model complete.')
print(f'Baseline per-night depredation probability:      {p_baseline*100:.2f}%')
print(f'Connectivity retrofit per-night probability:     {p_scenarioB*100:.2f}%')
print(f'Compensation-only per-night probability:         {p_scenarioC*100:.2f}%')
for k, v in costs.items():
    print(f'{k:22s}  annual cost/km^2 = \${v:.0f}')
print(f'Cumulative risk integral over livestock axis:    {cum_risk:.2f}')

Click Run to execute the Python code

Code will be executed with Python 3 on the server

Key References

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• Lande, R. (1993). “Risks of population extinction from demographic and environmental stochasticity and random catastrophes.” American Naturalist, 142, 911–927.

• Ludwig, S. A. et al. (2019). “LoRaWAN-based wildlife monitoring collars.” IEEE Sensors Journal, 19, 13–26.

• Thel, L. et al. (2022). “PAMGuard applications for savanna gunshot detection.” Bioacoustics, 31, 1–18.

• Wrege, P. H. et al. (2017). “Acoustic monitoring for conservation in tropical forests: examples from forest elephants.” Methods in Ecology and Evolution, 8, 1292–1301.

• Katzner, T. E. et al. (2012). “Assessing acoustic monitoring efficacy for vertebrates.” PLoS ONE, 7, e53891.

• Bernard, A. et al. (2022). “CNN-based classification of forest elephant vocalizations.” Ecological Informatics, 68, 101555.

• Lethbridge, M. et al. (2019). “Aerial surveillance for anti-poaching in southern African protected areas.” Conservation Biology, 33, 1100–1108.

• Brady, M. J. et al. (2019). “Capture myopathy in wildlife.” Veterinary Clinics North America, 22, 105–117.

• Oya Erciyas, I. (2003). “Capture stress and rhabdomyolysis in ungulates.” Journal of Wildlife Diseases, 39, 423–429.

• Lindsey, P. A. et al. (2018). “Rhino horn dehorning: a review of the evidence.” Biological Conservation, 226, 229–235.

• Linnell, J. D. C. et al. (2005). “The linkage between conservation strategies for large carnivores and biodiversity.” Large Carnivores and the Conservation of Biodiversity.

• Saura, S. & Pascual-Hortal, L. (2007). “A new habitat availability index for landscape connectivity.” Landscape and Urban Planning, 83, 91–103.

• McNaughton, S. J. (1979). “Grazing as an optimization process.” American Naturalist, 113, 691–703.

• Naidoo, R. et al. (2016). “Estimating economic losses to tourism in Africa from the illegal killing of elephants.” Nature Communications, 7, 13379.

• Lindsey, P. A. et al. (2019). “Trophy hunting and conservation of African lions.” Conservation Letters, 12, e12647.

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